Datasets:
Infi-MM
/
InfiMM-WebMath-40B

Dataset card Data Studio Files Community
3
URL
stringlengths
15
1.68k
text_list
sequencelengths
1
199
image_list
sequencelengths
1
199
metadata
stringlengths
1.19k
3.08k
https://www.omnicalculator.com/chemistry/equilibrium-constant
[ "# Equilibrium Constant Calculator\n\nCreated by Dominika Śmiałek, MD, PhD candidate\nReviewed by Dominik Czernia, PhD and Jack Bowater\nLast updated: Jun 27, 2023\n\nThis equilibrium constant calculator will help you understand reversible chemical reactions, which are reactions in which both the forward and backward reactions occur simultaneously.\n\nAfter a certain amount of time, an equilibrium is formed, meaning that the rate of reactants being turned into products is the same as the rate of products being turned back into reactants. At this point, the reaction is considered stable. To determine the state of this equilibrium, the reaction quotient should remain constant. With this tool, you can calculate the value of an equilibrium constant for a reaction while learning how to calculate the equilibrium constant with ease!\n\nBelow you can find the reversible reaction and equilibrium constant equations:\n\na[A] + b[B] ⇌ c[C] + d[D]\n\nK = ([C]c × [D]d)/([B]b × [A]a),\n\nwhere [A] and [B] are the molar concentrations of the reactants, and [C] and [D] are the molar concentrations of the products. To understand those concepts better, take a look at the molarity calculator\n\nCalculating the value of the equilibrium constant for a reaction is helpful when determining the amount of each substance formed at equilibrium as a ratio of each other. The constant doesn't depend on the initial concentrations of the reactants and products, as the same ratio will always be reached after a certain period of time. However, the constant may be influenced by:\n\n• Temperature;\n• Solvent; and\n• Ionic strength.\n\nIf the reaction is still underway, with oscillations between reagents and products, you have to use the reaction quotient calculator instead. However, even if it applies in a different context, it is defined in the same way as the equilibrium constant!\n\n## When is equilibrium constant used?\n\nEquilibrium constants are useful if you want to understand biochemical processes such as oxygen transport by hemoglobin or acid-base homeostasis in humans. The changes in acid-base homeostasis are mainly reflected in changes in the arterial and venous blood pH. Doctors will also check the equilibrium constant of transferrin in the blood, as transferrin saturation is a symptom of iron deficiency anemia.\n\nThis equation helps explain what will be favored by the equilibrium – the reactants or the products. This can give important information about the nature of the reaction and its mechanism. You will find more on this topic below.\n\n## Equilibrium constant equation\n\nThe equilibrium constant of a reaction relates to all of the species present in the reaction. However, in this calculator, we assume that there is a maximum of two main reactants and two main products. For the hypothetical reaction:\n\na[A] + b[B] ⇌ c[C] + d[D]\n\nthe equilibrium constant equation has the following formula:\n\nK = ([C]c × [D]d)/([B]b × [A]a)\n\nThe constant K reflect two measurements of quantity:\n\n• Kc - represents concentration, molarity, expressed as moles per liter (M=mol/L)\n• Kp - a function of both reactants and products partial pressure, usually in atmospheres, useful for calculations in the gas phase\n\nIf K > 1 – equilibrium favors the products\n\nIf K < 1 – equilibrium favors the reactants\n\nIf K = 1 – the mixture contains similar amounts of both products and reactants at equilibrium\n\nIf you're not sure how to switch from moles to other units and the other way around, take a look at our mole calculator.\n\n## Let's calculate the value of the equilibrium constant for a reaction\n\nTo give you more insight into how this equation works in practice, we created this example.\n\nYou have a mixture of gaseous sulfur dioxide and oxygen, from which you can react to form sulfur trioxide. This is one of the steps in synthesizing sulphuric acid:\n\n2 SO₂ + O₂ ⇌ 2 SO₃\n\nTherefore the equilibrium constant equation for this reaction is:\n\nK = [SO₃]²/([SO₂]² × [O₂])\n\nThe reaction mixture is left for a while until an equilibrium is established. The reactants and products have the following concentrations:\n\n• SO₂: 0.03 mol/L\n• O₂: 0.035 mol/L\n• SO₃: 0.5 mol/L\n\nWhen you put these numbers into the equation, K is found to be:\n\nK = 0.05²/(0.03² × 0.035)\n\nK = 7.937 × 10³\n\nAs K > 1, the equilibrium favors the products.\n\nIn our example, the concentrations of reactants and products at equilibrium were provided. We then used this information to calculate the equilibrium constant. But what if you knew the equilibrium constant and the unknown was the initial concentration or coefficient of a component? Well, don't worry! Our calculator works in reverse – so it solves both kinds of problems. Just input all of the data you have, and the results will be computed for you in an instance.\n\n## How to calculate the equilibrium constant?\n\nThis paragraph mainly focuses on how the equilibrium constant is determined analytically. To calculate the value of the equilibrium constant for a reaction, you need to measure (maybe with our titration calculator) the concentrations of the reactants and/or products. There are both experimental and computational methods for constant evaluation. Among experimental methods, you can find:\n\n• Potentiometry\n• Spectrophotometry\n• NMR chemical shift\n• Calorimetry\n\nWithin computational methods, there are:\n\n• Chemical model\n• Speciation calculations\n• Refinement\n• Model selection.\n\nAlthough you already know how to calculate equilibrium constant, save yourself some time and make use of our calculator!\n\n## FAQ\n\n### What is an equilibrium constant?\n\nThe equilibrium constant, K, determines the ratio of products and reactants of a reaction at equilibrium.\n\nFor example, having a reaction a[A] + b[B] ⇌ c[C] + d[D], you should allow the reaction to reach equilibrium and then calculate the ratio of the concentrations of the products to the concentrations of the reactants:\n\nK = ([C]c × [D]d)/([B]b × [A]a).\n\n### How can I write an equilibrium constant expression?\n\nTo write out an equilibrium constant expression, follow these steps:\n\n1. Calculate the product of the equilibrium concentrations of the products (raised to their coefficients in the balanced chemical equation).\n\n2. Calculate the product of equilibrium concentrations of reactants (raised to their coefficients in the balanced chemical equation).\n\n3. Find the ratio of the two products.\n\nFor example, the equilibrium constant for the reaction Cl₂ + 2NO₂ ⇌ 2NO₂Cl will be [NO₂Cl]²/([Cl₂] × [NO₂]²).\n\n### How can I find the equilibrium constant?\n\nLet's say you have a reaction of synthesis of ammonia: N₂ + 3H₂ ⇌ 2NH₃, where the concentrations are: N₂ = 0.04 mol/L, H₂ = 0.125 mol/L, and NH₃ = 0.003 mol/L.\n\nTo find its equilibrium constant:\n\n1. Write the equilibrium constant equation:\n\nK = ([NH₃]2)/([H₂]3 × [N₂]1).\n\n2. Enter the concentration:\n\nK = ([0.003 mol/L]2)/([0.125 mol/L]3 × [0.04 mol/L]1) = 0.1152 = 1.152 × 10⁻¹.\n\n### What changes the equilibrium constant?\n\nThe equilibrium constant is changed by temperature, the direction of the writing equation, the stoichiometry of the chemical equation, and concentration units. In contrast, the equilibrium constant does not depend on changes in concentration or pressure or the presence of a catalyst.\n\n### What will be the concentration of reactant if the equilibrium constant is 0.03?\n\n1.33 mol/L, assuming that you have a reaction of [A] + [B] ⇌ [C] + [D], and concentration of A is 0.5 mol/L, C is 0.2 mol/L, and D is 0.1 mol/L. To find it:\n\n1. Write the equilibrium constant equation:\n\nK = ([C] × [D])/([B] × [A]).\n\n2. Solve for [B]:\n\n[B] = ([C] × [D])/(K × [A]).\n\n3. Enter data:\n\n[B] = (0.2 × 0.1)/(0.03 × 0.5) = 1.33 mol/L.\n\nDominika Śmiałek, MD, PhD candidate\na[A] + b[B] ⇌ c[C] + d[D]\nConcentration: [A]\nM\nCoefficient: a\nConcentration: [B]\nM\nCoefficient: b\nConcentration: [C]\nM\nCoefficient: c\nConcentration: [D]\nM\nCoefficient: d\nEquilibrium constant\nPeople also viewed…\n\n### Alien civilization\n\nThe alien civilization calculator explores the existence of extraterrestrial civilizations by comparing two models: the Drake equation and the Astrobiological Copernican Limits👽\n\n### Electronegativity\n\nThis electronegativity calculator is an efficient tool to calculate the type of bond formed between two atoms based on their electronegativities.\n\n### Molar mass\n\nCheck how many grams are contained in 1 mole of any element or chemical compound with this molar mass calculator.\n\n### Sunbathing\n\nDo you always remember to put on sunscreen before going outside? Are you sure that you use enough? The Sunbathing Calculator ☀ will tell you when's the time to go back under an umbrella not to suffer from a sunburn!" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9043671,"math_prob":0.99155766,"size":7414,"snap":"2023-40-2023-50","text_gpt3_token_len":1757,"char_repetition_ratio":0.23832658,"word_repetition_ratio":0.04995905,"special_character_ratio":0.2375236,"punctuation_ratio":0.115440115,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99873155,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-02T18:11:35Z\",\"WARC-Record-ID\":\"<urn:uuid:f0608430-5d9c-4814-b79a-3adabad05749>\",\"Content-Length\":\"516982\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5f9a2ba6-13cb-4339-9a16-be9081ccee54>\",\"WARC-Concurrent-To\":\"<urn:uuid:192faeee-16bb-4a19-b873-3c552f11e429>\",\"WARC-IP-Address\":\"68.70.205.3\",\"WARC-Target-URI\":\"https://www.omnicalculator.com/chemistry/equilibrium-constant\",\"WARC-Payload-Digest\":\"sha1:25G7PEDPDGFHZGALDVOSHJ7FYSQQC4D6\",\"WARC-Block-Digest\":\"sha1:ILFAEUKCP65GESML7XR3BHPR53INYFE6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100448.65_warc_CC-MAIN-20231202172159-20231202202159-00118.warc.gz\"}"}
https://wiki.math.ucr.edu/index.php?title=009A_Sample_Final_A,_Problem_5&direction=next&oldid=280
[ "# 009A Sample Final A, Problem 5\n\n5. Consider the function   $h(x)={\\frac {x^{3}}{3}}-2x^{2}-5x+{\\frac {35}{3}}}.$", null, "(a) Find the intervals where the function is increasing and decreasing.\n(b) Find the local maxima and minima.\n(c) Find the intervals on which $f(x)$", null, "is concave upward and concave downward.\n(d) Find all inflection points.\n(e) Use the information in the above to sketch the graph of $f(x)$", null, ".\n\nFoundations:\nWe learn a lot about the shape of a function's graph from its derivatives. When a first derivative is positive, the function is increasing (heading uphill). When the first derivative is negative, it is decreasing (heading downhill). Of particular interest is when the first derivative at a point is zero. If f '(z) = 0 at a point z, and the first derivative splits around it (either f '(x) < 0 for x < z and f '(x) > 0 for x > z or f '(x) > 0 for x < z and f '(x) < 0 for x > z), then the point (z,f(z)) is a local maximum or minimum, respectively.\nThe second derivative tells us how the first derivative is changing. If the second derivative is positive, the first derivative (the slope of the tangent line) is increasing. This is equivalent to the graph \"turning left\" if we consider moving from negative x-values to positive. We call this \"concave up\". The parabola y = x2 is an example of a purely concave up graph, and its second derivative is the constant function y \" = 2.\nIf the second derivative is negative, then the first derivative is decreasing. This means we are turning right as we move from negative x-values to positive. This is called \"concave down\". The inverted parabola y = -x2 is an example of a purely concave down graph.\nA point z where the second derivative is zero, and the sign of the second derivative splits around it (either f \"(x) < 0 for x < z and f \"(x) > 0 for x > z, or f \"(x) > 0 for x < z and f \"(x) < 0 for x > z), then the point (z,f(z) is an inflection point.\n\nOf course, there are tests we use to find local extrema (maxima and minima, which is the plural of maximum and minimum). We are assuming the function f is continuous and differentiable in an interval containing the point x0.\nFirst Derivative Test: If at a point x0, f '(x0) = 0, and f '(x) < 0 for x < x0 while f '(x) > 0 for x > x0, then f(x0) is a local minimum.\nOn the other hand, if f '(x0) = 0, and f '(x) > 0 for x < x0 while f '(x) < 0 for x > x0, then f(x0) is a local maximum.\nSecond Derivative Test: If at a point x0, f '(x0) = 0, and f \"(x0) > 0, then f(x0) is a local minimum. On the other hand, if f \"(x0) < 0, then f(x0) is a local maximum. If f \"(x0) = 0, the test is inconclusive.\n\nSolution:\n\nFind the Derivatives and Their Roots:\nNote that\n$f'(x)=x^{2}-4x-5=(x-5)(x+1),$", null, "while\n$f''(x)=2x-4.$", null, "The roots of f ' are -1 and 5, while the only root of f \" is 2.\nProduce Sign Charts and Evaluate:\nSince all of our tests rely on the signs of our derivatives, we need to produce sign charts. For the first derivative, we can test values below -1, between -1 and 5 and above 5. For example:\n$f'(-10)=(-)(-)=(+),\\quad f'(0)=(-)(+)=(-),\\quad f'(10)=(+)(+)=(+).$", null, "From this, we can build a sign chart:\n $x:$", null, "$x<-1$", null, "$x=-1$", null, "$-1", null, "$x=5$", null, "$x>5$", null, "$f'(x):$", null, "$(+)$", null, "$0$", null, "$(-)$", null, "$0$", null, "$(+)$", null, "This gives us the following answers:\n(a) The function is increasing on $(\\infty ,-1)$", null, "and $(5,\\infty )$", null, ", and decreasing on $(-1,5)$", null, ".\n(b) The first derivative test shows\n$f(-1)=-{\\frac {1}{3}}-2+5+{\\frac {35}{3}}=14\\,{\\frac {1}{3}}$", null, "is a local maximum, while\n$f(5)={\\frac {125}{3}}-50-25+{\\frac {35}{\\,3}}=-75+{\\frac {160}{3}}=-\\,{\\frac {65}{\\,3}}.$", null, "is a local minimum.\nThe second derivative has only the single root x = 2, so we need only look at values for x < 2 and x > 2. These values are clearly negative and positive, respectively, so we have a sign chart:\n $x:$", null, "$x<2$", null, "$x=2$", null, "$x>2$", null, "$f''(x):$", null, "$(-)$", null, "$0$", null, "$(+)$", null, "This gives us the following answers:\n(c) The function is concave downward on $(-\\infty ,2)$", null, "and concave upward on $(2,\\infty )$", null, ".\n(d) The function has an inflection point at $(2,f(2))=\\left(2,-{\\frac {11}{3}}\\right).$", null, "Graph:\nThis is part (e) of the problem. We wish to use all our results. In the image, the dots represent the two local extrema at x = -1 and x = 5, as well as the inflection point at x = 2. The graph is drawn in blue where it is concave downward, and in red where it is concave upward." ]
[ null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/159925d375f44133df27169b401c03fd52aa8169", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/276e6d15db510bb0103d797f38e64d5ac8575705", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/64edea0a2e656360773be187c7059abff0bdd51e", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/6d8a980547d97220ea44fda8d6743a1ade16c135", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/a464b07701efcc30dd421d9a5c6f9d8a8612b23f", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/dda0e91b50acb810626cf0443c062e228c7c7fc0", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/4fefa55268918f98da2e0dcc19ea86d78f84ac56", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/6725c8181c2f25378d3fea8f7472f71ed1165ea7", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/e0f8441cf157c3f0ed6b88edd716956517c9d66c", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9899c5b54bff58ffa57ce52e49243906433b3f3e", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/b0599f51a519c4889c37c4be73239f9210f07495", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/329f8c1ec9a4bd1c8e882e368f2de3800f16fc65", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f517743bc5ea05fb95e6c16f833fd5ad59f43025", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/329f8c1ec9a4bd1c8e882e368f2de3800f16fc65", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/47c7211c7fc59ccf55abfce2c39a216f558c1564", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/31fd20e58b5bb4269078efb6650a0a2cdceaa326", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/16e10cd43a8768c588f9f505576fb64f30f1ca81", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/beed0d0481e822319a30281c51dc8f097b476922", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/89bbe9b9887cb7ff4a01057491d1dd2abe0ad924", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/a464b07701efcc30dd421d9a5c6f9d8a8612b23f", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/3fe4c94bf3a8ff251787ffddfdbee18f32d14edc", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9f39b6e42e5ffb81ac7b051b9e48b9a91d0713c7", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9f5baa43d43733ac518c4ba02435283386d87553", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/0e7840c0418b440720045d21e1b36cc1a703e1c0", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f517743bc5ea05fb95e6c16f833fd5ad59f43025", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/329f8c1ec9a4bd1c8e882e368f2de3800f16fc65", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/b72469fc96768a210b6899f2b55783086964e692", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/4d433bf548e2cd81d0d5d5bb833ad6fc470ad2b7", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf0aeea18c6ad3b438b67a7dbd4725355c697a4", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8567981,"math_prob":0.9999434,"size":3802,"snap":"2022-05-2022-21","text_gpt3_token_len":1058,"char_repetition_ratio":0.15955766,"word_repetition_ratio":0.2051948,"special_character_ratio":0.29694897,"punctuation_ratio":0.111519605,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999906,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68],"im_url_duplicate_count":[null,null,null,null,null,null,null,6,null,6,null,6,null,null,null,10,null,null,null,6,null,null,null,6,null,8,null,null,null,null,null,null,null,null,null,null,null,4,null,6,null,6,null,6,null,5,null,null,null,null,null,null,null,null,null,6,null,null,null,null,null,null,null,10,null,null,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-17T20:14:14Z\",\"WARC-Record-ID\":\"<urn:uuid:6770c8f1-9d4a-411b-a3d8-89d604735667>\",\"Content-Length\":\"58054\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b0594e92-c661-4c36-aac2-a1c531f99177>\",\"WARC-Concurrent-To\":\"<urn:uuid:a490c253-608a-44be-b4bd-dbb46644a739>\",\"WARC-IP-Address\":\"169.235.128.27\",\"WARC-Target-URI\":\"https://wiki.math.ucr.edu/index.php?title=009A_Sample_Final_A,_Problem_5&direction=next&oldid=280\",\"WARC-Payload-Digest\":\"sha1:DGGP6WYHH4JG7HG5WMBRKXEBOH23FJ3A\",\"WARC-Block-Digest\":\"sha1:MOTMHBNI3SKIZ6KGZ5ICANBCUNVYDR7C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662520817.27_warc_CC-MAIN-20220517194243-20220517224243-00469.warc.gz\"}"}
https://projecteuclid.org/Proceedings/berkeley-symposium-on-mathematical-statistics-and-probability/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and/toc/bsmsp/1200513615
[ "Home > Proceedings > Berkeley Symp. on Math. Statist. and Prob. > Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 3: Physical Sciences\nFifth Berkeley Symposium on Mathematical Statistics and Probability\nJune 21-July 18, 1965 and December 27, 1965-January 7, 1966 | Statistical Laboratory of the University of California, Berkeley\nProceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 3: Physical Sciences\n\nEditor(s) Lucien M. Le Cam, Jerzy Neyman\n\nBerkeley Symp. on Math. Statist. and Prob., 5.3: 324pp. (1967).", null, "View All Abstracts +\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, - (1967).", null, "E. M. Burbidge , G. R. Burbidge\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 1-18 (1967).", null, "W. H. McCrea\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 19-29 (1967).", null, "Thornton Page\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 31-49 (1967).", null, "Beverly T. Lynds\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 51-60 (1967).", null, "W. C. Livingston\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 61-72 (1967).", null, "R. L. Dobrushin\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 73-87 (1967).", null, "J. M. Hammersley\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 89-117 (1967).", null, "KEYWORDS: 60.40\nHerbert Solomon\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 119-134 (1967).", null, "KEYWORDS: 65.10, 52.00\nM. S. Bartlett\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 135-153 (1967).", null, "KEYWORDS: 62.85\nBenoit Mandelbrot\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 155-179 (1967).", null, "John Bather , Herman Chernoff\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 181-207 (1967).", null, "KEYWORDS: 62.45, 93.00\nRichard Bellman\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 209-215 (1967).", null, "P. Whittle\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 217-227 (1967).", null, "KEYWORDS: 93.60\nRichard E. Barlow , A. W. Marshall\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 229-257 (1967).", null, "Yu. K. Belyaev , B. V. Gnedenko , A. D. Soloviev\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 259-270 (1967).", null, "Z. W. Birnbaum , J. D. Esary\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 271-283 (1967).", null, "KEYWORDS: 62.80\nB. V. Gnedenko\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 285-291 (1967).", null, "KEYWORDS: 62.80\nFrank Proschan , Ronald Pyke\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 293-312 (1967).", null, "KEYWORDS: 62.75\nA. D. Soloviev\nBerkeley Symposium on Mathematical Statistics and Probability Vol. 5.3, 313-324 (1967).", null, "KEYWORDS: 62.80" ]
[ null, "https://projecteuclid.org/images/proceedings/cover_bsmsp.jpg", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null, "https://projecteuclid.org/Content/themes/SPIEImages/OpenAccessIcon.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6389516,"math_prob":0.806464,"size":847,"snap":"2022-05-2022-21","text_gpt3_token_len":264,"char_repetition_ratio":0.09015421,"word_repetition_ratio":0.045454547,"special_character_ratio":0.24321133,"punctuation_ratio":0.26966292,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986593,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-21T02:43:41Z\",\"WARC-Record-ID\":\"<urn:uuid:9587f02e-3292-4e24-9d6e-cf92e6246ac7>\",\"Content-Length\":\"186876\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:87bd89cc-ddf5-4d19-8609-f7358ab51a53>\",\"WARC-Concurrent-To\":\"<urn:uuid:c0805c34-6b14-4afd-a46e-a07dee6e7414>\",\"WARC-IP-Address\":\"107.154.79.145\",\"WARC-Target-URI\":\"https://projecteuclid.org/Proceedings/berkeley-symposium-on-mathematical-statistics-and-probability/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and/toc/bsmsp/1200513615\",\"WARC-Payload-Digest\":\"sha1:3FA2463EPO5YB24TAS2B3JCKARKDKRFM\",\"WARC-Block-Digest\":\"sha1:ITDLGOIKFQQDT5N3A362HJVQMZG5SAM7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320302715.38_warc_CC-MAIN-20220121010736-20220121040736-00583.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-5-section-5-5-dividing-polynomials-exercise-set-page-386/60
[ "Introductory Algebra for College Students (7th Edition)\n\n-2x$^2$+4x\nDivide the polynomial by the monomial by separating the polynomial into individual terms and dividing each one by the monomial. Then cancel out common factors of the coefficients and subtract the powers of the variables to simplify. $\\frac{10x^3-20x^2}{-5x}$=$\\frac{10x^3}{-5x}$+$\\frac{-20x^2}{-5x}$=-2x$^{(3-1)}$+4x$^{(2-1)}$=-2x$^2$+4x Check the answer. -5x(-2x$^2$+4x)=10x$^{(1+2)}$-20x$^{(1+1)}$=10x$^3$-20x$^2$" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.61511236,"math_prob":0.99998045,"size":451,"snap":"2019-43-2019-47","text_gpt3_token_len":189,"char_repetition_ratio":0.14317673,"word_repetition_ratio":0.0,"special_character_ratio":0.42350334,"punctuation_ratio":0.03409091,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000045,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-15T21:00:18Z\",\"WARC-Record-ID\":\"<urn:uuid:07f7c621-368e-43bc-8454-e562d66d2e6f>\",\"Content-Length\":\"88969\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7232d4c3-11df-4b61-be5d-c50395a2e7ad>\",\"WARC-Concurrent-To\":\"<urn:uuid:dbcd2d35-3f77-4162-af3e-37b93f97bfea>\",\"WARC-IP-Address\":\"54.210.73.90\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-5-section-5-5-dividing-polynomials-exercise-set-page-386/60\",\"WARC-Payload-Digest\":\"sha1:GJG3TZ3R6Z3UKXNATDI6AGBFUZLBYTRF\",\"WARC-Block-Digest\":\"sha1:5M44LZWKCLZVTVPJ2VT56BMTKNWJ3ZMS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986660323.32_warc_CC-MAIN-20191015205352-20191015232852-00226.warc.gz\"}"}
https://zh.m.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E5%85%83
[ "# 最小元\n\n$(A,\\leq )$", null, "偏序集$B\\subseteq A$", null, "$y\\in B$", null, "，若对于所有的$x\\in B$", null, "都有$y\\leq x$", null, "，则称$y$", null, "$B$", null, "最小元" ]
[ null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/8dccbed0945476c5f14b21d76e3d936f4acf547b", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/fb8124cb68686ede7083aa2a5a821f262eb62954", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/01ccabd006952897bb52668533010cb9e4ab3f77", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9aac01724708de4e1d41423bc64b35e9d94c9009", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7de6a6e4f44d9dfcbfaadbdcf388d4b8a6fed109", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a", null ]
{"ft_lang_label":"__label__zh","ft_lang_prob":0.75561684,"math_prob":1.00001,"size":436,"snap":"2021-43-2021-49","text_gpt3_token_len":280,"char_repetition_ratio":0.36342594,"word_repetition_ratio":0.0,"special_character_ratio":0.30045873,"punctuation_ratio":0.028985508,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000014,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-26T15:39:34Z\",\"WARC-Record-ID\":\"<urn:uuid:10fc9c9d-94bd-4235-a859-0f934cae9f97>\",\"Content-Length\":\"33100\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ab8e34eb-8dfa-4dfc-a1f3-c824b8012c53>\",\"WARC-Concurrent-To\":\"<urn:uuid:527ed03e-9c0a-47b3-9cf7-7830b1b234b0>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://zh.m.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E5%85%83\",\"WARC-Payload-Digest\":\"sha1:YGPI7DJ7WPOM64SNGSSIAXMAUTFECMDG\",\"WARC-Block-Digest\":\"sha1:BYPRZOAOMTH7MLM54EIB2WM5GZ7IODNK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323587908.20_warc_CC-MAIN-20211026134839-20211026164839-00070.warc.gz\"}"}
https://www.hunker.com/13416849/how-to-figure-out-a-45-degree-angle
[ "# How to Figure Out a 45-Degree Angle\n\nHunker may earn compensation through affiliate links in this story.\n\n#### Things You'll Need\n\n• Ruler\n\n• Right angle (such as a carpenter's square or the corner of factory-cut cardboard)\n\nIf you need to figure out a 45-degree angle and you don't have a protractor handy, you can create a workaround. A 45-degree angle is half the size of right angle, which is 90 degrees. Working with a ruler and a square or other right angle substitute, you can make the angle without any special tools. The 45-degree angle can be useful for projects like painting diagonals on walls, marking trim, or completing crafts and decoration projects. You may want to use the first 45-degree angle you make as a template so that you can use it to mark other angles easily.\n\n## Step 1\n\nMark a piece of paper (or whatever surface you are working on) with a right angle. Use the square or whatever substitute right angle you have to trace the angle. The back of a pad of paper or even a magazine will suffice.\n\n## Step 2\n\nMeasure off a distance (the length is unimportant) from the point of the angle, and mark it on one leg of the angle.\n\n## Step 3\n\nMeasure and mark the identical distance on the other leg.\n\n## Step 4\n\nDraw a diagonal line between the two points on the legs of the right angle.\n\n## Step 5\n\nMeasure the length of the diagonal line and make a mark at its center point. Divide the total distance by two to ascertain this measurement.\n\n## Step 6\n\nDraw a line from the corner of the original right angle to the center point on the diagonal line between the legs of the angle. This bisects the right angle, creating two 45-degree angles." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9202011,"math_prob":0.90901303,"size":1812,"snap":"2021-31-2021-39","text_gpt3_token_len":404,"char_repetition_ratio":0.1460177,"word_repetition_ratio":0.0,"special_character_ratio":0.21688741,"punctuation_ratio":0.07417583,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.972171,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-18T19:44:59Z\",\"WARC-Record-ID\":\"<urn:uuid:701ca4e1-8fb8-4ef7-9d3d-809d1b0c9685>\",\"Content-Length\":\"834843\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:627b2d60-9e4e-44f5-9b5f-4c1b0b8a2676>\",\"WARC-Concurrent-To\":\"<urn:uuid:3c8aaf51-b5fb-4895-8c55-410ca62c6f67>\",\"WARC-IP-Address\":\"96.17.143.183\",\"WARC-Target-URI\":\"https://www.hunker.com/13416849/how-to-figure-out-a-45-degree-angle\",\"WARC-Payload-Digest\":\"sha1:ER5P46YQGLIBN26KTW47VNBVASQOEYCV\",\"WARC-Block-Digest\":\"sha1:BAXFJTSU73NKNUNMIT5XWCRMY6AS5G3J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056572.96_warc_CC-MAIN-20210918184640-20210918214640-00580.warc.gz\"}"}
https://forum.worldviz.com/showpost.php?s=bcb3782be764ac3b83b29ea0b223e669&p=19983&postcount=1
[ "Thread: Mark & Print Oculus data View Single Post\n#1\n tianmoran", null, "Member Join Date: Nov 2016 Posts: 16\nMark & Print Oculus data\n\nHi there,\n\nI'm coding for an experiment but muddled with some trouble. My goal is to record the Oculus data(position, euler) every 50ms. At the same time, I need to mark some events, like below the events are 'cylinder is on', 'key pressed', 'cylinder is off'. So I put a variable called 'Event' and hope to change its value right after each event happens. Unfortunately, it didn't work.\n\nI kind of know why it's not working. But is there any solution on that?\n\nThank you so much if anyone would like to help me out!!!\n\nCode:\n```import viz\nimport vizact\nimport vizshape\nimport vizinput\nimport vizinfo\nimport time\nimport random\nimport oculus\nimport vizfx\nimport numpy\nfrom numpy import *\n\nviz.go()\n\n##### SET UP OCULUS\nhmd = oculus.Rift()\noculusView.setOffset([0,0.5,-1])\n\ndef Demo():\nglobal acc, RT, Keycode, trialNo, oculus, oculusView, Cond, FMM, Code_direct, Event, trial, block, unit, acc, RT, Keycode, trialNo, oculus, oculusView,oculus_timer, Group, Code_Type, Code_Letter, FirstTrial\nFirstTrial = 1\nInstr.setPosition(0,0,0)\nInstr.color(0.5,0,0)\nInstr.visible(viz.OFF)\n\nOculusdata = open('testtest'+ \"_Oculus.txt\",'a',1)\n\nfor trial in range(10):\n\n###### Calculating Reaction Time\ndef df():\nglobal startTime\nstartTime = viz.tick()\nprint str(trial), 'startTime', startTime\nInstr.visible(viz.ON)\nyield vizact.ontimer2(1,0,df)\nEvent = 0\n\ndef waitkeydown():\nglobal r, KeyPress, startTime\n\nif r.key == 'j':\nacc[trial] = 1\nKeycode[trial] = 2 \t### Key J is pressed\nelif r.key == 'f':\nacc[trial] = 0\nKeycode[trial]= 1 \t\t### Key F is pressed\n\nEvent = 1\nInstr.visible(viz.OFF)\nEvent = 2\n\ndef printOculusData():\nglobal oculus_timer\noculus_timer = viz.tick()\nOculusData = \"%s\\t%s\\t%s\\t%s\\t%s\\n\" %(trial, Event,oculus_timer,oculusView.getPosition(), oculusView.getEuler())\nOculusdata.write(OculusData)\nif FirstTrial == 1:\nvizact.ontimer(0.05,printOculusData)\nFirstTrial = 0" ]
[ null, "https://forum.worldviz.com/images/statusicon/user_offline.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.57143706,"math_prob":0.9706684,"size":2170,"snap":"2022-27-2022-33","text_gpt3_token_len":656,"char_repetition_ratio":0.12973222,"word_repetition_ratio":0.0073260074,"special_character_ratio":0.2797235,"punctuation_ratio":0.24,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96973604,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-02T02:06:30Z\",\"WARC-Record-ID\":\"<urn:uuid:113a05be-4bcc-414d-a85d-c05a308cdcf2>\",\"Content-Length\":\"14984\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da90e817-8a38-42ed-a16d-170a251892ba>\",\"WARC-Concurrent-To\":\"<urn:uuid:1ff6a077-a6d9-4504-86a3-bbbd1568c95f>\",\"WARC-IP-Address\":\"3.215.177.236\",\"WARC-Target-URI\":\"https://forum.worldviz.com/showpost.php?s=bcb3782be764ac3b83b29ea0b223e669&p=19983&postcount=1\",\"WARC-Payload-Digest\":\"sha1:52CVCUBUUUYEURBTZN3R55INUH3Q6EWS\",\"WARC-Block-Digest\":\"sha1:R22KJTFMQBFNGIIVTV6426UGFEUVOINC\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103983398.56_warc_CC-MAIN-20220702010252-20220702040252-00381.warc.gz\"}"}
https://lbartman.com/4th-grade-respect-worksheets/
[ "## ↤ l\n\n👤 will chen 🗓 May 17, 2021, 11:49 pm ( Last Modified )\n\nWinter Word Puzzles. Now that I’ve gotten up our Christmas word puzzles, I wanted to add a ‘secular’ alternative with these winter word puzzles.These are great for 3rd, 4th and 5th grade students – maybe even 6th grade. Another set of worksheets that you can pair with these word puzzles are our winter mad libs found here..Need elementary math resources? Use Lesson Planet to find curriculum covering topics such as counting, shapes (like this shape-dice printable!), addition, subtraction, time (this time concept book is fantastic), measurement, and arithmetic.Try this interactive to help youngsters understand the relationship between addition and subtraction. For more advanced classes, find lessons on geometry ..We would like to show you a description here but the site won’t allow us..Worksheets. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resources.\n\nTake A Sneak Peak At The Movies Coming Out This Week (8/12) #BanPaparazzi – Hollywood.com will not post paparazzi photos; New Movie Releases This Weekend: March 5th – March 7th..\n\nRelated to \"4th Grade Respect Worksheets\" ⤵\n\nName : __________________\n\nSeat Num. : __________________\n\nDate : __________________\n\n62 + 37 = ...\n\n49 + 68 = ...\n\n38 + 54 = ...\n\n21 + 48 = ...\n\n90 + 24 = ...\n\n71 + 61 = ...\n\n51 + 23 = ...\n\n47 + 22 = ...\n\n16 + 31 = ...\n\n32 + 41 = ...\n\n70 + 47 = ...\n\n60 + 38 = ...\n\n28 + 39 = ...\n\n96 + 61 = ...\n\n35 + 21 = ...\n\n96 + 70 = ...\n\n98 + 72 = ...\n\n88 + 51 = ...\n\n22 + 70 = ...\n\n75 + 69 = ...\n\n53 + 53 = ...\n\n66 + 97 = ...\n\n65 + 12 = ...\n\n92 + 49 = ...\n\n48 + 84 = ...\n\n53 + 92 = ...\n\n60 + 96 = ...\n\n53 + 79 = ...\n\n26 + 31 = ...\n\n74 + 85 = ...\n\n22 + 55 = ...\n\n48 + 33 = ...\n\n63 + 55 = ...\n\n78 + 41 = ...\n\n26 + 83 = ...\n\n47 + 93 = ...\n\n16 + 60 = ...\n\n83 + 44 = ...\n\n78 + 20 = ...\n\n64 + 60 = ...\n\n77 + 81 = ...\n\n38 + 93 = ...\n\n43 + 30 = ...\n\n97 + 66 = ...\n\n80 + 63 = ...\n\n36 + 32 = ...\n\n25 + 65 = ...\n\n68 + 92 = ...\n\n83 + 60 = ...\n\n64 + 99 = ...\n\n23 + 80 = ...\n\n11 + 99 = ...\n\n51 + 22 = ...\n\n29 + 86 = ...\n\n53 + 19 = ...\n\n22 + 21 = ...\n\n88 + 93 = ...\n\n97 + 88 = ...\n\n46 + 93 = ...\n\n34 + 47 = ...\n\n48 + 55 = ...\n\n46 + 66 = ...\n\n26 + 92 = ...\n\n95 + 11 = ...\n\n85 + 71 = ...\n\n51 + 65 = ...\n\n66 + 19 = ...\n\n25 + 90 = ...\n\n84 + 29 = ...\n\n19 + 23 = ...\n\n68 + 86 = ...\n\n30 + 55 = ...\n\n21 + 20 = ...\n\n38 + 34 = ...\n\n36 + 71 = ...\n\n93 + 55 = ...\n\n99 + 57 = ...\n\n20 + 62 = ...\n\n75 + 49 = ...\n\n79 + 66 = ...\n\n81 + 41 = ...\n\n47 + 20 = ...\n\n85 + 77 = ...\n\n63 + 63 = ...\n\n37 + 24 = ...\n\n93 + 79 = ...\n\n66 + 63 = ...\n\n80 + 46 = ...\n\n67 + 16 = ...\n\n93 + 48 = ...\n\n45 + 51 = ...\n\n35 + 64 = ...\n\n78 + 68 = ...\n\n43 + 82 = ...\n\n42 + 91 = ...\n\n83 + 23 = ...\n\n41 + 62 = ...\n\n15 + 16 = ...\n\n83 + 67 = ...\n\n31 + 82 = ...\n\n24 + 14 = ...\n\n78 + 34 = ...\n\n42 + 46 = ...\n\n74 + 12 = ...\n\n31 + 13 = ...\n\n46 + 90 = ...\n\n12 + 37 = ...\n\n76 + 71 = ...\n\n86 + 88 = ...\n\n47 + 76 = ...\n\n64 + 31 = ...\n\n59 + 97 = ...\n\n10 + 64 = ...\n\n26 + 76 = ...\n\n67 + 18 = ...\n\n28 + 41 = ...\n\n29 + 64 = ...\n\n92 + 83 = ...\n\n64 + 29 = ...\n\n56 + 63 = ...\n\n72 + 58 = ...\n\n22 + 25 = ...\n\n83 + 97 = ...\n\n59 + 22 = ...\n\n17 + 56 = ...\n\n78 + 37 = ...\n\n14 + 87 = ...\n\n47 + 67 = ...\n\n57 + 37 = ...\n\n98 + 49 = ...\n\n29 + 83 = ...\n\n91 + 17 = ...\n\n92 + 19 = ...\n\n87 + 24 = ...\n\n68 + 20 = ...\n\n87 + 42 = ...\n\n32 + 74 = ...\n\n82 + 50 = ...\n\n78 + 67 = ...\n\n64 + 87 = ...\n\n34 + 68 = ...\n\n86 + 28 = ...\n\n70 + 23 = ...\n\n10 + 55 = ...\n\n52 + 60 = ...\n\n11 + 28 = ...\n\n87 + 96 = ...\n\n78 + 76 = ...\n\n55 + 26 = ...\n\n96 + 71 = ...\n\n32 + 25 = ...\n\n89 + 50 = ...\n\n87 + 76 = ...\n\n45 + 89 = ...\n\n90 + 65 = ...\n\n79 + 64 = ...\n\n86 + 42 = ...\n\n22 + 49 = ...\n\n79 + 80 = ...\n\n65 + 28 = ...\n\n86 + 19 = ...\n\n29 + 83 = ...\n\n39 + 12 = ...\n\n48 + 89 = ...\n\n76 + 61 = ...\n\n87 + 34 = ...\n\n16 + 74 = ...\n\n85 + 63 = ...\n\n85 + 32 = ...\n\n95 + 25 = ...\n\n60 + 92 = ...\n\n86 + 68 = ...\n\n85 + 97 = ...\n\n91 + 89 = ...\n\n72 + 15 = ...\n\n13 + 20 = ...\n\n86 + 76 = ...\n\n44 + 15 = ...\n\n65 + 63 = ...\n\n73 + 13 = ...\n\n30 + 85 = ...\n\n33 + 86 = ...\n\n91 + 91 = ...\n\n24 + 79 = ...\n\n88 + 64 = ...\n\n82 + 14 = ...\n\n38 + 18 = ...\n\n27 + 83 = ...\n\n37 + 40 = ...\n\n53 + 81 = ...\n\n78 + 72 = ...\n\n81 + 29 = ...\n\n35 + 66 = ...\n\n35 + 94 = ...\n\n43 + 90 = ...\n\n38 + 46 = ...\n\n56 + 89 = ...\n\n73 + 57 = ...\n\n44 + 36 = ...\n\n78 + 60 = ...\n\nshow printable version !!!hide the show", null, "Learning NIE Rocks! Teaching Respect", null, "PBIS / For Teachers", null, "4th Grade Math Worksheets Free And Printable - Appletastic Learning", null, "PBIS / For Teachers", null, "What Is Respect? Try This Free Printable Respect Worksheet For Kids. Teaching Kids Respect", null, "Free Printable Reading Worksheets For 4th Graders Four Seasons Log Kindergarten Super Teachers – Benchwarmerspodcast", null, "", null, "Respect Worksheets And Teaching Resources", null, "I Have Rights Worksheet This Is The Answer Key For The Theme Worksheet 1 Literal Equations", null, "Worksheet ~ Fantastic Printable Reading Materials For Kindergarten 1st Grade Activities Money And Coins Worksheets Respect Comprehension Geometry Lessons 65 Fantastic Printable Reading Materials For Kindergarten. Printable Reading Materials For ...", null, "Scientific Method Worksheet Primary 3rd Grade Science Worksheet Worksheets Math Trivia For Middle School Xl Math Time To The Hour And Half Hour Worksheets Volume Word Problems Worksheet 5th Grade Primary Two", null, "", null, "", null, "PBIS / For Teachers", null, "5 Free Back To School Printable Activities Free Activities For Kids", null, "Excelent Theme Practice Worksheets Worksheet Free 4th Grade Math – Benchwarmerspodcast", null, "55 Kindergarten Activities Worksheets Picture Inspirations – Liveonairbk", null, "Empathy Lesson Plans \\u0026 Worksheets Lesson Planet", null, "Authority Figures Worksheets For Kindergarten Worksheet For Kindergarten School Counseling Lessons", null, "Worksheet ~ Math For Second Graders Online Free Photo Ideas Respect Worksheets Elementary Students Energy Kids Multiplication Worksheet Coloring Printable Times Tables Create Your Own Facts 64 Math For Second Graders Online", null, "Worksheet Cleanliness Worksheets For Kindergarten Math 4th Grade – Benchwarmerspodcast", null, "1989 Generationinitiative Page 105: Animal Senses Worksheets. Doubles Facts Worksheets. First Grade Writing Worksheets. Math Adding And Subtracting Mathematics Grade 10 Exam Papers Best Place To Learn Math Quick Calculus Review Business", null, "Thinking Puzzles With Answers Addition Practice Worksheets 3rd Grade Free Common Core Math Worksheets 2nd Grade Respect Worksheets For Kids Counting Mixed Coins Math Is Math Go Math 4th Grade Practice Book", null, "Lesson Plan- Respect In Friendship", null, "", null, "Teaching Respect In The Modern Classroom – Proud To Be Primary", null, "Dividing By 5 Worksheet Plant Worksheets Elementary Second Grade Christmas Math Worksheets Respect Worksheets For Kids Dot Math Worksheets El Math Adding Subtracting Decimals Everyday Math Third Grade Fraction Websites For 4th", null, "Fairy Tale Story Writing Worksheets Ela 3rd- 5th Grades On Best Worksheets Collection 5066", null, "51 Amazing Reading Fluency Worksheets – Benchwarmerspodcast", null, "4 English Worksheets Learn - Worksheets Schools", null, "Respect: Quiz \\u0026 Worksheet For Kids Study.com", null, "Frickin' Packets Cult Of Pedagogy", null, "Sentences Worksheets Compound Sentences Worksheets", null, "4th Grade Common Core ELA (English Language Arts): Daily Practice Workbook - ArgoPrep", null, "", null, "", null, "Classroom Guidance Lesson - Respect Guidance Lessons", null, "Baltrop Org Number Tracing Worksheet Solving Solving Square Root Equations Worksheet Worksheets Adding And Subtracting Games For Kindergarten Does Kumon Help With Math Adding Games For First Grade Respect Worksheets For Middle", null, "42 Outstanding Elementary Math Worksheets Multipliying Picture Inspirations – Liveonairbk", null, "Instant Lesson Plans For Any Book (Perfect For Substitutes!) Scholastic", null, "Math Basic Concept Respect Worksheets For Kids Social Studies Worksheets Middle School Grammar Worksheets For High School Timetable Worksheets Ks2 Multiplication Sums For Grade 4 Kinds Of Numbers In Math Kinds Of", null, "Free 4th Grade Math Worksheets Fpr Numbers And Algebra Telling Time Printable Activities Free Math Worksheets Fpr 4th Grade Worksheet Algebraic Equations Worksheets For 8th Grade Year 3 Word Problems Multiplication Respect", null, "Jenniferelliskampani Page 203: 5th Grade Science Lab Equipment Worksheet. Hyperbole Worksheets 3rd Grade. Sixth Grade Math Worksheets. C1 Worksheets Transcendentalist Worksheet Rescheck Worksheet Blueback Worksheets Manifestation Worksheets First Grade ...", null, "4th Grd Respect Lesson", null, "Worksheet ~ Math For Second Graders Online Free Photo Ideas Respect Worksheets Elementary Students Energy Kids Multiplication Worksheet Coloring Printable Times Tables Create Your Own Facts 64 Math For Second Graders Online", null, "3rd Grade Math Worksheets Free And Printable - Appletastic Learning", null, "Englishlinx.com Theme Worksheets", null, "", null, "", null, "Fairy Tale Story Writing Worksheets Ela 3rd- 5th Grades On Best Worksheets Collection 5066", null, "Flood Worksheet For Grade 3 Printable Worksheets And Activities For Teachers", null, "", null, "Instant Lesson Plans For Any Book (Perfect For Substitutes!) Scholastic", null, "", null, "Fraction Or Decimal Lost And Found Worksheets Science Worksheets For Grade 2 First Grade Writing Worksheets Primary 1 Math Worksheets Grade 1 Reading Worksheets Math Scientist Math Scientist First Grade Activity Sheets", null, "Frickin' Packets Cult Of Pedagogy", null, "42 Astonishing English Worksheets Classroom – Liveonairbk", null, "Addition Practice Worksheets Spelling Contractions Worksheets Basic Math Worksheets Grade 5 Math Worksheets Long Multiplication Best Math Learning Math Add On Free Math Learning Games Math Dictionary Grade 10 Fun Math Multiplication", null, "Respect Song Worksheet", null, "", null, "What Does Respect Look Like Chart Teaching Kids Respect", null, "Printable Worksheets", null, "Psychology Hope Worksheets Printable Worksheets And Activities For Teachers", null, "3rd Grade Math Worksheets Free And Printable - Appletastic Learning", null, "Worksheet Free Third Grade Reading Passages With Questions Fluency Fiction – Benchwarmerspodcast", null, "Englishlinx.com Abbreviations Worksheets", null, "Add And Reduce Fractions 6th Grade Math Printables 4th Grade Math Word Problems Bar Graph Worksheets Everyday Mathematics Grade 3 Student Reference Book Printing Practice Worksheets Teaching Numbers To Preschoolers Worksheets Telling", null, "4th Grade Writing Prompts Worksheets (Page 1) - Line.17QQ.com", null, "10 Spectacular Main Idea Worksheets For 5Th Grade 2021", null, "FREE Book Report Template", null, "Ready-to-Use Social Skills Lessons \\u0026 Activities For Grades 7-12 Boys Town Press", null, "Step 4 Worksheets Kids Activities", null, "Instant Lesson Plans For Any Book (Perfect For Substitutes!) Scholastic", null, "Homework And Curriculum Mrs. Kilgallin's 4th Grade", null, "Character Education Worksheets", null, "Best Worksheets By Cleora Best Worksheets Collection", null, "Simplest Form Worksheets 6th Grade Printable 6th Grade Math Help Worksheets Free Worksheets For Grade 1 Mathway Graph Math K5 Learning Adding Worksheets Year 1 Math Addition Worksheets Ks2 Worksheets Family Times", null, "Measurement Worksheets Grade 3 Respect Worksheets For Kids Calligraphy Fonts Worksheets 6th Grade History Worksheets Times Table Grid Worksheet Fourth Grade Math Word Problems Printable Math Is Fun Multiplication Table First Grade", null, "Readers' Workshop - Mrs. Judy Araujo", null, "", null, "", null, "Classroom Guidance – The School Counselor Kind", null, "Worksheet ~ Kindergarten Activity Sheet Free Respect Letter Word End Of The 61 Stunning Kindergarten Activity Sheet. Free Kindergarten Activity Sheet Respect Free. Alphabet Kindergarten Activity Sheet On Adam And Eve. End", null, "", null, "My First Day Of Elementary Music Lesson Plans — Victoria Boler", null, "Englishlinx.com Capitalization Worksheets", null, "10 Spectacular Main Idea Worksheets Grade 3 2021", null, "Chapter 7 Weather And Climate Grade 4 Worksheets Pdf", null, "Dot Grid Printable Ukg Maths Worksheets Pdf Math Games For Third Grade Addition And Subtraction Worksheets Working Out Algebra Equations Grade 5 Math Worksheets South Africa 11th Grade Math Topics Puzzle Books", null, "5 Distance Learning Resources For Upper Elementary Classrooms - Appletastic Learning", null, "Frickin' Packets Cult Of Pedagogy", null, "", null, "", null, "" ]
[ null, "https://i0.wp.com/i.pinimg.com/originals/b8/a5/53/b8a553b513189cbd7de3a96f06d4e90a.jpg", null, "https://i0.wp.com/www.redlandsusd.net/cms/lib/CA01900901/Centricity/Domain/4821/Me%20Showing%20Respect%20Drawing.jpg", null, "https://i0.wp.com/appletasticlearning.com/wp-content/uploads/2020/03/Slide90.jpeg", null, "https://i0.wp.com/www.redlandsusd.net/cms/lib/CA01900901/Centricity/Domain/4821/What%20it%20means%20to%20me.jpg", null, "https://i0.wp.com/i.pinimg.com/originals/04/20/58/042058814e29fe66d27792b4413a8299.jpg", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/free-printable-reading-worksheets-for-4th-graders-four-seasons-log-kindergarten-super-teachers.jpg", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/shortage-with-questions-about-respect-grade-answers-and-multiple-choice-for-kids-ages-reading.jpg", null, "https://i0.wp.com/talkingtreebooks.com/images/category/good-traits-teaching/respect-worksheets-teaching-resources.jpg", null, "https://i0.wp.com/i.pinimg.com/originals/54/fb/b7/54fbb7f8cf6aa80b7f50f21fe61ab226.jpg", null, "https://i0.wp.com/bigmetalcoal.com/wp-content/uploads/2020/04/fantastic-printable-reading-materials-for-kindergarten-1st-grade-activities-money-and-coins-worksheets-respect-comprehension-geometry-lessons-1024x1333.jpg", null, "https://i0.wp.com/kingandsullivan.com/v/2020/07/scientific-method-worksheet-primary.jpg", null, "https://i0.wp.com/www.ereadingworksheets.com/reading-worksheets/context-clues/context-clues-1-7/preview/context-clues-1-7-01.jpg", null, "https://i0.wp.com/bigmetalcoal.com/wp-content/uploads/2020/04/life-skills-reading-worksheets-create-your-own-sight-word-informational-rubric-kindergarten-portfolio-halloween-party-for-toddlers-and-preschoolers-fun-ela-grade-math-geometry-vocabulary-805x1042.jpg", null, "https://i0.wp.com/www.redlandsusd.net/cms/lib/CA01900901/Centricity/Domain/4821/Acrostic%20Poem.jpg", null, "https://i0.wp.com/i.pinimg.com/originals/4d/7d/a4/4d7da4f04db3d9604528c04cef1bd42d.png", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/excelent-theme-practice-worksheets-worksheet-free-4th-grade-math.png", null, "https://i0.wp.com/www.liveonairbk.com/wp-content/uploads/kindergarten-activitiesksheets-picture-inspirations-milk-goes-to-4th-grade-respect.png", null, "https://i0.wp.com/content.lessonplanet.com/s3_uploads/original/08d538aa56779b38c225358c56ca90a2.jpg", null, "https://i0.wp.com/i.pinimg.com/originals/04/aa/4c/04aa4cd85d70880721b3f4846d5bca44.jpg", null, "https://i0.wp.com/bigmetalcoal.com/wp-content/uploads/2020/04/math-fornd-graders-online-free-photo-ideas-2nd-grade-word-problem-worksheets-and-printable-k5-worksheet-mixed-addition-subtraction-problems-scaled.gif", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/worksheet-cleanliness-worksheets-for-kindergarten-math-4th-grade.jpg", null, "https://i0.wp.com/www.1989generationinitiative.org/j/2020/07/worksheet-writing-worksheets-for-first-grade-second-sentence-kindergarten-1024x1325.jpg", null, "https://i0.wp.com/www.richmondplunge.org/e/2021/01/astonishing-respect-worksheets-for-kindergarten-benchwarmerspodcast-kids-church-lesson.jpg", null, "https://i0.wp.com/talkingtreebooks.com/images/teaching-resources-catalog/lesson-plans/sel-lesson-plan-respect-friendship.jpg", null, "https://i0.wp.com/www.eslprintables.com/previews/640487_1-adjectives_for_4th_grade.jpg", null, "https://i0.wp.com/lh3.googleusercontent.com/GCGneGof94w6CBazvJX8RRKWBdtCAHQx1czGaPfhP7x32Xo9ncVS3FcPbDTCn1t4M7qpPutOG9hju8A2Yh2wDIY\\u003ds0", null, "https://i0.wp.com/www.1989generationinitiative.org/j/2020/07/christmas-worksheets-and-printouts-second-grade-math-santasreindeersearchabcorder-learn.jpg", null, "https://i0.wp.com/nano.invitationurn.com/6273/5066/fairy-tale-story-writing-worksheets-ela-3rd-5th-grades.jpg", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/extraordinary-second-grade-reading-passage-doctorbedancing-worksheet-fluency-worksheets.jpg", null, "https://i0.wp.com/www.wannaveg.com/prints/printable-english-worksheets-learn-veterans-day-essay-examples-essays-layers-of-english-worksheets-learn.jpg", null, "https://i0.wp.com/study.com/academy/practice/respect-quiz-worksheet-for-kids.jpg", null, "https://i0.wp.com/x78251kcpll2l2t9e46kf96a-wpengine.netdna-ssl.com/wp-content/uploads/2018/03/Sample-Word-Search.png", null, "https://i0.wp.com/englishlinx.com/images/Compound-Sentences-Circling-P-1-Advanced.png", null, "https://i0.wp.com/argoprep.com/wp-content/uploads/2020/02/4th-Grade-ELA-39.jpg", null, "https://i0.wp.com/williamwithin.com/uploads/138595/reading-worksheets-second-grade-reading-worksheets.png", null, "https://i0.wp.com/www.ereadingworksheets.com/reading-worksheets/inferences-worksheet-04/preview/inferences-worksheet-04-01.jpg", null, "https://i0.wp.com/i.pinimg.com/736x/2d/5f/15/2d5f15c9805ba2e0a10cb70e2db25cf7.jpg", null, "https://i0.wp.com/kingandsullivan.com/v/2020/09/baltrop-org-number-tracing-worksheet-solving.jpg", null, "https://i0.wp.com/www.liveonairbk.com/wp-content/uploads/elementary-math-worksheets-multipliying-multiplication-word-problems-four-v4-outstanding-picture.jpg", null, "https://i0.wp.com/www.scholastic.com/content/dam/teachers/blogs/genia-connell/migrated-files/reading_response_summarizing.jpg", null, "https://i0.wp.com/www.1989generationinitiative.org/j/2020/06/prime-social-studies-worksheets-middle-school-with-images-math-play-dividing-by-worksheet-scaled.jpg", null, "https://i0.wp.com/www.richmondplunge.org/e/2020/08/free-4th-grade-math-worksheets-fpr-numbers-and-algebra-telling-time-printable-activities-692x1182.jpg", null, "https://i0.wp.com/jenniferelliskampani.com/z/2020/11/pronoun-worksheets-preschool-printable-and-activities-for-teachers-parents.jpg", null, "https://i0.wp.com/imgv2-1-f.scribdassets.com/img/document/192335655/original/d34440dacc/1608220040", null, "https://i0.wp.com/bigmetalcoal.com/wp-content/uploads/2020/04/math-for-second-graders-online-free-photo-ideas-respect-worksheets-elementary-students-energy-kids-multiplication-worksheet-coloring-printable-times-tables-create-your-own-facts-scaled.jpg", null, "https://i0.wp.com/appletasticlearning.com/wp-content/uploads/2020/03/Slide46-1.jpeg", null, "https://i0.wp.com/englishlinx.com/images/Theme-Matching-P-1-Intermediate.png", null, "https://i0.wp.com/williamwithin.com/uploads/248972/reading-worksheets-fourth-grade-reading-worksheets.png", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/outstandingano-reading-comprehension-photo-ideas-worksheet-pdf-with-answers-4th-grade.jpg", null, "https://i0.wp.com/nano.invitationurn.com/6275/6318/reading-worksheets-second-grade-reading-worksheets.png", null, "https://i0.wp.com/3.bp.blogspot.com/-QZ6shmn15hA/XJx1WzO2s0I/AAAAAAAAHpI/7WDmoLo1YdAKUKKDWd7MRvpRcgknQBAxwCLcBGAs/s1600/page0001.jpg", null, "https://i0.wp.com/www.ereadingworksheets.com/reading-worksheets/inferences-worksheet-02/preview/inferences-worksheet-02-01.jpg", null, "https://i0.wp.com/www.scholastic.com/content/dam/teachers/blogs/genia-connell/migrated-files/reading_response_visualizing_prompt.jpg", null, "https://i0.wp.com/jenniferelliskampani.com/z/2020/11/worksheet-amazing-free-graderksheets-division-reading-for-kids-science-pdf-math-grade-worksheets-kindergarten-answers.jpg", null, "https://i0.wp.com/www.1989generationinitiative.org/j/2020/07/science-worksheets-for-grade-share-printable-with-answers-matter-social-of-paper.jpg", null, "https://i0.wp.com/x78251kcpll2l2t9e46kf96a-wpengine.netdna-ssl.com/wp-content/uploads/2018/03/Sample-Reading-Worksheet.png", null, "https://i0.wp.com/www.liveonairbk.com/wp-content/uploads/classroom-rules-english-esl-worksheets-for-distance-learning-andee-posters-teacher-3rd-grade-measurement-activities-games-to-teachactions.jpg", null, "https://i0.wp.com/www.richmondplunge.org/e/2021/02/writing-worksheets-for-creative-kids-free-pdf-printables-edhelper-grade-3rd-easy-logic.jpg", null, "https://i0.wp.com/files.liveworksheets.com/def_files/2020/8/24/824235429477559/824235429477559001.jpg", null, "https://i0.wp.com/baltrop.org/m/2020/07/math-worksheet-comprehension-questions-for-2nd-grade-general-4th-ela-worksheets-stories.jpg", null, "https://i0.wp.com/i.pinimg.com/originals/42/a5/86/42a586aa810476aca21741268e87dc67.jpg", null, "https://i0.wp.com/www.bjcschooloutreach.org/Portals/0/Printables/Images/2020-04-16-Activity%20Chart.JPG", null, "https://i0.wp.com/playingwithhistory.com/wp-content/uploads/2020/02/4th-grade-paragraph-writing-worksheets-author-s-purpose-of-4th-grade-paragraph-writing-worksheets.jpg", null, "https://i0.wp.com/appletasticlearning.com/wp-content/uploads/2020/03/Triangles-Cover-1.jpg", null, "https://i0.wp.com/benchwarmerspodcast.org/x/2020/10/worksheet-free-third-grade-reading-passages-with-questions-fluency-fiction.png", null, "https://i0.wp.com/englishlinx.com/images/Abbreviating-Street-Names-Worksheet.png", null, "https://i0.wp.com/baltrop.org/m/2020/07/we-did-in-today-4th-grade-math-word-problems-south-blank-map-negative-and-positive-scaled.jpg", null, "https://i0.wp.com/img.17qq.com/images/scuctrhhx.jpeg", null, "https://i0.wp.com/www.uniqueideas.site/wp-content/uploads/worksheet-main-idea-worksheets-multiple-choice-context-clues-5th-4.jpg", null, "https://i0.wp.com/www.123homeschool4me.com/wp-content/uploads/2015/01/Book-Report-Template-1.jpg", null, "https://i0.wp.com/cdn11.bigcommerce.com/s-5buxwy8qxn/images/stencil/1280x1280/products/704/1676/85-081_RTU_Social-Skills_Lesson-Act__22807.1554919092.jpg", null, "https://i0.wp.com/williamwithin.com/uploads/473541/step-4-worksheets-tnpackfn-flickr.jpg", null, "https://i0.wp.com/www.scholastic.com/content/dam/teachers/blogs/genia-connell/migrated-files/reading_response_story_elements.jpg", null, "https://i0.wp.com/www.saintjamesschool.org/~dkilgallin@saintjamesschool.org/mrs-kilgallins-4th-grade/files/Documents/P.E.%20Field%20Day%20Activity%204.tiff", null, "https://i0.wp.com/talkingtreebooks.com/images/teaching-resources-catalog/worksheets/respect-worksheet-character-ed-sel.jpg", null, "https://i0.wp.com/nano.invitationurn.com/4526/2296/self-love-worksheets-life-planner-self-esteem-worksheets.jpg", null, "https://i0.wp.com/kingandsullivan.com/v/2020/08/simplest-form-worksheets-6th-grade-printable-692x1137.jpg", null, "https://i0.wp.com/www.1989generationinitiative.org/j/2020/07/singular-and-plural-nouns-worksheet-plurals-sentences-worksheets-measure-arc-length.jpg", null, "https://i0.wp.com/www.mrsjudyaraujo.com/wp-content/uploads/6a00e54faaf86b88330120a5f33613970b.jpeg", null, "https://i0.wp.com/www.ereadingworksheets.com/reading-worksheets/inferences-worksheet-05/preview/inferences-worksheet-05-01.jpg", null, "https://i0.wp.com/jenniferelliskampani.com/z/2020/11/worksheet-2ndeth-worksheets-3rd-regrouping-1st-free-second-games-awesome.jpg", null, "https://i0.wp.com/theschoolcounselorkind.files.wordpress.com/2020/09/worryandhope1.jpg", null, "https://i0.wp.com/bigmetalcoal.com/wp-content/uploads/2020/04/kindergarten-activity-sheet-letter-for-kinder-free-in-coloring-respect-template.png", null, "https://i0.wp.com/www.richmondplunge.org/e/2021/02/writing-worksheets-for-creative-kids-free-pdf-printables-edhelper-grade-5th-easy-logic.jpg", null, "https://i0.wp.com/images.squarespace-cdn.com/content/v1/55955001e4b0f2448bc55fa3/1533738640752-O1D1TML8OGTT7B4ZX5NL/ke17ZwdGBToddI8pDm48kHFg3lwAxHvaI5rSscPgwO17gQa3H78H3Y0txjaiv_0fDoOvxcdMmMKkDsyUqMSsMWxHk725yiiHCCLfrh8O1z5QHyNOqBUUEtDDsRWrJLTmjJyaSXAwc_BJvYKv4pjNuo0xLMToagxCDIwK1c7MZEgaoDsH5H7CFhkLT6CXjMBk/Walk+and+Stop.jpg", null, "https://i0.wp.com/englishlinx.com/images/Capitalizing-Days-and-Months-Worksheet.png", null, "https://i0.wp.com/www.uniqueideas.site/wp-content/uploads/reading-worksheets-for-4th-grade-reading-comprehension-worksheets.png", null, "https://i0.wp.com/samanthamarshall.com/images/chapter-7-weather-and-climate-grade-4-worksheets-pdf-2.jpg", null, "https://i0.wp.com/baltrop.org/m/2020/07/valuable-bible-tools-math-activities-grades-games-for-third-grade-respect-worksheets-scaled.jpg", null, "https://i0.wp.com/appletasticlearning.com/wp-content/uploads/2020/03/Slide92.jpeg", null, "https://i0.wp.com/x78251kcpll2l2t9e46kf96a-wpengine.netdna-ssl.com/wp-content/uploads/2018/03/Instead-of-Worksheets.png", null, "https://i0.wp.com/www.quotemaster.org/images/71/716e8709aad077c4916ad442c1f6a379.png", null, "https://i0.wp.com/samsfriedchickenanddonuts.com/wp-content/uploads/english-speaking-topics-for-ielts-free-worksheets-4th-grade-examples-sentences-public-answers-multiple.png", null, "https://i0.wp.com/www.thepositivebrothers.com/wp-content/uploads/2020/02/4th-grade-worksheet-on-context-clues.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7246931,"math_prob":0.99420565,"size":14781,"snap":"2021-21-2021-25","text_gpt3_token_len":3632,"char_repetition_ratio":0.24978006,"word_repetition_ratio":0.053791557,"special_character_ratio":0.33516002,"punctuation_ratio":0.25521958,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9954745,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188],"im_url_duplicate_count":[null,2,null,4,null,null,null,4,null,1,null,3,null,1,null,2,null,1,null,1,null,3,null,null,null,1,null,3,null,1,null,2,null,1,null,2,null,1,null,1,null,1,null,null,null,1,null,1,null,3,null,2,null,null,null,1,null,1,null,1,null,2,null,6,null,null,null,2,null,1,null,null,null,1,null,1,null,1,null,null,null,1,null,8,null,2,null,1,null,1,null,null,null,1,null,1,null,1,null,1,null,2,null,null,null,null,null,1,null,null,null,null,null,1,null,1,null,1,null,3,null,1,null,1,null,1,null,null,null,3,null,1,null,1,null,3,null,1,null,null,null,1,null,1,null,null,null,1,null,5,null,1,null,9,null,4,null,2,null,null,null,8,null,1,null,1,null,1,null,2,null,null,null,6,null,6,null,1,null,2,null,null,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-18T04:38:52Z\",\"WARC-Record-ID\":\"<urn:uuid:ebfc3d86-b59a-498f-8178-62a506968203>\",\"Content-Length\":\"210595\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:881db49c-f4ab-433a-af6b-1dc98698e791>\",\"WARC-Concurrent-To\":\"<urn:uuid:9f1ea852-ae6d-40a9-b4de-f9c2ff455311>\",\"WARC-IP-Address\":\"104.21.30.232\",\"WARC-Target-URI\":\"https://lbartman.com/4th-grade-respect-worksheets/\",\"WARC-Payload-Digest\":\"sha1:N3RYC2NXU35UTNPHM3HRWT6L6NFSIFBJ\",\"WARC-Block-Digest\":\"sha1:U2XJDR7ZN4KRDUZIVR6US7PN6RVXSP2Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989820.78_warc_CC-MAIN-20210518033148-20210518063148-00201.warc.gz\"}"}
http://questions.instantgrades.com/in-the-figure-below-two-point-particles-are-fixed-on-an-x-axis-separated-by-a-distance-d-particle-a-has-mass-ma-and-particle-b-has-mass-2-00ma-a-third-particle-c-of-mass-55-0ma-is-to-be-placed-on/
[ "Interested in a PLAGIARISM-FREE paper based on these particular instructions?...with 100% confidentiality?\n\n# In the figure below, two point particles are fixed on an x axis separated by a distance d. Particle A has mass mA and particle B has mass 2.00mA. A third particle C, of mass 55.0mA, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?\n\nIn the figure below, two point particles are fixed on an x axis separated by a distance d. Particle A has mass mA and particle B has mass 2.00mA. A third particle C, of mass 55.0mA, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?\n\nInterested in a PLAGIARISM-FREE paper based on these particular instructions?...with 100% confidentiality?" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9085961,"math_prob":0.95542616,"size":599,"snap":"2022-27-2022-33","text_gpt3_token_len":143,"char_repetition_ratio":0.14453782,"word_repetition_ratio":0.16161616,"special_character_ratio":0.23038398,"punctuation_ratio":0.15503876,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98130983,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-05T10:29:08Z\",\"WARC-Record-ID\":\"<urn:uuid:96c3fe19-6015-406f-b256-bc476d9b3bec>\",\"Content-Length\":\"25104\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7c63edb8-8ea9-42ad-b73e-f660bd24db0a>\",\"WARC-Concurrent-To\":\"<urn:uuid:ca488c55-d797-414b-886b-9b267f08908e>\",\"WARC-IP-Address\":\"172.67.194.163\",\"WARC-Target-URI\":\"http://questions.instantgrades.com/in-the-figure-below-two-point-particles-are-fixed-on-an-x-axis-separated-by-a-distance-d-particle-a-has-mass-ma-and-particle-b-has-mass-2-00ma-a-third-particle-c-of-mass-55-0ma-is-to-be-placed-on/\",\"WARC-Payload-Digest\":\"sha1:33KN7SFFFEL22YXPXIZHGCU2LY7AJ234\",\"WARC-Block-Digest\":\"sha1:EL5WBD6UQADYUJMGAN7AHPOWBU5Q2SLB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104542759.82_warc_CC-MAIN-20220705083545-20220705113545-00075.warc.gz\"}"}
https://openstax.org/books/introductory-business-statistics/pages/9-1-null-and-alternative-hypotheses
[ "# 9.1Null and Alternative Hypotheses\n\nIntroductory Business Statistics9.1 Null and Alternative Hypotheses\n\nThe actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.\n\nH0: The null hypothesis: It is a statement of no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.\n\nHa: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we cannot accept H0. The alternative hypothesis is the contender and must win with significant evidence to overthrow the status quo. This concept is sometimes referred to the tyranny of the status quo because as we will see later, to overthrow the null hypothesis takes usually 90 or greater confidence that this is the proper decision.\n\nSince the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.\n\nAfter you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are \"cannot accept H0\" if the sample information favors the alternative hypothesis or \"do not reject H0\" or \"decline to reject H0\" if the sample information is insufficient to reject the null hypothesis. These conclusions are all based upon a level of probability, a significance level, that is set my the analyst.\n\nTable 9.1 presents the various hypotheses in the relevant pairs. For example, if the null hypothesis is equal to some value, the alternative has to be not equal to that value.\n\nH0 Ha\nequal (=) not equal (≠)\ngreater than or equal to (≥) less than (<)\nless than or equal to (≤) more than (>)\nTable 9.1\n\n### Note\n\nAs a mathematical convention H0 always has a symbol with an equal in it. Ha never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test.\n\n### Example 9.1\n\nH0: No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30\nHa: More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30\n\n### Example 9.2\n\nWe want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:\nH0: μ = 2.0\nHa: μ ≠ 2.0\n\n### Example 9.3\n\nWe want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:\nH0: μ ≥ 5\nHa: μ < 5" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.92596406,"math_prob":0.9009522,"size":2631,"snap":"2019-51-2020-05","text_gpt3_token_len":594,"char_repetition_ratio":0.15188427,"word_repetition_ratio":0.09071274,"special_character_ratio":0.22767009,"punctuation_ratio":0.102713175,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9756876,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-09T09:42:25Z\",\"WARC-Record-ID\":\"<urn:uuid:d18aeff7-7a33-4ab2-8fb0-566268fcc5d6>\",\"Content-Length\":\"176050\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2bd365ac-d2a8-4e40-9ac5-26efae35cffb>\",\"WARC-Concurrent-To\":\"<urn:uuid:b22a8aba-9f4f-4daa-9b49-711e21ef40ab>\",\"WARC-IP-Address\":\"99.84.181.10\",\"WARC-Target-URI\":\"https://openstax.org/books/introductory-business-statistics/pages/9-1-null-and-alternative-hypotheses\",\"WARC-Payload-Digest\":\"sha1:LJC7ZRYZYO52C62VOAFYU3RBFPU5YRV6\",\"WARC-Block-Digest\":\"sha1:OP7N5RGXSNCJAPZRTGWNO4IRFMT4GPMR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540518627.72_warc_CC-MAIN-20191209093227-20191209121227-00457.warc.gz\"}"}
https://typeset.io/topics/multivariate-normal-distribution-3bbd5jb4
[ "Topic\n\n# Multivariate normal distribution\n\nAbout: Multivariate normal distribution is a(n) research topic. Over the lifetime, 8304 publication(s) have been published within this topic receiving 324203 citation(s). The topic is also known as: multivariate Gaussian distribution & joint normal distribution.\n##### Papers\nMore filters\n\nBook\n01 Jan 1982-\nAbstract: (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.\n\n11,666 citations\n\nBook\n14 Sep 1984-\nAbstract: Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance Matrix.4. The Distributions and Uses of Sample Correlation Coefficients.5. The Generalized T2-Statistic.6. Classification of Observations.7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance.8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance9. Testing Independence of Sets of Variates.10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices.11. Principal Components.12. Cononical Correlations and Cononical Variables.13. The Distributions of Characteristic Roots and Vectors.14. Factor Analysis.15. Pattern of Dependence Graphical Models.Appendix A: Matrix Theory.Appendix B: Tables.References.Index.\n\n9,680 citations\n\nBook\n01 Jan 1976-\nAbstract: A text designed to make multivariate techniques available to behavioural, social, biological and medical students. Special features include an approach to multivariate inference based on the union-intersection and generalized likelihood ratio principles.\n\n5,797 citations\n\nJournal ArticleDOI\nAbstract: A common concern when faced with multivariate data with missing values is whether the missing data are missing completely at random (MCAR); that is, whether missingness depends on the variables in the data set. One way of assessing this is to compare the means of recorded values of each variable between groups defined by whether other variables in the data set are missing or not. Although informative, this procedure yields potentially many correlated statistics for testing MCAR, resulting in multiple-comparison problems. This article proposes a single global test statistic for MCAR that uses all of the available data. The asymptotic null distribution is given, and the small-sample null distribution is derived for multivariate normal data with a monotone pattern of missing data. The test reduces to a standard t test when the data are bivariate with missing data confined to a single variable. A limited simulation study of empirical sizes for the test applied to normal and nonnormal data suggests th...\n\n4,890 citations\n\nBook\n01 Jun 1970-\nAbstract: Foreword.Preface.PART ONE. SURVEY OF PROBABILITY THEORY.Chapter 1. Introduction.Chapter 2. Experiments, Sample Spaces, and Probability.2.1 Experiments and Sample Spaces.2.2 Set Theory.2.3 Events and Probability.2.4 Conditional Probability.2.5 Binomial Coefficients.Exercises.Chapter 3. Random Variables, Random Vectors, and Distributions Functions.3.1 Random Variables and Their Distributions.3.2 Multivariate Distributions.3.3 Sums and Integrals.3.4 Marginal Distributions and Independence.3.5 Vectors and Matrices.3.6 Expectations, Moments, and Characteristic Functions.3.7 Transformations of Random Variables.3.8 Conditional Distributions.Exercises.Chapter 4. Some Special Univariate Distributions.4.1 Introduction.4.2 The Bernoulli Distributions.4.3 The Binomial Distribution.4.4 The Poisson Distribution.4.5 The Negative Binomial Distribution.4.6 The Hypergeometric Distribution.4.7 The Normal Distribution.4.8 The Gamma Distribution.4.9 The Beta Distribution.4.10 The Uniform Distribution.4.11 The Pareto Distribution.4.12 The t Distribution.4.13 The F Distribution.Exercises.Chapter 5. Some Special Multivariate Distributions.5.1 Introduction.5.2 The Multinomial Distribution.5.3 The Dirichlet Distribution.5.4 The Multivariate Normal Distribution.5.5 The Wishart Distribution.5.6 The Multivariate t Distribution.5.7 The Bilateral Bivariate Pareto Distribution.Exercises.PART TWO. SUBJECTIVE PROBABILITY AND UTILITY.Chapter 6. Subjective Probability.6.1 Introduction.6.2 Relative Likelihood.6.3 The Auxiliary Experiment.6.4 Construction of the Probability Distribution.6.5 Verification of the Properties of a Probability Distribution.6.6 Conditional Likelihoods.Exercises.Chapter 7. Utility.7.1 Preferences Among Rewards.7.2 Preferences Among Probability Distributions.7.3 The Definitions of a Utility Function.7.4 Some Properties of Utility Functions.7.5 The Utility of Monetary Rewards.7.6 Convex and Concave Utility Functions.7.7 The Anxiomatic Development of Utility.7.8 Construction of the Utility Function.7.9 Verification of the Properties of a Utility Function.7.10 Extension of the Properties of a Utility Function to the Class ?E.Exercises.PART THREE. STATISTICAL DECISION PROBLEMS.Chapter 8. Decision Problems.8.1 Elements of a Decision Problem.8.2 Bayes Risk and Bayes Decisions.8.3 Nonnegative Loss Functions.8.4 Concavity of the Bayes Risk.8.5 Randomization and Mixed Decisions.8.6 Convex Sets.8.7 Decision Problems in Which ~2 and D Are Finite.8.8 Decision Problems with Observations.8.9 Construction of Bayes Decision Functions.8.10 The Cost of Observation.8.11 Statistical Decision Problems in Which Both ? and D contains Two Points.8.12 Computation of the Posterior Distribution When the Observations Are Made in More Than One Stage.Exercises.Chapter 9. Conjugate Prior Distributions.9.1 Sufficient Statistics.9.2 Conjugate Families of Distributions.9.3 Construction of the Conjugate Family.9.4 Conjugate Families for Samples from Various Standard Distributions.9.5 Conjugate Families for Samples from a Normal Distribution.9.6 Sampling from a Normal Distribution with Unknown Mean and Unknown Precision.9.7 Sampling from a Uniform Distribution.9.8 A Conjugate Family for Multinomial Observations.9.9 Conjugate Families for Samples from a Multivariate Normal Distribution.9.10 Multivariate Normal Distributions with Unknown Mean Vector and Unknown Precision matrix.9.11 The Marginal Distribution of the Mean Vector.9.12 The Distribution of a Correlation.9.13 Precision Matrices Having an Unknown Factor.Exercises.Chapter 10. Limiting Posterior Distributions.10.1 Improper Prior Distributions.10.2 Improper Prior Distributions for Samples from a Normal Distribution.10.3 Improper Prior Distributions for Samples from a Multivariate Normal Distribution.10.4 Precise Measurement.10.5 Convergence of Posterior Distributions.10.6 Supercontinuity.10.7 Solutions of the Likelihood Equation.10.8 Convergence of Supercontinuous Functions.10.9 Limiting Properties of the Likelihood Function.10.10 Normal Approximation to the Posterior Distribution.10.11 Approximation for Vector Parameters.10.12 Posterior Ratios.Exercises.Chapter 11. Estimation, Testing Hypotheses, and linear Statistical Models.11.1 Estimation.11.2 Quadratic Loss.11.3 Loss Proportional to the Absolute Value of the Error.11.4 Estimation of a Vector.11.5 Problems of Testing Hypotheses.11.6 Testing a Simple Hypothesis About the Mean of a Normal Distribution.11.7 Testing Hypotheses about the Mean of a Normal Distribution.11.8 Deciding Whether a Parameter Is Smaller or larger Than a Specific Value.11.9 Deciding Whether the Mean of a Normal Distribution Is Smaller or larger Than a Specific Value.11.10 Linear Models.11.11 Testing Hypotheses in Linear Models.11.12 Investigating the Hypothesis That Certain Regression Coefficients Vanish.11.13 One-Way Analysis of Variance.Exercises.PART FOUR. SEQUENTIAL DECISIONS.Chapter 12. Sequential Sampling.12.1 Gains from Sequential Sampling.12.2 Sequential Decision Procedures.12.3 The Risk of a Sequential Decision Procedure.12.4 Backward Induction.12.5 Optimal Bounded Sequential Decision procedures.12.6 Illustrative Examples.12.7 Unbounded Sequential Decision Procedures.12.8 Regular Sequential Decision Procedures.12.9 Existence of an Optimal Procedure.12.10 Approximating an Optimal Procedure by Bounded Procedures.12.11 Regions for Continuing or Terminating Sampling.12.12 The Functional Equation.12.13 Approximations and Bounds for the Bayes Risk.12.14 The Sequential Probability-ratio Test.12.15 Characteristics of Sequential Probability-ratio Tests.12.16 Approximating the Expected Number of Observations.Exercises.Chapter 13. Optimal Stopping.13.1 Introduction.13.2 The Statistician's Reward.13.3 Choice of the Utility Function.13.4 Sampling Without Recall.13.5 Further Problems of Sampling with Recall and Sampling without Recall.13.6 Sampling without Recall from a Normal Distribution with Unknown Mean.13.7 Sampling with Recall from a Normal Distribution with Unknown Mean.13.8 Existence of Optimal Stopping Rules.13.9 Existence of Optimal Stopping Rules for Problems of Sampling with Recall and Sampling without Recall.13.10 Martingales.13.11 Stopping Rules for Martingales.13.12 Uniformly Integrable Sequences of Random Variables.13.13 Martingales Formed from Sums and Products of Random Variables.13.14 Regular Supermartingales.13.15 Supermartingales and General Problems of Optimal Stopping.13.16 Markov Processes.13.17 Stationary Stopping Rules for Markov Processes.13.18 Entrance-fee Problems.13.19 The Functional Equation for a Markov Process.Exercises.Chapter 14. Sequential Choice of Experiments.14.1 Introduction.14.2 Markovian Decision Processes with a Finite Number of Stages.14.3 Markovian Decision Processes with an Infinite Number of Stages.14.4 Some Betting Problems.14.5 Two-armed-bandit Problems.14.6 Two-armed-bandit Problems When the Value of One Parameter Is Known.14.7 Two-armed-bandit Problems When the Parameters Are Dependent.14.8 Inventory Problems.14.9 Inventory Problems with an Infinite Number of Stages.14.10 Control Problems.14.11 Optimal Control When the Process Cannot Be Observed without Error.14.12 Multidimensional Control Problems.14.13 Control Problems with Actuation Errors.14.14 Search Problems.14.15 Search Problems with Equal Costs.14.16 Uncertainty Functions and Statistical Decision Problems.14.17 Sufficient Experiments.14.18 Examples of Sufficient Experiments.Exercises.References.Supplementary Bibliography.Name Index.Subject Index.\n\n4,255 citations\n\n##### Network Information\n###### Related Topics (5)\nTest statistic\n\n9K papers, 425.6K citations\n\n94% related\nNonparametric statistics\n\n19.9K papers, 844.1K citations\n\n93% related\nNonparametric regression\n\n7.6K papers, 354.4K citations\n\n93% related\nEfficient estimator\n\n6.5K papers, 228.9K citations\n\n93% related\nBias of an estimator\n\n6.1K papers, 171.9K citations\n\n93% related\n##### Performance\n###### Metrics\nNo. of papers in the topic in previous years\nYearPapers\n20227\n2021273\n2020326\n2019259\n2018241\n2017291\n\n###### Top Attributes\n\nShow by:\n\nTopic's top 5 most impactful authors\n\nNarayanaswamy Balakrishnan\n\n37 papers, 1.1K citations\n\nArjun K. Gupta\n\n37 papers, 989 citations\n\nMuni S. Srivastava\n\n35 papers, 1.3K citations" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.69898313,"math_prob":0.77100784,"size":15684,"snap":"2022-27-2022-33","text_gpt3_token_len":3599,"char_repetition_ratio":0.17321429,"word_repetition_ratio":0.029442692,"special_character_ratio":0.20798266,"punctuation_ratio":0.21218343,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9744244,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-18T20:39:05Z\",\"WARC-Record-ID\":\"<urn:uuid:67b59d1c-143b-48f3-925c-5157c0a39303>\",\"Content-Length\":\"246259\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:acd4e65d-fc9e-4c13-9016-2af22289f1a8>\",\"WARC-Concurrent-To\":\"<urn:uuid:bd6a0b41-cd86-4cee-9c9b-43090e4c951e>\",\"WARC-IP-Address\":\"13.32.151.107\",\"WARC-Target-URI\":\"https://typeset.io/topics/multivariate-normal-distribution-3bbd5jb4\",\"WARC-Payload-Digest\":\"sha1:L2SOAV7DPWZFFKDMBSPOOOAGQJDQ326G\",\"WARC-Block-Digest\":\"sha1:QESPXCNPR37SVJEWDOVQ4256CUHGXN5X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573399.40_warc_CC-MAIN-20220818185216-20220818215216-00665.warc.gz\"}"}
http://allenfleishmanbiostatistics.com/Articles/2012/04/5-a-accepting-the-null-hypothesis-a-bayesian-approach/
[ "# 5.A Accepting the Null-Hypothesis a Bayesian approach\n\nThe following blog was written by Randy Gallistel, PhD of Rutgers.  It presents a Bayesian approach to hypothesis testing.  It was written on April 23, 2012, but will eventually appear to have an earlier date, to sort it immediately after my original (Frequentist) blog.\n\nThe Bayesian would say that the truism that one cannot prove the null is a consequence of a misformulation of the inference problem. If we agree that hypothesis-testing statistics is the mathematics of probabilistic inference and if we resort to probabilistic inference only when we are faced with some uncertainty as to which conclusion to draw, then the NHST formulation of the problem is ruled out because, given that formulation, we have no uncertainty: Only one possible conclusion is to be tested against the data, the null conclusion, and we are a priori certain that it cannot be true. Thus, there is no inference problem.\n\nOne might object that this is not so; the alternative is that there is “some” (positive!) effect. But until we specify what we understand by “some”, this is not a well-formulated alternative. For example, in a typical pharmacological clinical trial, “some” effect could mean that the drug had an effect anywhere between 0 and complete cure in every patient (maximum possible effect). If that is what we understand “some” effect to mean, then for most drugs, the null conclusion (no positive effect) has a greater likelihood than the “some” (positive) effect conclusion.\n\nThe Bayesian computation tells us how well each possible conclusion (aka hypothesis) predicts the data that we have gathered. The possible hypotheses are represented by prior distributions. These prior distributions may be thought of as bets made by each hypothesis before the data are examined. Each hypothesis has a unit mass of prior probability with which to bet. The null conclusion bets it all on 0. The unlimited “some” hypothesis spreads its unit mass of prior probability out over all possible effect sizes.The question then becomes which of these prior probability distributions does a better job of predicting the likelihood function.\n\nLikelihood is sometimes called the reverse probability. In forward probability, we assume that we know the distribution (that is, we know its form and the values of its parameters) and we use this knowledge to predict how probable different outcomes are. In reverse probability (likelihood), we assume we know the data and we use the data to compute how likely those data would be for various assumptions about the distribution from which they came (assumptions about the form and about the values of the parameters of the distribution from which the data may have come). The likelihood function tells us the likelihood for all different values of the parameters of an assumed distribution. The highly likely values are the ones that predict what we have observed; the highly unlikely ones are the ones that predict that we should not have observed what we have in fact observed\n\nThe possibilities for which probabilities are defined in a probability distribution are mutually exclusive and exhaustive, so their probabilities must sum (integrate) to one. Reverse probabilities (likelihoods), by contrast, are neither mutually exclusive nor exhaustive. It is possible to have two hypotheses that are distinct but overlapping and they may both either predict the data we have with absolute certainty (in which case, they both have a likelihood of 1) or not at all (in which case, they both have a likelihood of 0). Generally, however, one hypothesis does a better job of predicting our data than the other, in which case that hypothesis is more likely than the alternative. The Bayes Factor is the ratio of the likelihoods, in other words, the likelihood of the one hypothesis relative to the other.\n\nSuppose the data suggest only a weak positive effect. That means that we COULD have got those data with reasonable probability even if there is in fact no effect (the null hypothesis), whereas, we could not have got those data if the effect of the drug were so great as to completely cure every patient, which is one of the states of the world encompassed by the unbridled version of the “some” hypothesis. The marginal likelihood of an hypothesis is its average likelihood over each possible value of (say) its mean that is compassed by the associated prior probability function. Because weakly positive results are inconsistent with all the stronger forms of “some”, the marginal likelihood of the unbridled “some” hypothesis is low. The null places all its chips on a single value 0, so the “average” for this hypothesis is simply the likelihood at that value, and, as already noted, if the data are weak, then the likelihood that the true effect is 0 is substantial.\n\nThus, the Bayesian would argue that when we formulate the inference problem in such a way that there actually is some uncertainty–hence, something to be inferred–the data may very well favor the null hypothesis. The frequentist objects that when we frame the inference problem this way, our inference will depend on the upper limit that we put on what we understand by ‘some,’ and that is true. But there is no reason not to compute the Bayes Factor (the ratio of the marginal likelihoods) as a function of this upper limit. If the Bayes Factor in favor of the null approaches 1 from above as the upper limit goes to 0, that is, as “some effect” becomes indistinguishable for “no effect”, then we can conclude that the inference to the null is to be preferred over ANY (positive!) alternative to it.\n\nWhen the null is actually true, the data will yield such a function 50% of the time. And, when the pharmacological effect is actually slightly or strongly negative (deleterious), the data will yield such a function even more often. Moreover, this will be true no matter how small the N. Thus, we have a rational basis for favoring one conclusion over the other no matter how little data we have.\n\nWhen, by chance, the function relating the odds in favor of the null to the upper limit on “some positive effect” dips slightly below 1 for some non-zero assumption about the upper limit, it will not go very far below 1, that is, the “some effect” hypothesis cannot attain high relative likelihood when there is in fact no effect or when the effect is weak and we have little data. Therefore, if we insist that we want some reasonable odds (say 10:1) in favor of “some” (positive) effect before we put the drug on the market, we will more often than not conclude that there is no effect or none worth considering. And that is what we should conclude. Not because it is necessarily true–nothing is certain but death and taxes–but because that is what is consistent with the data we have and the principle that a drug should not be marketed unless the data we have make us reasonably confident that it will do good.\n\nThis entry was posted in Biostatistics, Uncategorized. Bookmark the permalink." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9581658,"math_prob":0.9662052,"size":6893,"snap":"2020-10-2020-16","text_gpt3_token_len":1400,"char_repetition_ratio":0.14936855,"word_repetition_ratio":0.027562447,"special_character_ratio":0.19875236,"punctuation_ratio":0.082095385,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98665935,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-22T07:12:46Z\",\"WARC-Record-ID\":\"<urn:uuid:0b39764b-d2bb-48a3-98b4-4470375926f6>\",\"Content-Length\":\"32478\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4d6bc741-1f6a-43c1-960b-1ddbbb32eb64>\",\"WARC-Concurrent-To\":\"<urn:uuid:0ab095e9-9d0c-4771-ac7f-e79d639cf21a>\",\"WARC-IP-Address\":\"184.168.137.128\",\"WARC-Target-URI\":\"http://allenfleishmanbiostatistics.com/Articles/2012/04/5-a-accepting-the-null-hypothesis-a-bayesian-approach/\",\"WARC-Payload-Digest\":\"sha1:KMRW3NRZQ5DH5DPLZYWBO4FQGD53JUDC\",\"WARC-Block-Digest\":\"sha1:BQQ53HC5DDOIF4235YKZWNBDPVGCTXW7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145654.0_warc_CC-MAIN-20200222054424-20200222084424-00204.warc.gz\"}"}
https://formulasearchengine.com/wiki/Representation_theory
[ "# Representation theory\n\n{{#invoke:Hatnote|hatnote}}\n\nRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation is matrix multiplication.\n\nRepresentation theory is a powerful tool because it reduces problems in abstract algebra to problems in linear algebra, a subject that is well understood. Furthermore, the vector space on which a group (for example) is represented can be infinite-dimensional, and by allowing it to be, for instance, a Hilbert space, methods of analysis can be applied to the theory of groups. Representation theory is also important in physics because, for example, it describes how the symmetry group of a physical system affects the solutions of equations describing that system.\n\nA striking feature of representation theory is its pervasiveness in mathematics. There are two sides to this. First, the applications of representation theory are diverse: in addition to its impact on algebra, representation theory:\n\nThe second aspect is the diversity of approaches to representation theory. The same objects can be studied using methods from algebraic geometry, module theory, analytic number theory, differential geometry, operator theory, algebraic combinatorics and topology.\n\nThe success of representation theory has led to numerous generalizations. One of the most general is in category theory. The algebraic objects to which representation theory applies can be viewed as particular kinds of categories, and the representations as functors from the object category to the category of vector spaces. This description points to two obvious generalizations: first, the algebraic objects can be replaced by more general categories; second, the target category of vector spaces can be replaced by other well-understood categories.\n\nA representation should not be confused with a presentation.\n\n## Definitions and concepts\n\nLet V be a vector space over a field F. For instance, suppose V is Rn or Cn, the standard n-dimensional space of column vectors over the real or complex numbers respectively. In this case, the idea of representation theory is to do abstract algebra concretely by using n × n matrices of real or complex numbers.\n\nThere are three main sorts of algebraic objects for which this can be done: groups, associative algebras and Lie algebras.\n\nThis generalizes to any field F and any vector space V over F, with linear maps replacing matrices and composition replacing matrix multiplication: there is a group GL(V,F) of automorphisms of V, an associative algebra EndF(V) of all endomorphisms of V, and a corresponding Lie algebra gl(V,F).\n\n### Definition\n\nThere are two ways to say what a representation is. The first uses the idea of an action, generalizing the way that matrices act on column vectors by matrix multiplication. A representation of a group G or (associative or Lie) algebra A on a vector space V is a map\n\n$\\Phi \\colon G\\times V\\to V\\quad {\\text{or}}\\quad \\Phi \\colon A\\times V\\to V$", null, "with two properties. First, for any g in G (or a in A), the map\n\n{\\begin{aligned}\\varphi (g)\\colon V&\\to V\\\\v&\\mapsto \\Phi (g,v)\\end{aligned}}", null, "is linear (over F). Second, if we introduce the notation g · v for Φ (g, v), then for any g1, g2 in G and v in V:\n\n$(1)\\quad e\\cdot v=v$", null, "$(2)\\quad g_{1}\\cdot (g_{2}\\cdot v)=(g_{1}g_{2})\\cdot v$", null, "where e is the identity element of G and g1g2 is product in G. The requirement for associative algebras is analogous, except that associative algebras do not always have an identity element, in which case equation (1) is ignored. Equation (2) is an abstract expression of the associativity of matrix multiplication. This doesn't hold for the matrix commutator and also there is no identity element for the commutator. Hence for Lie algebras, the only requirement is that for any x1, x2 in A and v in V:\n\n$(2')\\quad x_{1}\\cdot (x_{2}\\cdot v)-x_{2}\\cdot (x_{1}\\cdot v)=[x_{1},x_{2}]\\cdot v$", null, "where [x1, x2] is the Lie bracket, which generalizes the matrix commutator MNNM.\n\nThe second way to define a representation focuses on the map φ sending g in G to a linear map φ(g): VV, which satisfies\n\n$\\varphi (g_{1}g_{2})=\\varphi (g_{1})\\circ \\varphi (g_{2})\\quad {\\text{for all }}g_{1},g_{2}\\in G\\,\\!$", null, "and similarly in the other cases. This approach is both more concise and more abstract. From this point of view:\n\n### Terminology\n\nThe vector space V is called the representation space of φ and its dimension (if finite) is called the dimension of the representation (sometimes degree, as in ). It is also common practice to refer to V itself as the representation when the homomorphism φ is clear from the context; otherwise the notation (V,φ) can be used to denote a representation.\n\nWhen V is of finite dimension n, one can choose a basis for V to identify V with Fn and hence recover a matrix representation with entries in the field F.\n\nAn effective or faithful representation is a representation (V,φ) for which the homomorphism φ is injective.\n\n### Equivariant maps and isomorphisms\n\nIf V and W are vector spaces over F, equipped with representations φ and ψ of a group G, then an equivariant map from V to W is a linear map α: VW such that\n\n$\\alpha (g\\cdot v)=g\\cdot \\alpha (v)$", null, "for all g in G and v in V. In terms of φ: G → GL(V) and ψ: G → GL(W), this means\n\n$\\alpha \\circ \\phi (g)=\\psi (g)\\circ \\alpha$", null, "for all g in G.\n\nEquivariant maps for representations of an associative or Lie algebra are defined similarly. If α is invertible, then it is said to be an isomorphism, in which case V and W (or, more precisely, φ and ψ) are isomorphic representations.\n\nIsomorphic representations are, for all practical purposes, \"the same\": they provide the same information about the group or algebra being represented. Representation theory therefore seeks to classify representations \"up to isomorphism\".\n\n### Subrepresentations, quotients, and irreducible representations\n\nIf (W,ψ) is a representation of (say) a group G, and V is a linear subspace of W that is preserved by the action of G in the sense that g · vV for all vV (Serre calls these V stable under G), then V is called a subrepresentation: by defining φ(g) to be the restriction of ψ(g) to V, (V, φ) is a representation of G and the inclusion of V into W is an equivariant map. The quotient space W/V can also be made into a representation of G.\n\nIf W has exactly two subrepresentations, namely the trivial subspace {0} and W itself, then the representation is said to be irreducible; if W has a proper nontrivial subrepresentation, the representation is said to be reducible.\n\nThe definition of an irreducible representation implies Schur's lemma: an equivariant map α: VW between irreducible representations is either the zero map or an isomorphism, since its kernel and image are subrepresentations. In particular, when V = W, this shows that the equivariant endomorphisms of V form an associative division algebra over the underlying field F. If F is algebraically closed, the only equivariant endomorphisms of an irreducible representation are the scalar multiples of the identity.\n\nIrreducible representations are the building blocks of representation theory: if a representation W is not irreducible then it is built from a subrepresentation and a quotient that are both \"simpler\" in some sense; for instance, if W is finite-dimensional, then both the subrepresentation and the quotient have smaller dimension.\n\n### Direct sums and indecomposable representations\n\nIf (V,φ) and (W,ψ) are representations of (say) a group G, then the direct sum of V and W is a representation, in a canonical way, via the equation\n\n$g\\cdot (v,w)=(g\\cdot v,g\\cdot w).$", null, "The direct sum of two representations carries no more information about the group G than the two representations do individually. If a representation is the direct sum of two proper nontrivial subrepresentations, it is said to be decomposable. Otherwise, it is said to be indecomposable.\n\nIn favourable circumstances, every representation is a direct sum of irreducible representations: such representations are said to be semisimple. In this case, it suffices to understand only the irreducible representations. In other cases, one must understand how indecomposable representations can be built from irreducible representations as extensions of a quotient by a subrepresentation.\n\n## Branches and topics\n\nRepresentation theory is notable for the number of branches it has, and the diversity of the approaches to studying representations of groups and algebras. Although, all the theories have in common the basic concepts discussed already, they differ considerably in detail. The differences are at least 3-fold:\n\n1. Representation theory depends upon the type of algebraic object being represented. There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour.\n2. Representation theory depends upon the nature of the vector space on which the algebraic object is represented. The most important distinction is between finite-dimensional representations and infinite-dimensional ones. In the infinite-dimensional case, additional structures are important (e.g. whether or not the space is a Hilbert space, Banach space, etc.). Additional algebraic structures can also be imposed in the finite-dimensional case.\n3. Representation theory depends upon the type of field over which the vector space is defined. The most important case is the field of complex numbers. The other important cases are the field of real numbers, finite fields, and fields of p-adic numbers. Additional difficulties arise for fields of positive characteristic and for fields that are not algebraically closed.\n\n### Finite groups\n\n{{#invoke:main|main}}\n\nGroup representations are a very important tool in the study of finite groups. They also arise in the applications of finite group theory to geometry and crystallography. Representations of finite groups exhibit many of the features of the general theory and point the way to other branches and topics in representation theory.\n\nOver a field of characteristic zero, the representation theory of a finite group G has a number of convenient properties. First, the representations of G are semisimple (completely reducible). This is a consequence of Maschke's theorem, which states that any subrepresentation V of a G-representation W has a G-invariant complement. One proof is to choose any projection π from W to V and replace it by its average πG defined by\n\n$\\pi _{G}(x)={\\frac {1}{|G|}}\\sum _{g\\in G}g\\cdot \\pi (g^{-1}\\cdot x).$", null, "πG is equivariant, and its kernel is the required complement.\n\nThe finite-dimensional G-representations can be understood using character theory: the character of a representation φ: G → GL(V) is the class function χφ: GF defined by\n\n$\\chi _{\\varphi }(g)=\\mathrm {Tr} (\\varphi (g))\\,$", null, "where $\\mathrm {Tr}$", null, "is the trace. An irreducible representation of G is completely determined by its character.\n\nMaschke's theorem holds more generally for fields of positive characteristic p, such as the finite fields, as long as the prime p is coprime to the order of G. When p and |G| have a common factor, there are G-representations that are not semisimple, which are studied in a subbranch called modular representation theory.\n\nAveraging techniques also show that if F is the real or complex numbers, then any G-representation preserves an inner product $\\langle \\cdot ,\\cdot \\rangle$", null, "on V in the sense that\n\n$\\langle g\\cdot v,g\\cdot w\\rangle =\\langle v,w\\rangle$", null, "for all g in G and v, w in W. Hence any G-representation is unitary.\n\nUnitary representations are automatically semisimple, since Maschke's result can be proven by taking the orthogonal complement of a subrepresentation. When studying representations of groups that are not finite, the unitary representations provide a good generalization of the real and complex representations of a finite group.\n\nResults such as Maschke's theorem and the unitary property that rely on averaging can be generalized to more general groups by replacing the average with an integral, provided that a suitable notion of integral can be defined. This can be done for compact groups or locally compact groups, using Haar measure, and the resulting theory is known as abstract harmonic analysis.\n\nOver arbitrary fields, another class of finite groups that have a good representation theory are the finite groups of Lie type. Important examples are linear algebraic groups over finite fields. The representation theory of linear algebraic groups and Lie groups extends these examples to infinite-dimensional groups, the latter being intimately related to Lie algebra representations. The importance of character theory for finite groups has an analogue in the theory of weights for representations of Lie groups and Lie algebras.\n\nRepresentations of a finite group G are also linked directly to algebra representations via the group algebra F[G], which is a vector space over F with the elements of G as a basis, equipped with the multiplication operation defined by the group operation, linearity, and the requirement that the group operation and scalar multiplication commute.\n\n### Modular representations\n\n{{#invoke:main|main}}\n\nModular representations of a finite group G are representations over a field whose characteristic is not coprime to |G|, so that Maschke's theorem no longer holds (because |G| is not invertible in F and so one cannot divide by it). Nevertheless, Richard Brauer extended much of character theory to modular representations, and this theory played an important role in early progress towards the classification of finite simple groups, especially for simple groups whose characterization was not amenable to purely group-theoretic methods because their Sylow 2-subgroups were \"too small\".\n\nAs well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.\n\n### Unitary representations\n\n{{#invoke:main|main}}\n\nA unitary representation of a group G is a linear representation φ of G on a real or (usually) complex Hilbert space V such that φ(g) is a unitary operator for every gG. Such representations have been widely applied in quantum mechanics since the 1920s, thanks in particular to the influence of Hermann Weyl, and this has inspired the development of the theory, most notably through the analysis of representations of the Poincaré group by Eugene Wigner. One of the pioneers in constructing a general theory of unitary representations (for any group G rather than just for particular groups useful in applications) was George Mackey, and an extensive theory was developed by Harish-Chandra and others in the 1950s and 1960s.\n\nA major goal is to describe the \"unitary dual\", the space of irreducible unitary representations of G. The theory is most well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations are strongly continuous. For G abelian, the unitary dual is just the space of characters, while for G compact, the Peter–Weyl theorem shows that the irreducible unitary representations are finite-dimensional and the unitary dual is discrete. For example, if G is the circle group S1, then the characters are given by integers, and the unitary dual is Z.\n\nFor non-compact G, the question of which representations are unitary is a subtle one. Although irreducible unitary representations must be \"admissible\" (as Harish-Chandra modules) and it is easy to detect which admissible representations have a nondegenerate invariant sesquilinear form, it is hard to determine when this form is positive definite. An effective description of the unitary dual, even for relatively well-behaved groups such as real reductive Lie groups (discussed below), remains an important open problem in representation theory. It has been solved for many particular groups, such as SL(2,R) and the Lorentz group.\n\n### Harmonic analysis\n\n{{#invoke:main|main}}\n\nThe duality between the circle group S1 and the integers Z, or more generally, between a torus Tn and Zn is well known in analysis as the theory of Fourier series, and the Fourier transform similarly expresses the fact that the space of characters on a real vector space is the dual vector space. Thus unitary representation theory and harmonic analysis are intimately related, and abstract harmonic analysis exploits this relationship, by developing the analysis of functions on locally compact topological groups and related spaces.\n\nA major goal is to provide a general form of the Fourier transform and the Plancherel theorem. This is done by constructing a measure on the unitary dual and an isomorphism between the regular representation of G on the space L2(G) of square integrable functions on G and its representation on the space of L2 functions on the unitary dual. Pontrjagin duality and the Peter–Weyl theorem achieve this for abelian and compact G respectively.\n\nAnother approach involves considering all unitary representations, not just the irreducible ones. These form a category, and Tannaka–Krein duality provides a way to recover a compact group from its category of unitary representations.\n\nIf the group is neither abelian nor compact, no general theory is known with an analogue of the Plancherel theorem or Fourier inversion, although Alexander Grothendieck extended Tannaka–Krein duality to a relationship between linear algebraic groups and tannakian categories.\n\nHarmonic analysis has also been extended from the analysis of functions on a group G to functions on homogeneous spaces for G. The theory is particularly well developed for symmetric spaces and provides a theory of automorphic forms (discussed below).\n\n### Lie groups\n\n{{#invoke:main|main}} Template:Lie groups\n\nA Lie group is a group that is also a smooth manifold. Many classical groups of matrices over the real or complex numbers are Lie groups. Many of the groups important in physics and chemistry are Lie groups, and their representation theory is crucial to the application of group theory in those fields.\n\nThe representation theory of Lie groups can be developed first by considering the compact groups, to which results of compact representation theory apply. This theory can be extended to finite-dimensional representations of semisimple Lie groups using Weyl's unitary trick: each semisimple real Lie group G has a complexification, which is a complex Lie group Gc, and this complex Lie group has a maximal compact subgroup K. The finite-dimensional representations of G closely correspond to those of K.\n\nA general Lie group is a semidirect product of a solvable Lie group and a semisimple Lie group (the Levi decomposition). The classification of representations of solvable Lie groups is intractable in general, but often easy in practical cases. Representations of semidirect products can then be analysed by means of general results called Mackey theory, which is a generalization of the methods used in Wigner's classification of representations of the Poincaré group.\n\n### Lie algebras\n\n{{#invoke:main|main}}\n\nA Lie algebra over a field F is a vector space over F equipped with a skew-symmetric bilinear operation called the Lie bracket, which satisfies the Jacobi identity. Lie algebras arise in particular as tangent spaces to Lie groups at the identity element, leading to their interpretation as \"infinitesimal symmetries\". An important approach to the representation theory of Lie groups is to study the corresponding representation theory of Lie algebras, but representations of Lie algebras also have an intrinsic interest.\n\nLie algebras, like Lie groups, have a Levi decomposition into semisimple and solvable parts, with the representation theory of solvable Lie algebras being intractable in general. In contrast, the finite-dimensional representations of semisimple Lie algebras are completely understood, after work of Élie Cartan. A representation of a semisimple Lie algebra g is analysed by choosing a Cartan subalgebra, which is essentially a generic maximal subalgebra h of g on which the Lie bracket is zero (\"abelian\"). The representation of g can be decomposed into weight spaces that are eigenspaces for the action of h and the infinitesimal analogue of characters. The structure of semisimple Lie algebras then reduces the analysis of representations to easily understood combinatorics of the possible weights that can occur.\n\n#### Infinite-dimensional Lie algebras\n\nThere are many classes of infinite-dimensional Lie algebras whose representations have been studied. Among these, an important class are the Kac–Moody algebras. They are named after Victor Kac and Robert Moody, who independently discovered them. These algebras form a generalization of finite-dimensional semisimple Lie algebras, and share many of their combinatorial properties. This means that they have a class of representations that can be understood in the same way as representations of semisimple Lie algebras.\n\nAffine Lie algebras are a special case of Kac–Moody algebras, which have particular importance in mathematics and theoretical physics, especially conformal field theory and the theory of exactly solvable models. Kac discovered an elegant proof of certain combinatorial identities, Macdonald identities, which is based on the representation theory of affine Kac–Moody algebras.\n\n#### Lie superalgebras\n\n{{#invoke:main|main}}\n\nLie superalgebras are generalizations of Lie algebras in which the underlying vector space has a Z2-grading, and skew-symmetry and Jacobi identity properties of the Lie bracket are modified by signs. Their representation theory is similar to the representation theory of Lie algebras.\n\n### Linear algebraic groups\n\nLinear algebraic groups (or more generally, affine group schemes) are analogues in algebraic geometry of Lie groups, but over more general fields than just R or C. In particular, over finite fields, they give rise to finite groups of Lie type. Although linear algebraic groups have a classification that is very similar to that of Lie groups, their representation theory is rather different (and much less well understood) and requires different techniques, since the Zariski topology is relatively weak, and techniques from analysis are no longer available.\n\n### Invariant theory\n\n{{#invoke:main|main}}\n\nInvariant theory studies actions on algebraic varieties from the point of view of their effect on functions, which form representations of the group. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. The modern approach analyses the decomposition of these representations into irreducibles.\n\nInvariant theory of infinite groups is inextricably linked with the development of linear algebra, especially, the theories of quadratic forms and determinants. Another subject with strong mutual influence is projective geometry, where invariant theory can be used to organize the subject, and during the 1960s, new life was breathed into the subject by David Mumford in the form of his geometric invariant theory.\n\nThe representation theory of semisimple Lie groups has its roots in invariant theory and the strong links between representation theory and algebraic geometry have many parallels in differential geometry, beginning with Felix Klein's Erlangen program and Élie Cartan's connections, which place groups and symmetry at the heart of geometry. Modern developments link representation theory and invariant theory to areas as diverse as holonomy, differential operators and the theory of several complex variables.\n\n### Automorphic forms and number theory\n\n{{#invoke:main|main}}\n\nAutomorphic forms are a generalization of modular forms to more general analytic functions, perhaps of several complex variables, with similar transformation properties. The generalization involves replacing the modular group PSL2 (R) and a chosen congruence subgroup by a semisimple Lie group G and a discrete subgroup Γ. Just as modular forms can be viewed as differential forms on a quotient of the upper half space H = PSL2 (R)/SO(2), automorphic forms can be viewed as differential forms (or similar objects) on Γ\\G/K, where K is (typically) a maximal compact subgroup of G. Some care is required, however, as the quotient typically has singularities. The quotient of a semisimple Lie group by a compact subgroup is a symmetric space and so the theory of automorphic forms is intimately related to harmonic analysis on symmetric spaces.\n\nBefore the development of the general theory, many important special cases were worked out in detail, including the Hilbert modular forms and Siegel modular forms. Important results in the theory include the Selberg trace formula and the realization by Robert Langlands that the Riemann-Roch theorem could be applied to calculate the dimension of the space of automorphic forms. The subsequent notion of \"automorphic representation\" has proved of great technical value for dealing with the case that G is an algebraic group, treated as an adelic algebraic group. As a result an entire philosophy, the Langlands program has developed around the relation between representation and number theoretic properties of automorphic forms.\n\n### Associative algebras\n\n{{#invoke:main|main}}\n\nIn one sense, associative algebra representations generalize both representations of groups and Lie algebras. A representation of a group induces a representation of a corresponding group ring or group algebra, while representations of a Lie algebra correspond bijectively to representations of its universal enveloping algebra. However, the representation theory of general associative algebras does not have all of the nice properties of the representation theory of groups and Lie algebras.\n\n#### Module theory\n\n{{#invoke:main|main}}\n\nWhen considering representations of an associative algebra, one can forget the underlying field, and simply regard the associative algebra as a ring, and its representations as modules. This approach is surprisingly fruitful: many results in representation theory can be interpreted as special cases of results about modules over a ring.\n\n#### Hopf algebras and quantum groups\n\n{{#invoke:main|main}}\n\nHopf algebras provide a way to improve the representation theory of associative algebras, while retaining the representation theory of groups and Lie algebras as special cases. In particular, the tensor product of two representations is a representation, as is the dual vector space.\n\nThe Hopf algebras associated to groups have a commutative algebra structure, and so general Hopf algebras are known as quantum groups, although this term is often restricted to certain Hopf algebras arising as deformations of groups or their universal enveloping algebras. The representation theory of quantum groups has added surprising insights to the representation theory of Lie groups and Lie algebras, for instance through the crystal basis of Kashiwara.\n\n## Generalizations\n\n### Set-theoretic representations\n\n{{#invoke:main|main}}\n\nA set-theoretic representation (also known as a group action or permutation representation) of a group G on a set X is given by a function ρ from G to XX, the set of functions from X to X, such that for all g1, g2 in G and all x in X:\n\n$\\rho (1)[x]=x$", null, "$\\rho (g_{1}g_{2})[x]=\\rho (g_{1})[\\rho (g_{2})[x]].$", null, "This condition and the axioms for a group imply that ρ(g) is a bijection (or permutation) for all g in G. Thus we may equivalently define a permutation representation to be a group homomorphism from G to the symmetric group SX of X.\n\n### Representations in other categories\n\nEvery group G can be viewed as a category with a single object; morphisms in this category are just the elements of G. Given an arbitrary category C, a representation of G in C is a functor from G to C. Such a functor selects an object X in C and a group homomorphism from G to Aut(X), the automorphism group of X.\n\nIn the case where C is VectF, the category of vector spaces over a field F, this definition is equivalent to a linear representation. Likewise, a set-theoretic representation is just a representation of G in the category of sets.\n\nFor another example consider the category of topological spaces, Top. Representations in Top are homomorphisms from G to the homeomorphism group of a topological space X.\n\nTwo types of representations closely related to linear representations are:" ]
[ null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/554f7968d420a977d216144fe674bcf49762d6ea", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/fdfd9ef74ab87ba0d72dcec39ad511d9ed994f91", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/11e48cda002a00961b415a63af5ad805818e84f3", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/1c48782a2a4cf8f742afcbd57ff8e8e6d4c14948", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f161cc2d8891fa83e92614158722dd4713c0bdba", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/8987415b7a9cf22d44f2d0e4c3f4fe3947acfa8c", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/c4c7dd9baac24b5d6f52fa609268cbb5d2041f74", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc5d540c4ff3112042ae8ee7cf4af6cc892bec8", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/ef925aec3bf01f6dc03edfd67350cc0cde7f98fb", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/102e42fa4a3b751894462bdb1e945c1c93f059da", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7d5bfe5bcaaa1d69fe751f8d17cbd85697355a91", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/2a5bad9608c98c03b423fa3a618b5a04c9ce5a39", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9a50080b735975d8001c9552ac2134b49ad534c0", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/5647fc6115ed105c0d45268819e9e9045ceea974", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/120857e96706f618d4b481e02c9ace79e8a12a0f", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/debb023e3f5e4ff703726b78494d7cc8acad5391", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87891185,"math_prob":0.9468753,"size":36031,"snap":"2019-26-2019-30","text_gpt3_token_len":7982,"char_repetition_ratio":0.23218697,"word_repetition_ratio":0.06001864,"special_character_ratio":0.20132664,"punctuation_ratio":0.113803,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9902451,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"im_url_duplicate_count":[null,10,null,4,null,10,null,10,null,10,null,2,null,10,null,4,null,10,null,10,null,4,null,10,null,null,null,10,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-22T05:44:38Z\",\"WARC-Record-ID\":\"<urn:uuid:7ab2c373-9568-484e-9699-3e576d2bbfdd>\",\"Content-Length\":\"134122\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de09d53e-b87b-42b8-b408-e8454fb2988d>\",\"WARC-Concurrent-To\":\"<urn:uuid:59aaa019-5f1f-4109-8465-e89f56b2e63c>\",\"WARC-IP-Address\":\"132.195.228.228\",\"WARC-Target-URI\":\"https://formulasearchengine.com/wiki/Representation_theory\",\"WARC-Payload-Digest\":\"sha1:KMRK5B6VV46NYGSFXXCBQ77CYZTLUTOJ\",\"WARC-Block-Digest\":\"sha1:4GD7EM5HOCLZUYFRFD7GIBUTRODRQUBX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195527531.84_warc_CC-MAIN-20190722051628-20190722073628-00036.warc.gz\"}"}
https://www.dataunitconverter.com/exabyte-to-petabit
[ "# EB to Pbit Calculator - Convert Exabytes to Petabits", null, "## Conversion History (Last 6)\n\nInput Exabyte - and press Enter\nEB\n\n## EB to Pbit - Conversion Formula and Steps\n\nExabyte and Petabit are units of digital information used to measure storage capacity and data transfer rate. Both are decimal units. One Exabyte is equal to 1000^6 bytes. One Petabit is equal to 1000^5 bits. There are 0.000125 Exabytes in one Petabit. - view the difference between both units", null, "Source Data UnitTarget Data Unit\nExabyte (EB)\nEqual to 1000^6 bytes\n(Decimal Unit)\nPetabit (Pbit)\nEqual to 1000^5 bits\n(Decimal Unit)\n\nThe formula of converting the Exabyte to Petabit is represented as follows :\n\nPbit = EB x (8x1000)\n\nBelow conversion diagram will help you to visualize the Exabyte to Petabit calculation steps in a simplified manner.\n\n÷ 8\n÷ 1000\nPetabit [Pbit]\nPetabyte [PB]\nExabyte [EB]\nx 8\nx 1000\n\nNow let us apply the above formula and, write down the steps to convert from Exabyte (EB) to Petabit (Pbit).\n\n1. STEP 1 → Petabit = Exabyte x (8x1000)\n2. STEP 2 → Petabit = Exabyte x 8000\n\nExample : If we apply the above steps, conversion from 10 EB to Pbit, will be processed as below.\n\n1. = 10 x (8x1000)\n2. = 10 x 8000\n3. = 80000\n4. i.e. 10 EB is equal to 80,000 Pbit.\n\n(Result rounded off to 40 decimal positions.)\n\nYou can use above formula and steps to convert Exabyte to Petabit using any of the programming language such as Java, Python or Powershell.\n\n#### Definition : Exabyte\n\nAn Exabyte (EB) is a unit of measurement for digital information storage. It is equal to 1,000,000,000,000,000,000 (one quintillion) bytes, It is commonly used to measure the storage capacity of large data centers, computer hard drives, flash drives, and other digital storage devices.\n\n#### Definition : Petabit\n\nA Petabit (Pb or Pbit) is a unit of measurement for digital information transfer rate. It is equal to 1,000,000,000,000,000 (one quadrillion) bits. It is commonly used to measure the speed of data transfer over computer networks, such as internet connection speeds.\n\n### Excel Formula to convert from EB to Pbit\n\nApply the formula as shown below to convert from Exabyte to Petabit.\n\nABC\n1Exabyte (EB)Petabit (Pbit)\n21=A2 * 8000\n3" ]
[ null, "https://www.dataunitconverter.com/images/certificate_precise.png", null, "https://www.dataunitconverter.com/showimage.php/Exabyte_to_Petabit_Dataunitconverter.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.79457986,"math_prob":0.99199146,"size":2646,"snap":"2023-14-2023-23","text_gpt3_token_len":703,"char_repetition_ratio":0.16010597,"word_repetition_ratio":0.03524229,"special_character_ratio":0.27135298,"punctuation_ratio":0.11045365,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9975213,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-21T11:30:08Z\",\"WARC-Record-ID\":\"<urn:uuid:27b0fc25-6d4a-490d-85c7-d904efb937e1>\",\"Content-Length\":\"65824\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54efcf49-0784-4fec-b7ae-c85972c1ce88>\",\"WARC-Concurrent-To\":\"<urn:uuid:e34c5ee5-7653-40e5-8314-73d2b87141d1>\",\"WARC-IP-Address\":\"64.227.22.174\",\"WARC-Target-URI\":\"https://www.dataunitconverter.com/exabyte-to-petabit\",\"WARC-Payload-Digest\":\"sha1:U6ROQG3KVFNJN6NQTY7GHW25J2ICR7TT\",\"WARC-Block-Digest\":\"sha1:2PR3LR7TFCDKU2ENKEWCQGXDUBMWR5FF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296943695.23_warc_CC-MAIN-20230321095704-20230321125704-00513.warc.gz\"}"}
https://www.geeksforgeeks.org/atomiclong-doublevalue-method-in-java-with-examples/?ref=rp
[ "Related Articles\nAtomicLong doubleValue() method in Java with examples\n• Last Updated : 29 Jan, 2019\n\nThe Java.util.concurrent.atomic.AtomicLong.doubleValue() is an inbuilt method in java which returns the current value of the AtomicLong as a Double data-type after performing primitive conversion.\n\nSyntax:\n\n```public double doubleValue()\n```\n\nParameters: The function does not accepts any parameter.\n\nReturn value: The function returns the numeric value represented by this object after conversion to type double.\n\nBelow programs illustrate the above method:\n\nProgram 1:\n\n `// Java program that demonstrates``// the doubleValue() function`` ` `import` `java.util.concurrent.atomic.AtomicLong;`` ` `public` `class` `GFG {``    ``public` `static` `void` `main(String args[])``    ``{`` ` `        ``// Initially value as 0``        ``AtomicLong val = ``new` `AtomicLong(``0``);`` ` `        ``val.addAndGet(``7``);`` ` `        ``// Prints the updated value``        ``System.out.println(``\"Previous value: \"``                           ``+ val);`` ` `        ``// Gets the double value``        ``double` `res = val.doubleValue();`` ` `        ``System.out.println(``\"Double value: \"``                           ``+ res);``    ``}``}`\nOutput:\n```Previous value: 7\nDouble value: 7.0\n```\n\nProgram 2:\n\n `// Java program that demonstrates``// the doubleValue() function`` ` `import` `java.util.concurrent.atomic.AtomicLong;`` ` `public` `class` `GFG {``    ``public` `static` `void` `main(String args[])``    ``{`` ` `        ``// Initially value as 18``        ``AtomicLong val = ``new` `AtomicLong(``18``);`` ` `        ``val.addAndGet(``7``);`` ` `        ``// Gets the double value``        ``System.out.println(``\"Previous value: \"``                           ``+ val);`` ` `        ``// Decreases the value by 1``        ``double` `res = val.doubleValue();`` ` `        ``System.out.println(``\"Double value: \"``                           ``+ res);``    ``}``}`\nOutput:\n```Previous value: 25\nDouble value: 25.0\n```\n\nAttention reader! Don’t stop learning now. Get hold of all the important Java Foundation and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.\n\nMy Personal Notes arrow_drop_up" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.65971446,"math_prob":0.6250629,"size":1881,"snap":"2021-04-2021-17","text_gpt3_token_len":430,"char_repetition_ratio":0.14864145,"word_repetition_ratio":0.296875,"special_character_ratio":0.23444976,"punctuation_ratio":0.19526628,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97416836,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-11T02:19:19Z\",\"WARC-Record-ID\":\"<urn:uuid:035dfb11-0add-4b35-ab91-44f1939fafdd>\",\"Content-Length\":\"90769\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6e55a8c9-529e-48f5-b96f-a35fc1dc6c9d>\",\"WARC-Concurrent-To\":\"<urn:uuid:091e8b8a-d4ed-4cf9-9348-f0e72f09981a>\",\"WARC-IP-Address\":\"23.12.145.47\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/atomiclong-doublevalue-method-in-java-with-examples/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:LGTFLH63756CXKSBLCBBDAYLD2D4U625\",\"WARC-Block-Digest\":\"sha1:AKPGHJKCXOHXHLKA7ZFVTANVZFFIPYMC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038060603.10_warc_CC-MAIN-20210411000036-20210411030036-00001.warc.gz\"}"}
https://codegolf.stackexchange.com/questions/6443/pythagorean-triplets
[ "# Pythagorean Triplets\n\nThe Pythagorean Theorem states that for a right triangle with sides a, b, and c, a2+b2=c2.\n\nA Pythagorean triplet is a set of three numbers, where a2+b2=c2, a To extend this even further, a primitive Pythagorean triplet is a Pythagorean triplet where gcd(a,b,c)=1.\n\nThe goal is to find 100 primitive Pythagorean triplets.\n\nInput: No input.\n\nOutput: 100 primitive Pythagorean triplets, in whatever order and shape, as long as the output contains only those triplets.\n\nShortest code wins. Good luck!\n\n• Is a < b or are (a,b,c) and (b,c,a) 2 solutions. – user unknown Jun 22 '12 at 23:44\n• @user unknown: a<b<c – beary605 Jun 23 '12 at 0:49\n• They're called \"triples\", not \"triplets\". – mbomb007 Oct 28 '16 at 15:04\n\n## Python, 42\n\ni=4\nwhile i<203:print 2*i,i*i-1,i*i+1;i+=2\n\n• i**2 -> i*i to save a couple of characters. – breadbox Jun 23 '12 at 3:17\n• I should mark this as cheating, but oh well. :) – beary605 Jun 23 '12 at 16:00\n• How is it cheating? – grc Jun 24 '12 at 1:09\n• \"hoping for brute force\" -- there's something you don't hear every day. – breadbox Jun 25 '12 at 16:14\n• @beary605 why have you accepted the answer that isn't the shortest? – Griffin Jun 27 '12 at 15:35\n\n# Javascript, 44 characters\n\nUpdate:\n\nfor(i=s=0;i^400;)s+=[i+=4,r=i*i/4-1,r+2]+' '\n\n\nI should have looked up an algorithm first. Well, can't beat python anyway.\n\nRun in a console to see the result.\n\nOld, slow, brute-force variant (140 characters)\n\nfor(q=a=[];563>++a;)for(b=a;--b;)(k=Math.sqrt(a*a+b*b))==~~k==function c(e,d,f){return f?c(c(f,e),d):d?c(d,e%d):e}(a,b,k)&&q.push([b,a,k]);q\n\n\n## J, 646038 49 characters\n\n100$}.~.(/:~*(0<*/*1=+./))\"1[4$.$.(=/+/~)2^~i.699 Should've realised that such a big gain was probably flawed. Still uses the brute-force method, but done a bit more efficiently. Explanation: x=.2^~i.699 generates a list of ints from 0 to 699 and squares 2^~ them (~ here reverses the order of the arguments). (=+/~) is a hook that generates an addition table and compares the result to the list. This gives me a three dimensional array with items which are either 1 or 0. A 1 means that a2+b2=c2. $. converts to a sparse array. For my smaller (9) example I get:\n\n $.(=/+/~)2^~i.9 0 0 0 | 1 1 0 1 | 1 1 1 0 | 1 2 0 2 | 1 2 2 0 | 1 3 0 3 | 1 3 3 0 | 1 4 0 4 | 1 4 4 0 | 1 5 0 5 | 1 5 3 4 | 1 5 4 3 | 1 5 5 0 | 1 6 0 6 | 1 6 6 0 | 1 7 0 7 | 1 7 7 0 | 1 8 0 8 | 1 8 8 0 | 1 4$. just gives me the left part of this list.\n\n(/:~*(0<*/*1=+./))\"1[ decides which rows meet the criteria. (verb)\"1 tells the verb to act on the individual rows rather than on the list. [ just separates the 1 and 4, otherwise J will think that 1 4 is a list of 2 numbers. '1=+./' gets the GCD of the three numbers and checks if it's 1. */ multiplies each triple together (getting 0 if it contains a 0) and these two are multiplied together. 0< turns the result into a boolean. * multiplies this result by each triple which eliminates all triples which contain a 0 or have a GCD which is not 1. /:~ sorts each triple.\n\n~. selects the unique items from the list.\n\n}. removes the first item (0 0 0) from the list.\n\n100\\$ takes the first 100 items from the list.\n\nThe above is my answer to this question, but as a matter of interest I implemented grc's method, (27 characters):\n\n2(*,.<:@^~,.>:@^~)2*2+i.100\n\n\n### Scala 180:\n\ndef g(a:Int,b:Int):Int=if(a==b)a else\nif(a>b)g(a-b,b)else\ng(b,a)\nfor(c<-(5 to 629);\na<-(1 to c-2);\nb<-(a to c-1);\nif((a*a+b*b==c*c)&&g(c,g(a,b))==1)&&a<400)println(a+\" \"+b+\" \"+c)\n\n\nUngolfed:\n\ndef gcd (a: Int, b: Int) : Int = if (a == b)\na else\nif (a > b) gcd (a-b, b) else\ngcd (b, a)\n\ndef gcd (a: Int, b: Int, c:Int): Int = gcd (c, gcd (a, b))\n\ndef pythagorean (a: Int, b: Int, c: Int) = (a * a + b * b == c * c)\n\nfor (c <- (5 to 629);\na <- (1 to c-2);\nb <- (a to c-1);\nif (pythagorean (a, b, c) && gcd (a, b, c) == 1)) yield {\nprintln (a + \"² + \" + b + \"² = \" + c + \"² => \" + (a*a) + \" + \" + (b*b) + \" = \" + (c*c))\nc*c\n}\n\n\n## APL (31)\n\n↑{(2×⍵),(A-1),1+A←⍵×⍵}¨2+2×⍳100\n\n\nIt uses basically the same approach as the Python program.\n\n# MATLAB 29\n\ni=2:2:200;[2*i;i.*i-1;i.*i+1]\n\n\nMathematica 33\n\n{2#,#^2-1,#^2+1}&/@Range[4,203,2]\n\n\n# APL(NARS), 26 chars, 52 bytes\n\n{k(4×⍵),2+k←¯1+×⍨2×⍵}¨⍳100\n\n\ntest:\n\n a←{k(4×⍵),2+k←¯1+×⍨2×⍵}¨⍳100\n≢a\n100\n+/{(x y z)←⍵⋄(z*2)=(y*2)+x*2}¨a\n100\n+/{∨/⍵}¨a\n100\n10↑a\n3 4 5 15 8 17 35 12 37 63 16 65 99 20 101 143 24 145 195 28 197 255 32 257 323 36 325 399 40 401\n\n\n## R, 49 characters\n\ntranslated from the Python solution:\n\ni=4;while(i<203){print(c(2*i,i*i-1,i*i+1));i=i+2}\n\n• You should take advantage of the functional nature of R i=seq(2,200,2);c(2*i,i*i-1,i*i+1) (though the output is a bit messy). – Griffin Jun 26 '12 at 13:55\n• Ops! I posted without taking a look at all the other answers! :-P – Paolo Jun 26 '12 at 14:01" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.80684614,"math_prob":0.9876371,"size":1695,"snap":"2020-45-2020-50","text_gpt3_token_len":641,"char_repetition_ratio":0.11709048,"word_repetition_ratio":0.0,"special_character_ratio":0.4141593,"punctuation_ratio":0.12926829,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9952671,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-26T09:58:34Z\",\"WARC-Record-ID\":\"<urn:uuid:58bf43f4-c9c0-4b53-9e0a-11928acd9ef7>\",\"Content-Length\":\"231046\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:961a59b4-39af-4c7a-851a-c54d2d6f3cf3>\",\"WARC-Concurrent-To\":\"<urn:uuid:f4d27e52-be9d-4105-b96b-284b4e3b3bf8>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://codegolf.stackexchange.com/questions/6443/pythagorean-triplets\",\"WARC-Payload-Digest\":\"sha1:CY7JNFL3GHJ7HC5VZS43YTU2GE5NUULK\",\"WARC-Block-Digest\":\"sha1:KNLLRREGP52OCHJKN4T5FZXGPDZVP3FQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141187753.32_warc_CC-MAIN-20201126084625-20201126114625-00622.warc.gz\"}"}
https://scikit-image.org/docs/dev/auto_examples/transform/plot_register_rotation.html
[ "# Polar and Log-Polar Transformations¶\n\nRotation differences between two images can be converted to translation differences along the angular coordinate ($$\\theta$$) axis of the polar-transformed images. Scaling differences can be converted to translation differences along the radial coordinate ($$\\rho$$) axis if it is first log transformed (i.e., $$\\rho = \\ln\\sqrt{x^2 + y^2}$$). Thus, in this example, we use phase correlation (feature.register_translation) to recover rotation and scaling differences between two images that share a center point.\n\n## Recover rotation difference with a polar transform¶\n\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom skimage import data\nfrom skimage.feature import register_translation\nfrom skimage.transform import warp_polar, rotate\nfrom skimage.util import img_as_float\n\nangle = 35\nimage = data.retina()\nimage = img_as_float(image)\nrotated = rotate(image, angle)\n\nfig, axes = plt.subplots(2, 2, figsize=(8, 8))\nax = axes.ravel()\nax.set_title(\"Original\")\nax.imshow(image)\nax.set_title(\"Rotated\")\nax.imshow(rotated)\nax.set_title(\"Polar-Transformed Original\")\nax.imshow(image_polar)\nax.set_title(\"Polar-Transformed Rotated\")\nax.imshow(rotated_polar)\nplt.show()\n\nshifts, error, phasediff = register_translation(image_polar, rotated_polar)\nprint(\"Expected value for counterclockwise rotation in degrees: \"\nf\"{angle}\")\nprint(\"Recovered value for counterclockwise rotation: \"\nf\"{shifts}\")", null, "Out:\n\nExpected value for counterclockwise rotation in degrees: 35\nRecovered value for counterclockwise rotation: 35.0\n\n\n## Recover rotation and scaling differences with log-polar transform¶\n\nfrom skimage.transform import rescale\n\n# radius must be large enough to capture useful info in larger image\nangle = 53.7\nscale = 2.2\nimage = data.retina()\nimage = img_as_float(image)\nrotated = rotate(image, angle)\nrescaled = rescale(rotated, scale, multichannel=True)\nscaling='log', multichannel=True)\nscaling='log', multichannel=True)\n\nfig, axes = plt.subplots(2, 2, figsize=(8, 8))\nax = axes.ravel()\nax.set_title(\"Original\")\nax.imshow(image)\nax.set_title(\"Rotated and Rescaled\")\nax.imshow(rescaled)\nax.set_title(\"Log-Polar-Transformed Original\")\nax.imshow(image_polar)\nax.set_title(\"Log-Polar-Transformed Rotated and Rescaled\")\nax.imshow(rescaled_polar)\nplt.show()\n\n# setting upsample_factor can increase precision\ntparams = register_translation(image_polar, rescaled_polar, upsample_factor=20)\nshifts, error, phasediff = tparams\nshiftr, shiftc = shifts[:2]\n\n# Calculate scale factor from translation\nshift_scale = 1 / (np.exp(shiftc / klog))\n\nprint(f\"Expected value for cc rotation in degrees: {angle}\")\nprint(f\"Recovered value for cc rotation: {shiftr}\")\nprint()\nprint(f\"Expected value for scaling difference: {scale}\")\nprint(f\"Recovered value for scaling difference: {shift_scale}\")", null, "Out:\n\nExpected value for cc rotation in degrees: 53.7\nRecovered value for cc rotation: 53.75\n\nExpected value for scaling difference: 2.2\nRecovered value for scaling difference: 2.1981889915232165\n\n\nTotal running time of the script: ( 0 minutes 5.883 seconds)\n\nGallery generated by Sphinx-Gallery" ]
[ null, "https://scikit-image.org/docs/dev/_images/sphx_glr_plot_register_rotation_001.png", null, "https://scikit-image.org/docs/dev/_images/sphx_glr_plot_register_rotation_002.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.5656977,"math_prob":0.98788387,"size":3441,"snap":"2020-10-2020-16","text_gpt3_token_len":910,"char_repetition_ratio":0.14925808,"word_repetition_ratio":0.11948052,"special_character_ratio":0.2531241,"punctuation_ratio":0.16521738,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99592394,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-29T21:58:10Z\",\"WARC-Record-ID\":\"<urn:uuid:7fd71bac-2365-42fa-b91e-8c0f1d738eb5>\",\"Content-Length\":\"39659\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:699b60b7-3b79-4ce3-8c0e-1af743b44882>\",\"WARC-Concurrent-To\":\"<urn:uuid:f4419a6b-1443-4d03-b224-1fdd7f25373d>\",\"WARC-IP-Address\":\"185.199.110.153\",\"WARC-Target-URI\":\"https://scikit-image.org/docs/dev/auto_examples/transform/plot_register_rotation.html\",\"WARC-Payload-Digest\":\"sha1:DGVRXJIIBMXETJ62NAN5M6OJAI3WT3ZN\",\"WARC-Block-Digest\":\"sha1:BMZH5KQTWQU5GSOC6MPMSH3WL3LMGB6R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370496227.25_warc_CC-MAIN-20200329201741-20200329231741-00500.warc.gz\"}"}
https://www.esaral.com/q/mark-the-tick-against-the-correct-answer-in-the-following-76534
[ "", null, "# Mark the tick against the correct answer in the following:\n\nQuestion:\n\nMark the tick against the correct answer in the following:\n\nRange of $\\operatorname{coses}^{-1} \\times$ is\n\nA. $\\left(\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right)$\n\nB. $\\left[\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right]$\n\nC. $\\left[\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right]-\\{0\\}$\n\nD. None of these\n\nSolution:\n\nTo Find: The range of $\\operatorname{cosec}^{-1}(x)$\n\nHere,the inverse function is given by $y=\\mathrm{f}^{-1}(x)$\n\nThe graph of the function $y=\\operatorname{cosec}^{-1}(x)$ can be obtained from the graph of\n\n$Y=\\operatorname{cosec} x$ by interchanging $x$ and $y$ axes.i.e, if $(a, b)$ is a point on $Y=\\operatorname{cosec} x$ then $(b, a)$ is the point on the function $y=\\operatorname{cosec}^{-1}(x)$\n\nBelow is the Graph of the range of $\\operatorname{cosec}^{-1}(x)$", null, "From the graph it is clear that the range of $\\operatorname{cosec}^{-1}(x)$ is restricted to interval\n\n$\\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]-\\{0\\}$" ]
[ null, "https://www.facebook.com/tr", null, "https://www.esaral.com/media/uploads/2022/02/25/image68263.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.631105,"math_prob":0.99998677,"size":893,"snap":"2023-14-2023-23","text_gpt3_token_len":323,"char_repetition_ratio":0.1991001,"word_repetition_ratio":0.0,"special_character_ratio":0.36730123,"punctuation_ratio":0.08938547,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000075,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-06T19:51:05Z\",\"WARC-Record-ID\":\"<urn:uuid:1bd02ced-9b7b-4c7f-9f93-54f149171662>\",\"Content-Length\":\"25675\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76a06f34-de9d-4710-842c-4912905e9ecb>\",\"WARC-Concurrent-To\":\"<urn:uuid:62527b49-430c-4ef5-8950-3981947a765c>\",\"WARC-IP-Address\":\"172.67.213.11\",\"WARC-Target-URI\":\"https://www.esaral.com/q/mark-the-tick-against-the-correct-answer-in-the-following-76534\",\"WARC-Payload-Digest\":\"sha1:LLRKXUXW2S3J2QWYLEDX2UAFZSBCIIUH\",\"WARC-Block-Digest\":\"sha1:VNXHNUVAJU5UR4O6QH2C2SB2YXYJBHGO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224653071.58_warc_CC-MAIN-20230606182640-20230606212640-00478.warc.gz\"}"}
https://www.scec.org/publication/326
[ "## Discrete Scale Invariance, Complex Fractal Dimensions and log-periodic fluctuations in Seismicity\n\nHubert Saleur, Charles G. Sammis, & Didier Sornette\n\nPublished August 10, 1996, SCEC Contribution #326\n\nWe discuss in detail the concept of discrete scale invariance and show how it leads to complex critical exponents and hence to the log-periodic corrections to scaling exhibited by various measures of seismic activity close to a large earthquake singularity. Discrete scale invariance is first illustrated on a geometrical fractal, the Sierpinsky gasket, which is shown to be fully described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor. Then, a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of the different terms in the discrete renormalization group formalism introduced to tackle this problem. As a more specific example of rupture relevant for earthquakes, we propose a solution of the hierarchical time-dependent fiber bundle of Newman et al. which exhibits explicitly a discrete renormalization group from which log-periodic corrections follow. We end by pointing out that discrete scale invariance does not necessarily require an underlying geometrical hierarchical structure. A hierarchy may appear “spontaneously” from the physics and/or the dynamics in a Euclidean (nonhierarchical) heterogeneous system. We briefly discuss a simple dynamical model of such mechanism, in terms of a random walk (or diffusion) of the seismic energy in a random heterogeneous system.\n\nCitation\nSaleur, H., Sammis, C. G., & Sornette, D. (1996). Discrete Scale Invariance, Complex Fractal Dimensions and log-periodic fluctuations in Seismicity. Journal of Geophysical Research, 101(B8), 17661-17677. doi: 10.1029/96JB00876." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.82944095,"math_prob":0.8458644,"size":1922,"snap":"2020-45-2020-50","text_gpt3_token_len":428,"char_repetition_ratio":0.10583942,"word_repetition_ratio":0.043636363,"special_character_ratio":0.20343392,"punctuation_ratio":0.11598746,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96417236,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-21T22:15:41Z\",\"WARC-Record-ID\":\"<urn:uuid:70fbc9b1-1986-472e-9119-f95b8fcaf509>\",\"Content-Length\":\"19727\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:430a1ad1-1210-4927-b169-d5a7bc84d2a7>\",\"WARC-Concurrent-To\":\"<urn:uuid:8e34f046-2f79-4ca9-94da-f03943d865e3>\",\"WARC-IP-Address\":\"52.36.134.75\",\"WARC-Target-URI\":\"https://www.scec.org/publication/326\",\"WARC-Payload-Digest\":\"sha1:KQM7LUYTXVNOSG7DV2I676GSHI3KXKTU\",\"WARC-Block-Digest\":\"sha1:E7TQ4MG3DU7RPV4PCKAFYVJ7SYUTJDOP\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107878633.8_warc_CC-MAIN-20201021205955-20201021235955-00448.warc.gz\"}"}
https://admin.clutchprep.com/organic-chemistry/practice-problems/51125/a-mixture-of-a-pair-of-enantiomers-has-30-ee-the-observed-rotation-of-this-mixtu
[ "# Problem: A mixture of a pair of enantiomers has 30% ee. The observed rotation of this mixture is +15º, and it is known by experiment that the (‐)‐enantiomer has the (R) configuration. (enantiomer excess (ee) = % one enantiomer – % the other enantiomer)(a) Calculate the percentage of (R) and (S) enantiomers of the natural product.(b) What is the optical rotation of a mixture of 20% (S) and 80% (R).\n\n###### Problem Details\n\nA mixture of a pair of enantiomers has 30% ee. The observed rotation of this mixture is +15º, and it is known by experiment that the (‐)‐enantiomer has the (R) configuration. (enantiomer excess (ee) = % one enantiomer – % the other enantiomer)\n\n(a) Calculate the percentage of (R) and (S) enantiomers of the natural product.\n\n(b) What is the optical rotation of a mixture of 20% (S) and 80% (R)." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.912791,"math_prob":0.9464396,"size":1212,"snap":"2020-34-2020-40","text_gpt3_token_len":285,"char_repetition_ratio":0.14983444,"word_repetition_ratio":0.071794875,"special_character_ratio":0.21617162,"punctuation_ratio":0.093023255,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96153796,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-11T07:54:24Z\",\"WARC-Record-ID\":\"<urn:uuid:fb1996cf-3c3c-469c-8c71-7fac03dfbe86>\",\"Content-Length\":\"93013\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:213e1b07-6f48-4381-848b-1a8489a14a76>\",\"WARC-Concurrent-To\":\"<urn:uuid:05391362-90c0-4a1e-b200-9ab36ece66ab>\",\"WARC-IP-Address\":\"35.153.26.168\",\"WARC-Target-URI\":\"https://admin.clutchprep.com/organic-chemistry/practice-problems/51125/a-mixture-of-a-pair-of-enantiomers-has-30-ee-the-observed-rotation-of-this-mixtu\",\"WARC-Payload-Digest\":\"sha1:MIGRLXEEN63FQ2K2POXLRCBTDRY34VSI\",\"WARC-Block-Digest\":\"sha1:ZSXFJIM3HDMMEOPO4RHKHX6KQVQBLCCL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738735.44_warc_CC-MAIN-20200811055449-20200811085449-00314.warc.gz\"}"}
https://optovr.com/free-basic-pre-algebra-worksheets/
[ "# Free Basic Pre Algebra Worksheets\n\n-algebra printable -algebra worksheets practice makes perfect, prepare a stronger base for algebra with this assemblage of -algebra worksheets featuring exercises on topics like fractions, decimals, integers, measurement, squaring numbers, order of operations, estimation, factors,, , ratio, percent, exponents, radicals, scientific notations, logarithms, absolute value, graph and more.\n\nNeed great -algebra worksheets to help your students learn basic math concepts if so, then look no further. here is a perfect and comprehensive collection of free -algebra worksheets that would help you or your students in -algebra preparation and practice.\n\n## List of Free Basic Pre Algebra Worksheets\n\nDownload our free mathematics worksheets for the -algebra test. hope you enjoy. Free -algebra worksheets created with infinite -algebra. printable in convenient format. Algebra worksheets. these worksheets are printable exercises of the highest quality.\n\nwriting reinforces maths learnt. these worksheets contain -algebra algebra exercises suitable for preschool, kindergarten, first grade to graders levels. the following algebra topics are covered among others. Testimonial my son has had the opportunity to work with and she has helped him to continue to love and learn math.\n\n### 1. Image Result Grade Math Worksheets Linear Equations Free Printable Algebra Test Train Problem Standards Lessons Basic Pre", null, "We have lots of -algebra and algebra worksheets on a variety of topics. worksheets include evaluating expressions, solving one-step equations, solving two-step equations, dependent and independent variables, and inequalities. evaluating expressions. this page has many worksheets and task cards on evaluating algebraic expressions.\n\n### 2. Solving Basic Equations Worksheets Free Pre Algebra", null, "Commonly used for weights and measures, especially for small measurements in cooking and carpentry. if you want to be proficient in basic math, and if you want to prepare for -algebra, you need to know the ins and outs of fractions. Bored with -algebra homeschooling -algebra confused by -algebra hate -algebra we can help.\n\n### 3. Grade Math Algebra Music Worksheets Free Coloring Pages Addition Drill Typing Games Simple Sign Integers Std Holiday Basic Pre", null, "Input output table worksheets for basic operations. algebra worksheets. converting ounces, tablespoons, and teaspoons. measurement worksheets gallons, quarts, pints and cups. Saxon algebra math lessons, program great common divisor, basic seventh grade math worksheets,, free algebra test, chapter -algebra.\n\n### 4. 3 Multiplication Worksheets Grade Math Test Operations Integers Basic Arithmetic Questions Rules Addition Subtraction Calculator Ideas Free Pre Algebra", null, "Every worksheet contains different assignments. to open and print the worksheets you will need to have a adobe acrobat reader installed. -algebra worksheets algebraic expressions worksheets. here is a graphic preview for all of the algebraic expressions worksheets.\n\nyou can select different variables to customize these algebraic expressions worksheets for your needs. Download free -algebra variable expressions equations worksheets below all worksheets are free to download and use for practice or in your classroom.\n\n### 5. Independent Living Skills Worksheets Life Lessons Free Printable Algebra Worksheet Grade Division Problems Basic Geometry 2 Mm Square Graph Paper Math Calculator Pre", null, "Learn -algebra for of the basic arithmetic and geometry skills needed for algebra. full curriculum of exercises and videos. This -algebra textbook (or ) is different from other math texts you have previously used in school where you were taught by a classroom teacher.", null, "Com. this math worksheet was created on -- and has been viewed, times this week and, times this month. it may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. Use our printable grade worksheets in your classroom as part of your lesson plan or hand them out as homework.\n\n### 7. Printable Algebra Worksheet Math Skills Practice Sheet Free Worksheets Word Problems Numbers Operations Grade Subtraction Adding Basic Pre", null, "On this page you find our -algebra, or introduction to algebra worksheets for grade (or ) math students. we have writing algebraic expressions worksheets, rewriting basic algebraic expression worksheets, using algebraic letters worksheets, solving basic algebraic expressions worksheets, worksheets with monomials, basic algebraic operation worksheets, evaluating and simplifying basic.\n\n### 8. Math Worksheets Grade Algebra Free Word Problems Multiplication High School Activity Sheets 4 Basic Pre", null, "If you would rather print the tests instead of taking them, then check out the following links. These algebra equations worksheets will produce distance, rate, and time word problems with ten problems per worksheet. you may select the numbers to be represented with digits or in words.\n\n### 9. Math References Teacher Algebra Worksheets Graders Unit Free Year 1 Player Games Grade Puzzles 3 Basic Pre", null, "Students, teachers, parents, and everyone can find solutions to their math problems instantly. Home kindergarten elementary middle school -algebra algebra geometry math worksheets free math worksheets. on this page you can find links to free math worksheets that are correlated to the tests found on this website.", null, "Our grade math worksheets cover topics from -algebra, algebra, and more. On these printable worksheets, students will evaluate basic algebraic expressions with variables. these worksheets align with common core standard. Our topics in -algebra worksheets are designed to supplement our topics in -algebra lessons.\n\n### 11. Grade Algebra Worksheets Math Free Basic Multiplication Games Play Worksheet Activities School Age Printable Sheets Pre", null, "The algebra course, often taught in the grade, covers linear equations, inequalities, functions, and graphs systems of equations and inequalities extension of the concept of a function exponential models and quadratic equations, functions, and graphs.\n\nkhan algebra course is built to deliver a comprehensive, illuminating, engaging, and common core aligned experience. Find worksheets about -algebra. worksheetworks.com is an resource used every day by thousands of teachers, students and parents. -algebra math review worksheets.\n\n### 12. Worksheet Math Worksheets Fore Photo 7 Algebra Grade Free 9 Inspirations Basic Pre", null, "Worksheet title select number of each type of equations one-step equations (e.g. x-) two-step equations (e.g. x) combining like terms on both sides distributive property. systems - solve for x and y. solve by adding solve by subtracting a mix of the above two require one multiplication step general system.\n\n### 13. Free Algebra Worksheets Answers Calculus Grade Math Drills Activities Base Mixed Addition Subtraction Multiplication Division Basic Pre", null, "There are a lot of questions that kids can solve that involve unknowns. These cool math worksheets will be for all grade in the k curriculum. most demanded grades math worksheets with answers all for kids will be provided. also gain access to free algebra worksheets with answers for early beginners including algebra practice problems worksheets, algebra word problems worksheets with answers.\n\nDadsworksheets.com - thousands of free math worksheets this site has over, different math worksheets from kindergarten to -algebra and growing. math maze generate a maze that practices any of the four operations. you can choose the difficulty level and size of maze.\n\n### 14. Factoring Quadratic Expressions Grade Algebra Worksheets Work Math Problems Addition Printable 9 Quiz Generator Free Activities Preschoolers Coloring Number Basic Pre", null, "Easy multiplication -algebra problems only positive results. -algebra diagnostic -test questions minutes multiple choice use the answer (which stands for none of the above) if the answer is not listed. which of the following is a factor of a) b) c) d) e).\n\nif n, then n a) b) c) d) e). Free algebra worksheets downloads, algebra worksheets, algebra worksheets grade, algebra worksheets grade, algebra worksheets grade, grade algebra worksheets, rd,, , , , grades. solving of equations that involves one unknown is known as algebra.\n\n### 15. Algebra Word Problems Algebraic Applications Worksheets Grade Math Addition Mathematics Practice Book Graph Paper Axis Free Division Table Printable Basic Pre", null, "Integer worksheets. worksheets about adding, subtracting, and multiplying integers. distributive property worksheet. worksheet about using the distributive property. greatest common factor worksheet. Easing into algebra is easier than you think, and simple word problems that correspond to basic algebra is one way to introduce and grade students to this topic area.\n\nthe worksheets in this section are broken into -algebra problems by operation, and have the basic find the missing number form. - algebra is mostly taught in the and grade. basic algebra worksheets if you are struggling with -algebra, let me tell you the key to master it.\n\n### 16. Algebra Word Problems Grade Math Worksheets Mixed Easy Large Addition General Learning Activities Mathematics Multiplication Question Generator Adding Free Basic Pre", null, "You need to practice a lot of questions, ranging from easy to hard problems. in the basic algebra worksheets here, you will get ample practice problems to work on and improve your skills. Free algebra worksheets created with infinite algebra. printable in convenient format.\n\n-algebra and algebra worksheets. on this page find a variety of -algebra and algebra. includes activities related to variables, expressions, equations, and inequalities. these are very basic inequality worksheets. students do not need to use any steps to isolate the variable.\n\n### 17. Algebra Worksheet Answers Resource Math Worksheets Adding Grade Summer Word Problems Dynamic Tutor Free Basic Pre", null, "They simply practice graphing the. Algebra worksheets for children -. - algebra and algebra worksheets for children in rd,, , and grades. these worksheets cover topics in algebra, algebra and algebra. click to print algebra worksheets below. algebra worksheets algebra.\n\nDownload the free basic algebra worksheet and print to give class assignment to your students or share the resources with parents of kids so that they can give worksheet to kid at home. after all these basic algebra worksheets will be done, kid will be master in basic algebra and will be ready to move to next level of algebra i.\n\n### 18. Algebra Multiple Choice Free Printable Math Equation Worksheets Fun Games Brain Teaser Puzzles Answers Rules Number Quiz Generator Grade 9 Basic Pre", null, "Plus each one comes with an answer key. algebra distance formula equation of circle factoring. factor worksheet functions and relations. domain and range linear equations. Looking for free -algebra resources tutor-usa offers free -algebra worksheets and for use by math teachers, students, and parents.\n\nmany of our -algebra worksheets contain an answer key and can be downloaded or printed, making them great for -algebra homework, classwork, or extra math practice. A variety of algebra worksheets that teachers can print and give to students as homework or classwork.\n\n### 19. Algebra Archives Den Free Basic Pre Worksheets", null, "All we ask is that you remove the logo. click on for answers. Free printable -algebra worksheets - also available there are a number of free -algebra worksheets for you to download, print, or solve. the worksheets cover division, equations, integers, order operations, variable expressions, and variables.\n\nAlgebra worksheets by specific topic area and level we have over free algebra worksheets to print. our algebra resources in this area are solid. we offer a wide variety of algebra formats and types. beginner and introduction level. these problems are a great starting pointing.\n\n### 20. Single Variable Equation Worksheet Worksheets Free Basic Pre Algebra", null, "Download printable algebra worksheets for algebra, algebra, -algebra, elementary algebra, and intermediate algebra. you can also complete the free algebra worksheets. an algebra solver resource to practice. Basic math tips fractions. fractions are a common way of describing parts of a whole.\n\n### 21. Worksheets Free Algebra Grade Answers Kindergarten Themes Solve Calculator Print 1 Grid Paper Funny Mathematics Tricks Geometry Problems Basic Pre", null, "Free algebra worksheets for teachers, parents, and kids. easily download and print our algebra worksheets. click on the free algebra worksheet you would like to print or download. this will take you to the individual page of the worksheet. you will then have two choices.\n\n### 22. Algebra Free Math Papers Printable Activities Worksheets Nation Skills Children Coloring Pages Toilet Paper Roll Crafts Basic Pre", null, "Tough algebra word problems. if you can solve these problems with no help, you must be a genius. Welcome to the algebra worksheets page at math-drills.com, where unknowns are common and variables are the norm. on this page, you will find algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions.\n\nthis page starts off with some missing numbers worksheets for younger students. Factors - prime algebra- worksheets and games. to link to this page, copy the following code to your site. Enjoy these free sheets. each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end.\n\n### 23. Math Algebra Archives Den Free Basic Pre Worksheets", null, "Sign up for our free newsletter by signing up, you agree to receive useful information and to our privacy policy. sign up for our free newsletter e-mail address create new worksheet. Free math lessons and math homework help from basic math to algebra, geometry and beyond.\n\n### 24. Basic Algebra Marker Coloring Simple Worksheets Writing Letters Pictures Hard Math Problems Free Printable Puzzles 1 Integers Grade 8 Pre", null, "E. system of equations. Algebra is a branch of math in which letters and symbols are used to represent numbers and quantities in formulas and equations. the assemblage of printable algebra worksheets encompasses topics like translating phrases, evaluating and simplifying algebraic expressions, solving equations, graphing linear and quadratic equations, comprehending linear and quadratic functions, inequalities.\n\nFree math worksheets for grade. this is a comprehensive collection of free printable math worksheets for grade and for -algebra, organized by topics such as expressions, integers, one-step equations, rational numbers, multi-step equations, inequalities, speed, time distance, graphing, slope, ratios, proportions, percent, geometry, and pi.\n\n### 25. Free Math Worksheets Printouts Algebra Graders Worksheet Distance Formula Fun Negative Number Grade Basic Pre", null, "-algebra and algebra. when you find yourself stuck with too many variables, use these explanations and tutorials to help you simplify. learn all the major algebraic properties and find plenty of example problems. Free algebra worksheets for teachers, parents, and kids.\n\neasily download and print our algebra worksheets. click on the free algebra worksheet you would like to print or download. this will take you to the individual page of the worksheet. you will then have two choices. There are a few basic skills that you must master before diving into the heart of algebra.\n\n### 26. Free Math Worksheets Grade Subtraction Single Digit Reading Basic Adding Algebra Problems Sum Code Worksheet Answers Teacher Sites Pre", null, "Algebra worksheets printable. these worksheets are printable exercises of the highest quality. writing reinforces maths learnt. these math worksheets for children contain -algebra algebra exercises suitable for preschool, kindergarten, first grade to eight graders, free worksheets, grade math worksheets.\n\nthe following algebra topics are covered among others. Free algebra worksheets algebra worksheets for multiplication equations, one step equations, subtraction equations, addition equations, addition and subtraction equations, two step equations. algebra work sheets generator name to appear on title rows columns font type algebra.\n\n### 27. Free Math Worksheets Grade Algebra Middle School Lesson Plans Multiplication Flash Games Children Solving Graphing Linear Equations Calculator Grid Paper Basic Pre", null, "Awareness of -algebra concepts use hands on equations materials. algebra worksheets create worksheet of simple algebra. lessons with algebraic equations learning to convert story problems to equations. greater than, less than bingo. handbook table of contents outlines algebra, by , , wade , and.\n\nalgebra, by , wade , , and. geometry, by , , and lee stiff although a significant effort was made to make the material in this study guide original, some. Get your kids ready for their middle school math adventure with our fifth grade algebra and functions worksheets and start by using your students multiplication skills to introduce basic algebraic concepts like solving for variables in one- and two-step equations.\n\n### 28. Free Algebra Worksheets Answers Math Multiplying Decimals Common Core Year 3 Sheets 2 Printable Flash Cards Games Fractions Basic Mathematics Pre", null, "Quickies worksheets. Maria millers -algebra worksheets with answers math mammoth books my favorite p re algebra worksheets with answers are maria millers math mammoth downloads. she has done a superior job of gathering together a wonderful math curriculum that you can either download or buy as a hard bound book.\n\n-algebra -algebra practice questions comparing fraction cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. -algebra lessons, worksheets, and resources.\n\n### 29. Quiz Worksheet Solving Absolute Equations Study Free Math Worksheets Expression Everyday Mathematics Program Basic Riddles Geometric Properties Easy Grade Problems Pre Algebra", null, "So today i want to share a list of free -algebra lessons and resources that will hopefully help your kids make sense of these challenging concepts please note this post includes affiliate links which help support the work of this site. read our full disclosure policy here.\n\n### 30. Grade Test Worksheet Revision Worksheets Math Quiz Printable 8 Learning Addition Practice Workbook 6 Teacher Edition Counting Free Basic Pre Algebra", null, "Free maths sums for class, do you have any free help with algebra problems, grade math text book, fractions to percent worksheet, factoring equations solver. Missing numbers worksheet -, large numbers worksheet, ordering numbers worksheet -, writing numbers worksheet, spelling numbers worksheet -, numbers worksheet mes, after numbers worksheet -, ordinal numbers worksheet elementary, numbers - worksheet, ordinal numbers worksheet early years, numbers -.\n\n### 31. Coloring Activities Algebra Worksheets Millimeter Paper Print Coin Grade Free Money Management Adding Fractions Kids Telling Time Year 3 Basic Pre", null, "Algebra worksheets free - basic worksheets - solve for x - basic algebra practice. radical expressions - questions with solutions for grade. similar images for variables math worksheets grade algebra. newspaper-print-curtains-india. Use the equations worksheet generator to create a limitless supply of linear equations for solving.\n\nalternatively, select from the list of -made worksheets below. simple linear equations. the worksheets below provide a gradual introduction that can help students learn how to solve equations that include letters. e.g. x. -algebra basic geometry telling analog time analog elapsed time greater than and less than money linear equations measurement conversions these -algebra worksheets require students solve for the missing multiplicand in a number sentence.\n\n### 32. Worksheet Free Basic Math Worksheets Grade Skills Algebra Writing Equations Solve Mathematics Home Problem Solver Rounding Money Pre", null, "-algebra has a ton of really easy to follow lessons and examples. -algebra worksheets. the free -algebra printable worksheets are oriented toward understanding patterns, relations, and functions representing and analyzing algebraic expressions, using number types like decimals, integers, fractions, comprehending ratios, proportions and more.\n\n### 33. Simple Algebra Worksheet Templates Word Free Premium Basic Pre Worksheets", null, "Helpful -algebra lessons and resources. Th grade algebra practice test - displaying top worksheets found for this concept. some of the worksheets for this concept are algebra diagnostic test questions minutes, grade mathematics practice test, grade algebra summer packet, parent and student study guide workbook, grade algebra end of the year test, algebra diagnostic test questions minutes.\n\n### 34. Grade Algebra Worksheets Math Multiplication Division Games Graders Fun Congruence 8 Mathematics Syllabus Free Basic Pre", null, "Free educational resources. helping teachers get the best resources for the classroom. always free. outstanding teachers deserve the best. join free outstanding teachers and get additional spelling tools and more feedback or contact us. These types of -algebra number problem worksheets help students develop algebraic thinking at the early stages.\n\n### 35. Algebra Calculator Free Math Worksheets Schoolers Anger Management Therapy Printable Logic Puzzles Kids Drills Fraction Site Simple Numeracy Test Basic Pre", null, "We work on like terms and learning that their are two sides to an. algebra is the first math course in high school and will guide you through among other things integers, one-step equations, inequalities and equations, graphs and functions, percent, probabilities.\n\nwe also present an introduction to geometry and right triangles. in algebra you will for example study review of natural number arithmetic new types of numbers such as integers. K- tests, math test, basic math tests, geometry tests, algebra tests.\n\n### 36. Free Printable Math Worksheets Kindergarten Grade Trigonometry Module Summer Multiplication Facts Book Algebra Fun Basic Pre", null, "Most of these skills you learned in your -algebra course, but ill review them here. if not sure if you need to review the basic skills, take the algebra readiness test. This free algebra worksheet contains problems on slope-intercept form, standard form, and point-slope form.\n\nit begins with a review of all forms then students must complete problems using each. worksheet (algebra). -algebra worksheets with terms-- practice solving for an unknown, in equations with two terms. use positive and negative integers. answer sheets available at the time of worksheet creation.\n\n### 37. Helpful Tips Math Algebra Worksheets Untitled Design Games Level 2 Grade Micro Lesson Free Basic Pre", null, "Algebra math printable worksheets for teachers, parents and kids to practice basic algebra, system of equations and quadratic equations. these worksheets are for different to master algebra topics. basic algebra. basic algebra is very basic level of algebra where student learns to find the value of a single variable.\n\n### 38. Kindergarten Drawing Worksheets Free Math Tracing Decimal Games Play Easy Algebra Problems Answers Problem Solver Integrated St Homework School Readiness Assessment Printable Basic Pre", null, "This book, for the most part, is your teacher and tutor and as such, it will guide your step-by-step learning. just as you should pay. Welcome to the translating algebraic phrases (simple version) (a) math worksheet from the algebra worksheets page at math-drills.\n\n### 39. Pin Human Body Worksheets Senses Algebra Grade Math Standards Free Timetable Year Simple Logic Puzzles Easy Fraction Decimal Basic Pre", null, "These equations worksheets are a good resource for students in the grade through the grade. About the author mark is the author of logic for dummies (wiley).he holds degrees in both and math from university. he has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software.\n\n### 40. Free Time Worksheets Kindergarten Lemony Algebra Denominator Math Spring Multiple Choice Maker Array Fluency Games Basic Pre", null, "Example -algebra worksheets with terms-- a bit more challenging exercises in finding an unknown value in equations with terms, and. This -algebra video tutorial provides an introduction basic overview into common topics taught in that course. it covers mathematical concepts such as.\n\nThe various resources listed below are aligned to the same standard, () taken from the (common core standards for mathematics) as the expressions and equations worksheet shown above. solve real-world and mathematical problems by writing and solving equations of the form x p q and q for cases in which p, q and x are all.\n\nShe has a great way of instructing, guiding and challenging a child and is someone i would strongly recommend. Free -algebra worksheets for teachers, parents, and kids. easily download and print our -algebra worksheets. click on the free -algebra worksheet you would like to print or download.\n\nthis will take you to the individual page of the worksheet. you will then have two choices. you can either print the screen utilizing the large image loaded on the web page or you can download the professional print ready file. Free math worksheets for -algebra." ]
[ null, "https://optovr.com/images/image-result-grade-math-worksheets-linear-equations-free-printable-algebra-test-train-problem-standards-lessons-basic-pre.jpg", null, "https://optovr.com/images/solving-basic-equations-worksheets-free-pre-algebra.jpg", null, "https://optovr.com/images/grade-math-algebra-music-worksheets-free-coloring-pages-addition-drill-typing-games-simple-sign-integers-std-holiday-basic-pre.jpg", null, "https://optovr.com/images/3-multiplication-worksheets-grade-math-test-operations-integers-basic-arithmetic-questions-rules-addition-subtraction-calculator-ideas-free-pre-algebra.jpg", null, "https://optovr.com/images/independent-living-skills-worksheets-life-lessons-free-printable-algebra-worksheet-grade-division-problems-basic-geometry-2-mm-square-graph-paper-math-calculator-pre.jpg", null, "https://optovr.com/images/links-free-math-worksheets-algebra-college-elementary-school-games-geometry-dummies-fact-triangles-interactive-squared-paper-adding-basic-pre.jpg", null, "https://optovr.com/images/printable-algebra-worksheet-math-skills-practice-sheet-free-worksheets-word-problems-numbers-operations-grade-subtraction-adding-basic-pre.jpg", null, "https://optovr.com/images/math-worksheets-grade-algebra-free-word-problems-multiplication-high-school-activity-sheets-4-basic-pre.jpg", null, "https://optovr.com/images/math-references-teacher-algebra-worksheets-graders-unit-free-year-1-player-games-grade-puzzles-3-basic-pre.jpg", null, "https://optovr.com/images/links-free-math-worksheets-algebra-high-school-answer-students-mathematics-7-ninth-grade-practice-year-test-basic-pre.jpg", null, "https://optovr.com/images/grade-algebra-worksheets-math-free-basic-multiplication-games-play-worksheet-activities-school-age-printable-sheets-pre.jpg", null, "https://optovr.com/images/worksheet-math-worksheets-fore-photo-7-algebra-grade-free-9-inspirations-basic-pre.jpg", null, "https://optovr.com/images/free-algebra-worksheets-answers-calculus-grade-math-drills-activities-base-mixed-addition-subtraction-multiplication-division-basic-pre.jpg", null, "https://optovr.com/images/factoring-quadratic-expressions-grade-algebra-worksheets-work-math-problems-addition-printable-9-quiz-generator-free-activities-preschoolers-coloring-number-basic-pre.jpg", null, "https://optovr.com/images/algebra-word-problems-algebraic-applications-worksheets-grade-math-addition-mathematics-practice-book-graph-paper-axis-free-division-table-printable-basic-pre.jpg", null, "https://optovr.com/images/algebra-word-problems-grade-math-worksheets-mixed-easy-large-addition-general-learning-activities-mathematics-multiplication-question-generator-adding-free-basic-pre.jpg", null, "https://optovr.com/images/algebra-worksheet-answers-resource-math-worksheets-adding-grade-summer-word-problems-dynamic-tutor-free-basic-pre.jpg", null, "https://optovr.com/images/algebra-multiple-choice-free-printable-math-equation-worksheets-fun-games-brain-teaser-puzzles-answers-rules-number-quiz-generator-grade-9-basic-pre.jpg", null, "https://optovr.com/images/algebra-archives-den-free-basic-pre-worksheets.jpg", null, "https://optovr.com/images/single-variable-equation-worksheet-worksheets-free-basic-pre-algebra.jpg", null, "https://optovr.com/images/worksheets-free-algebra-grade-answers-kindergarten-themes-solve-calculator-print-1-grid-paper-funny-mathematics-tricks-geometry-problems-basic-pre.jpg", null, "https://optovr.com/images/algebra-free-math-papers-printable-activities-worksheets-nation-skills-children-coloring-pages-toilet-paper-roll-crafts-basic-pre.jpg", null, "https://optovr.com/images/math-algebra-archives-den-free-basic-pre-worksheets.jpg", null, "https://optovr.com/images/basic-algebra-marker-coloring-simple-worksheets-writing-letters-pictures-hard-math-problems-free-printable-puzzles-1-integers-grade-8-pre.jpg", null, "https://optovr.com/images/free-math-worksheets-printouts-algebra-graders-worksheet-distance-formula-fun-negative-number-grade-basic-pre.jpg", null, "https://optovr.com/images/free-math-worksheets-grade-subtraction-single-digit-reading-basic-adding-algebra-problems-sum-code-worksheet-answers-teacher-sites-pre.jpg", null, "https://optovr.com/images/free-math-worksheets-grade-algebra-middle-school-lesson-plans-multiplication-flash-games-children-solving-graphing-linear-equations-calculator-grid-paper-basic-pre.jpg", null, "https://optovr.com/images/free-algebra-worksheets-answers-math-multiplying-decimals-common-core-year-3-sheets-2-printable-flash-cards-games-fractions-basic-mathematics-pre.jpg", null, "https://optovr.com/images/quiz-worksheet-solving-absolute-equations-study-free-math-worksheets-expression-everyday-mathematics-program-basic-riddles-geometric-properties-easy-grade-problems-pre-algebra.jpg", null, "https://optovr.com/images/grade-test-worksheet-revision-worksheets-math-quiz-printable-8-learning-addition-practice-workbook-6-teacher-edition-counting-free-basic-pre-algebra.jpg", null, "https://optovr.com/images/coloring-activities-algebra-worksheets-millimeter-paper-print-coin-grade-free-money-management-adding-fractions-kids-telling-time-year-3-basic-pre.jpg", null, "https://optovr.com/images/worksheet-free-basic-math-worksheets-grade-skills-algebra-writing-equations-solve-mathematics-home-problem-solver-rounding-money-pre.jpg", null, "https://optovr.com/images/simple-algebra-worksheet-templates-word-free-premium-basic-pre-worksheets.jpg", null, "https://optovr.com/images/grade-algebra-worksheets-math-multiplication-division-games-graders-fun-congruence-8-mathematics-syllabus-free-basic-pre.jpg", null, "https://optovr.com/images/algebra-calculator-free-math-worksheets-schoolers-anger-management-therapy-printable-logic-puzzles-kids-drills-fraction-site-simple-numeracy-test-basic-pre.jpg", null, "https://optovr.com/images/free-printable-math-worksheets-kindergarten-grade-trigonometry-module-summer-multiplication-facts-book-algebra-fun-basic-pre.jpg", null, "https://optovr.com/images/helpful-tips-math-algebra-worksheets-untitled-design-games-level-2-grade-micro-lesson-free-basic-pre.jpg", null, "https://optovr.com/images/kindergarten-drawing-worksheets-free-math-tracing-decimal-games-play-easy-algebra-problems-answers-problem-solver-integrated-st-homework-school-readiness-assessment-printable-basic-pre.jpg", null, "https://optovr.com/images/pin-human-body-worksheets-senses-algebra-grade-math-standards-free-timetable-year-simple-logic-puzzles-easy-fraction-decimal-basic-pre.jpg", null, "https://optovr.com/images/free-time-worksheets-kindergarten-lemony-algebra-denominator-math-spring-multiple-choice-maker-array-fluency-games-basic-pre.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87168103,"math_prob":0.9206851,"size":25486,"snap":"2021-04-2021-17","text_gpt3_token_len":4723,"char_repetition_ratio":0.22984852,"word_repetition_ratio":0.04546649,"special_character_ratio":0.1787648,"punctuation_ratio":0.11786543,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9974882,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80],"im_url_duplicate_count":[null,1,null,1,null,1,null,2,null,2,null,1,null,1,null,1,null,1,null,1,null,2,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,2,null,1,null,1,null,1,null,1,null,2,null,1,null,1,null,2,null,2,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-10T14:28:16Z\",\"WARC-Record-ID\":\"<urn:uuid:b584d938-3080-4d15-809f-4e8ff9fbe936>\",\"Content-Length\":\"84408\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b7c722d3-6127-4cbd-8247-5a0ab087f0c7>\",\"WARC-Concurrent-To\":\"<urn:uuid:730580af-dc53-44d5-a3cb-bfffd2ad8e0a>\",\"WARC-IP-Address\":\"104.21.5.91\",\"WARC-Target-URI\":\"https://optovr.com/free-basic-pre-algebra-worksheets/\",\"WARC-Payload-Digest\":\"sha1:OB5XVOPYLMSHG664MWJJYQOBG4YHPUQO\",\"WARC-Block-Digest\":\"sha1:DNKRB6AVQD6OMNCJ36CQ7QFHFP6QUX7J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038057142.4_warc_CC-MAIN-20210410134715-20210410164715-00207.warc.gz\"}"}
https://www.clipsal.com/faq/fa174756
[ "", null, "## Can a 60 Hz rated Transformer be energized with 50 Hz source?\n\nFA174756\n\n11 April 2022\n\nIssue:\nTransformers rated for 60 Hz ONLY are sometimes chosen to be installed in a location that has a 50 Hz Distribution system.\n\nProduct Line:\nLV Transformers\n\nEnvironment:\nApplies to MOST Transformers made by SquareD/Schneider Electric.  Exceptions are 9070 series Control Transformers and Export Model Transformers which are dual rated for 50Hz and 60Hz.\n\nCause:\nDomestic (USA) power systems are rated 60 Hz.   Many other power systems in the world are rated at 50 Hz.\n\nResolution:\nA 60 Hz rated transformer can only be used on a 60 Hz system (with certain exceptions -- read further.) Whereas a 50 or 50/60 Hz rated transformer can be used on either a 50 or a 60 Hz rated system.\nException: If the energizing voltage does not exceed 83% of the transformers nominal voltage, the transformer can be used. Remember that transformers are simple ratio devices and the output will also be lower. Another important factor to remember is that the transformer`s capacity will also have to be derated at the same ratio of the applied voltage divided by the nominal voltage.\n\nExample: An EXN30T3H, 30kVA 480 delta to 208Y/120 transformer 60 Hz, can be utilized on a 50 Hz system as long as the applied voltage does not exceed 50/60 or 5/6 of the nominal 480, or rather 400 volts. With 400 volts 50 Hz applied, the output voltage will be 400/480 * 208 = 173 volts line-to-line, and 100 volts line-to-neutral, or 173Y/100 50 Hz. As well, the capacity or kVA of the transformer will be 400/480 * 30 = 25kVA. Transformers cannot change frequency, thus frequency in = frequency out." ]
[ null, "https://pixel.quantserve.com/pixel/p-yEy7R7_vSeq3Y.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87670493,"math_prob":0.9333842,"size":1586,"snap":"2022-40-2023-06","text_gpt3_token_len":393,"char_repetition_ratio":0.16434893,"word_repetition_ratio":0.0,"special_character_ratio":0.2774275,"punctuation_ratio":0.096463025,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96577513,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-02T21:10:14Z\",\"WARC-Record-ID\":\"<urn:uuid:70faa7f6-f3c4-4210-a567-002d9b30ead2>\",\"Content-Length\":\"343003\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:02615135-e389-422d-a28c-f683979158f5>\",\"WARC-Concurrent-To\":\"<urn:uuid:1760a0c0-12f8-4706-bf1b-8572bc3e583c>\",\"WARC-IP-Address\":\"23.40.21.241\",\"WARC-Target-URI\":\"https://www.clipsal.com/faq/fa174756\",\"WARC-Payload-Digest\":\"sha1:3JGJPHA4XJTNORS3CUWPRDGU5H62UQBB\",\"WARC-Block-Digest\":\"sha1:W4NOB7B3UVAIGIPLDDOFLMMNRU7XTP2H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500041.18_warc_CC-MAIN-20230202200542-20230202230542-00035.warc.gz\"}"}
https://numbermatics.com/n/5085/
[ "# 5085\n\n## 5,085 is an odd composite number composed of three prime numbers multiplied together.\n\nWhat does the number 5085 look like?\n\nThis visualization shows the relationship between its 3 prime factors (large circles) and 12 divisors.\n\n5085 is an odd composite number. It is composed of three distinct prime numbers multiplied together. It has a total of twelve divisors.\n\n## Prime factorization of 5085:\n\n### 32 × 5 × 113\n\n(3 × 3 × 5 × 113)\n\nSee below for interesting mathematical facts about the number 5085 from the Numbermatics database.\n\n### Names of 5085\n\n• Cardinal: 5085 can be written as Five thousand and eighty-five.\n\n### Scientific notation\n\n• Scientific notation: 5.085 × 103\n\n### Factors of 5085\n\n• Number of distinct prime factors ω(n): 3\n• Total number of prime factors Ω(n): 4\n• Sum of prime factors: 121\n\n### Divisors of 5085\n\n• Number of divisors d(n): 12\n• Complete list of divisors:\n• Sum of all divisors σ(n): 8892\n• Sum of proper divisors (its aliquot sum) s(n): 3807\n• 5085 is a deficient number, because the sum of its proper divisors (3807) is less than itself. Its deficiency is 1278\n\n### Bases of 5085\n\n• Binary: 10011110111012\n• Base-36: 3X9\n\n### Squares and roots of 5085\n\n• 5085 squared (50852) is 25857225\n• 5085 cubed (50853) is 131483989125\n• The square root of 5085 is 71.3091859441\n• The cube root of 5085 is 17.1961141393\n\n### Scales and comparisons\n\nHow big is 5085?\n• 5,085 seconds is equal to 1 hour, 24 minutes, 45 seconds.\n• To count from 1 to 5,085 would take you about twenty-four minutes.\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 5085 cubic inches would be around 1.4 feet tall.\n\n### Recreational maths with 5085\n\n• 5085 backwards is 5805\n• The number of decimal digits it has is: 4\n• The sum of 5085's digits is 18\n• More coming soon!\n\nMLA style:\n\"Number 5085 - Facts about the integer\". Numbermatics.com. 2021. Web. 21 October 2021.\n\nAPA style:\nNumbermatics. (2021). Number 5085 - Facts about the integer. Retrieved 21 October 2021, from https://numbermatics.com/n/5085/\n\nChicago style:\nNumbermatics. 2021. \"Number 5085 - Facts about the integer\". https://numbermatics.com/n/5085/\n\nThe information we have on file for 5085 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!\n\nKeywords: Divisors of 5085, math, Factors of 5085, curriculum, school, college, exams, university, Prime factorization of 5085, STEM, science, technology, engineering, physics, economics, calculator, five thousand and eighty-five.\n\nOh no. Javascript is switched off in your browser.\nSome bits of this website may not work unless you switch it on." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87462616,"math_prob":0.9667899,"size":2631,"snap":"2021-43-2021-49","text_gpt3_token_len":705,"char_repetition_ratio":0.11305672,"word_repetition_ratio":0.025581395,"special_character_ratio":0.30900797,"punctuation_ratio":0.16153847,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9849499,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T08:31:38Z\",\"WARC-Record-ID\":\"<urn:uuid:c81cc3ca-5cf8-402e-bde3-b21237b79f7f>\",\"Content-Length\":\"17602\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9efd0f9d-53d8-42f6-b758-c80ead16f853>\",\"WARC-Concurrent-To\":\"<urn:uuid:3a837f49-2f90-4cd1-be1c-0ecf7fb3e66c>\",\"WARC-IP-Address\":\"72.44.94.106\",\"WARC-Target-URI\":\"https://numbermatics.com/n/5085/\",\"WARC-Payload-Digest\":\"sha1:P6PIUNOT2H33OIF7VZ6YQTK4QW7KUN5O\",\"WARC-Block-Digest\":\"sha1:TOIC5UJKQOI7OEJX6D6NTBLPGBSEFP5E\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585382.32_warc_CC-MAIN-20211021071407-20211021101407-00524.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-2-solving-equations-2-3-solving-multi-step-equations-lesson-check-page-97/8
[ "## Algebra 1\n\n-19$\\frac{3}{4}$\n-$\\frac{2}{9}$$x - 4 = \\frac{7}{18} Multiply each side by 18 to get rid of the denominators. 18(-\\frac{2}{9}$$x$ - $4$) = 18($\\frac{7}{18}$) -4$x$-72 = 7 -4$x$ = 79 Divide each side by 4 to isolate the variable. x=-$\\frac{79}{4}$ = -19$\\frac{3}{4}$" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.56023973,"math_prob":1.0000097,"size":296,"snap":"2022-27-2022-33","text_gpt3_token_len":130,"char_repetition_ratio":0.16438356,"word_repetition_ratio":0.0,"special_character_ratio":0.5540541,"punctuation_ratio":0.03125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000075,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-04T13:08:15Z\",\"WARC-Record-ID\":\"<urn:uuid:881d311a-ac29-478b-b504-76700b125b6b>\",\"Content-Length\":\"87775\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bf217586-173c-491f-9cdb-6110b1d5953a>\",\"WARC-Concurrent-To\":\"<urn:uuid:f4db24d5-a0bd-43bf-a5a3-d64939913616>\",\"WARC-IP-Address\":\"18.210.97.242\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-2-solving-equations-2-3-solving-multi-step-equations-lesson-check-page-97/8\",\"WARC-Payload-Digest\":\"sha1:4U5WZQGYO2CZMFDVWE3XHDQRDF3HTOAU\",\"WARC-Block-Digest\":\"sha1:5U3AZHMF62TIIOKR26JTV6R7TIRXH5M5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104375714.75_warc_CC-MAIN-20220704111005-20220704141005-00158.warc.gz\"}"}
https://nolver.net/home/pubtype/conference/
[ "### Filter by type:\n\nSort by year:\n\n#### Majorizing measures for the optimizer\n\nConferencePreprintprobability\nSander Borst, Daniel Dadush, Neil Olver and Makrand Sinha,\nAccepted to ICTS 2021\n\nThe theory of majorizing measures, extensively developed by Fernique, Talagrand and many others, provides one of the most general frameworks for controlling the behavior of stochastic processes. In particular, it can be applied to derive quantitative bounds on the expected suprema and the degree of continuity of sample paths for many processes.\n\nOne of the crowning achievements of the theory is Talagrand’s tight alternative characterization of the suprema of Gaussian processes in terms of majorizing measures. The proof of this theorem was difficult, and thus considerable effort was put into the task of developing both shorter and easier to understand proofs. A major reason for this difficulty was considered to be theory of majorizing measures itself, which had the reputation of being opaque and\nmysterious. As a consequence, most recent treatments of the theory (including by Talagrand himself) have eschewed the use of majorizing measures in favor of a purely combinatorial approach (the generic chaining) where objects based on sequences of partitions provide roughly matching upper and lower bounds on the desired expected supremum.\n\nIn this paper, we return to majorizing measures as a primary object of study, and give a viewpoint that we think is natural and clarifying from an optimization perspective. As our main contribution, we give an algorithmic proof\nof the majorizing measures theorem based on two parts:\n\n• We make the simple (but apparently new) observation that finding the best majorizing measure can be cast as a convex program.\nThis also allows for efficiently computing the measure using off-the-shelf methods from convex optimization.\n• We obtain tree-based upper and lower bound certificates by rounding, in a series of steps, the primal and dual solutions to this convex program.\n\nWhile duality has conceptually been part of the theory since its beginnings, as far as we are aware no explicit link to convex optimization has been previously made.\n\n#### Long term behavior of dynamic equilibria in fluid queuing networks\n\nagtConferenceJournal\nRoberto Cominetti, Jose Correa and Neil Olver\nAccepted to Operations Research. Conference version: IPCO 2017\n\n#### Approximate multi-matroid intersection via iterative refinement\n\napproximationConferenceJournal\nAndré Linhares, Neil Olver, Chaitanya Swamy, Rico Zenklusen\nMathematical Programming. Conference version: IPCO 2019. arXiv:1811.09027\n\nWe introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the classical steps of iterative relaxation approaches, we iteratively refine/split involved matroid constraints to obtain a more restrictive constraint system, that is amenable to iterative relaxation techniques. Hence, throughout the iterations, we both tighten constraints and later relax them by dropping constrains under certain conditions. Due to the refinement step, we can deal with considerably more general constraint classes than existing iterative relaxation/rounding methods, which typically round on one matroid polytope with additional simple cardinality constraints that do not overlap too much.\n\nWe show how our rounding method, combined with an application of a matroid intersection algorithm, yields the first 2-approximation for finding a maximum-weight common independent set in 3 matroids. Moreover, our 2-approximation is LP-based, and settles the integrality gap for the natural relaxation of the problem. Prior to our work, no better upper bound than 3 was known for the integrality gap, which followed from the greedy algorithm. We also discuss various other applications of our techniques, including an extension that allows us to handle a mixture of matroid and knapsack constraints.\n\n#### Algorithms for Flows Over Time with Scheduling Costs\n\nagtConferencenetwork\nDario Frascaria and Neil Olver\nIPCO 2020\n\nFlows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game.\n\n#### Fixed-order scheduling on parallel machines\n\napproximationConference\nThomas Bosman, Dario Frascaria, Neil Olver, Rene Sitters and Leen Stougie\nIPCO 2019\n\nWe consider the following natural scheduling problem: Given a sequence of jobs with weights and processing times, one needs to assign each job to one of m identical machines in order to minimize the sum of weighted completion times. The twist is that for machine the jobs assigned to it must obey the order of the input sequence, as is the case in multi-server queuing systems. We establish a constant factor approximation algorithm for this (strongly NP-hard) problem. Our approach is necessarily very different from what has been used for similar scheduling problems without the fixed-order assumption. We also give a QPTAS for the special case of unit processing times\n\n#### A Simpler and Faster Strongly Polynomial Algorithm for Generalized Flow Maximization\n\nConferenceJournalnetwork\nNeil Olver and László Végh\nAccepted to J. ACM, subject to minor revisions. Conference version: STOC 2017.\n\nWe present a new strongly polynomial algorithm for generalized flow maximization. The first strongly polynomial algorithm for this problem was given in [Végh 2016]; our new algorithm is much simpler, and much faster. The complexity bound $O((m+n\\log n)mn\\log (n^2/m))$ improves on the previous estimate in [ Végh 2016] by almost a factor $O(n^2)$. Even for small numerical parameter values, our algorithm is essentially as fast as the best weakly polynomial algorithms. The key new technical idea is relaxing primal feasibility conditions. This allows us to work almost exclusively with integral flows, in contrast to all previous algorithms for the problem.\n\n#### The Itinerant List Update Problem\n\napproximationConference\nNeil Olver, Kirk Pruhs, Kevin Schewior, Rene Sitters and Leen Stougie\nProceedings of the 16th Workshop on Approximation and Online Algorithms (WAOA)\n\n#### Fast, Deterministic and Sparse Dimensionality Reduction\n\nConferenceprobability\nDaniel Dadush, Cristóbal Guzman, Neil Olver\nSODA 2018\n\n#### Chain-constrained spanning trees\n\nConferenceJournalnetwork\nNeil Olver and Rico Zenklusen\nMathematical Programming 167(2):293–314. Conference version in IPCO 2013.\n\nWe consider the problem of finding a spanning tree satisfying a family of additional constraints. Several settings have been considered previously, the most famous being the problem of finding a spanning tree with degree constraints. Since the problem is hard, the goal is typically to find a spanning tree that violates the constraints as little as possible.\n\nIterative rounding became the tool of choice for constrained spanning tree problems. However, iterative rounding approaches are very hard to adapt to settings where an edge can be part of a super-constant number of constraints. We consider a natural constrained spanning tree problem of this type, namely where upper bounds are imposed on a family of cuts forming a chain. Our approach reduces the problem to a family of independent matroid intersection problems, leading to a spanning tree that violates each constraint by a factor of at most 9.\n\nWe also present strong hardness results: among other implications, these are the first to show, in the setting of a basic constrained spanning tree problem, a qualitative difference between what can be achieved when allowing multiplicative as opposed to additive constraint violations.\n\n#### On the Integrality Gap of the Prize-Collecting Steiner Forest LP\n\napproximationConferencenetwork\nJochen Koenemann, Kanstantsin Pashkovich, Neil Olver, R. Ravi, Chaitanya Swamy, Jens Vygen\nAPPROX 2017\n\n#### Exploring the tractability of the capped hose model\n\nConferencenetwork\nThomas Bosman, Neil Olver\nProceedings of the 25th Annual European Symposium on Algorithms (ESA)\n\n#### On the Equivalence of the Bidirected and Hypergraphic Relaxations for Steiner Tree\n\nConferenceJournalnetwork\nAndreas E. Feldmann, Jochen Koenemann, Neil Olver and Laura Sanità\nMathematical Programming 160:379-406. Conference version: APPROX 2014\n\nThe bottleneck of the currently best (ln(4) + epsilon)-approximation algorithm for the NP-hard Steiner tree problem is the solution of its large, so called hypergraphic, linear programming relaxation (HYP). Hypergraphic LPs are NP-hard to solve exactly, and it is a formidable computational task to even approximate them sufficiently well. We focus on another well-studied but poorly understood LP relaxation of the problem: the bidirected cut relaxation (BCR). This LP is compact, and can therefore be solved efficiently. Its integrality gap is known to be greater than 1.16, and while this is widely conjectured to be close to the real answer, only a (trivial) upper bound of 2 is known. In this paper, we give an efficient constructive proof that BCR and HYP are polyhedrally equivalent in instances that do not have an (edge-induced) claw on Steiner vertices, i.e., they do not contain a Steiner vertex with 3 Steiner neighbors. This implies faster ln(4)-approximations for these graphs, and is a significant step forward from the previously known equivalence for (so called quasi-bipartite) instances in which Steiner vertices form an independent set. We complement our results by showing that even restricting to instances where Steiner vertices induce one single star, determining whether the two relaxations are equivalent is NP-hard.\n\nConferenceprobability\nJosé Correa, Marcos Kiwi , Neil Olver and Alberto Vera\nWINE 2015\n\nMotivated by the recent emergence of the so-called opportunistic communication networks, we consider the issue of adaptivity in the most basic continuous time (asynchronous) rumor spreading process. In our setting a rumor has to be spread to a population; the service provider can push it at any time to any node in the network and has unit cost for doing this. On the other hand, as usual in rumor spreading, nodes share the rumor upon meeting and this imposes no cost on the service provider. Rather than fixing a budget on the number of pushes, we consider the cost version of the problem with a fixed deadline and ask for a minimum cost strategy that spreads the rumor to every node. A non-adaptive strategy can only intervene at the beginning and at the end, while an adaptive strategy has full knowledge and intervention capabilities. Our main result is that in the homogeneous case (where every pair of nodes randomly meet at the same rate) the benefit of adaptivity is bounded by a constant. This requires a subtle analysis of the underlying random process that is of interest in its own right.\n\n#### Decentralized utilitarian mechanisms for scheduling games\n\nagtConferenceJournal\nR. Cole, J. Correa, V. Gkatzelis, V. Mirrokni and N. Olver\nGames and Economic Behavior, Volume 92, pp 306–326, 2015. Conference version: STOC 2011\n\nGame Theory and Mechanism Design are by now standard tools for studying and designing massive decentralized systems. Unfortunately, designing mechanisms that induce socially efficient outcomes often requires full information and prohibitively large computational resources. In this work we study simple mechanisms that require only local information. Specifically, in the setting of a classic scheduling problem, we demonstrate local mechanisms that induce outcomes with social cost close to that of the socially optimal solution. Somewhat counter-intuitively, we find that mechanisms yielding Pareto dominated outcomes may in fact enhance the overall performance of the system, and we provide a justification of these results by interpreting these inefficiencies as externalities being internalized. We also show how to employ randomization to obtain yet further improvements. Lastly, we use the game-theoretic insights gained to obtain a new combinatorial approximation algorithm for the underlying optimization problem.\n\n#### Pipage Rounding, Pessimistic Estimators and Matrix Concentration\n\nConferenceprobability\nN. Harvey, N. Olver\nSODA 2014\n\nPipage rounding is a dependent random sampling technique that has several interesting properties and diverse applications.\nOne property that has been useful in applications is negative correlation of the resulting vector. There are some further properties that would be interesting to derive, but do not seem to follow from negative correlation. In particular, recent concentration results for sums of independent random matrices are not known to extend to a negatively dependent setting.\n\nWe introduce a simple but useful technique called concavity of pessimistic estimators. This technique allows us to show concentration of submodular functions and concentration of matrix sums under pipage rounding. The former result answers a question of Chekuri et al. (2009). To prove the latter result, we derive a new variant of Lieb’s celebrated concavity theorem in matrix analysis.\n\nWe provide numerous applications of these results. One is to spectrally-thin trees, a spectral analog of the thin trees that played a crucial role in the recent breakthrough on the asymmetric traveling salesman problem. We show a polynomial time algorithm that, given a graph where every edge has effective conductance at least $\\kappa$, returns an $O(\\kappa^{-1} \\cdot \\log n / \\log \\log n)$-spectrally-thin tree. There are further applications to rounding of semidefinite programs and to a geometric question of extracting a nearly-orthonormal basis from an isotropic distribution.\n\n#### Approximability of robust network design\n\napproximationConferenceJournalnetwork\nNeil Olver and Bruce Shepherd\nMathematics of Operations Research 39(2):561–572, 2014. Conference version: SODA 2010\n\nWe consider robust network design problems where the set of feasible demands may be given by an arbitrary polytope or convex body more generally. This model, introduced by Ben-Ameur and Kerivin (2003), generalizes the well studied virtual private network (VPN) problem. Most research in this area has focused on finding constant factor approximations for specific polytope of demands, such as the class of hose matrices used in the definition of VPN. As pointed out in Chekuri (2007), however, the general problem was only known to be APX-hard (based on a reduction from the Steiner tree problem). We show that the general robust design is hard to approximate to within logarithmic factors. We establish this by showing a general reduction of buy-at-bulk network design to the robust network design problem. In the second part of the paper, we introduce a natural generalization of the VPN problem. In this model, the set of feasible demands is determined by a tree with edge capacities; a demand matrix is feasible if it can be routed on the tree. We give a constant factor approximation algorithm for this problem that achieves factor 8 in general, and 2 for the case where the tree has unit capacities.\n\n#### The VPN Conjecture is true\n\nConferenceJournalnetwork\nNavin Goyal, Neil Olver and Bruce Shepherd\nJournal of the ACM, 60(3), 2013. Conference version: STOC 2008\n\nWe consider the following network design problem. We are  given an undirected graph $G=(V,E)$ with edges costs $c(e)$ and a set of terminal nodes $W$. A hose demand matrix for $W$ is any symmetric matrix $[D_{ij}]$ such that for each $i$, $\\sum_{j \\neq i} D_{ij} \\leq 1$. We must compute the minimum cost edge capacities that are able to support the oblivious routing of every hose matrix in the network. An oblivious routing template, in this context, is a simple path $P_{ij}$ for each pair $i,j \\in W$. Given such a template, if we are to route a demand matrix $D$, then for each $i,j$ we send $D_{ij}$ units of flow along each $P_{ij}$. Fingerhut et al. (1997) and Gupta et al. (2001) obtained a $2$-approximation for this problem, using a solution template in the form of a tree. It has been widely asked and subsequently conjectured that this solution actually results in the optimal capacity for the single path VPN design problem; this has become known as the VPN conjecture.\n\nThe conjecture has previously been proven for some restricted classes of graphs (Hurkens et al. 2005, Grandoni et al. 2007, Fiorini et al. 2007). Our main theorem establishes that this conjecture is true in general graphs. This proves that the single path VPN problem is solvable in polynomial time. We also show that the multipath version of the conjecture is false.\n\n#### Matroids and Integrality Gaps for Hypergraphic Steiner Tree Relaxations\n\nConferencenetwork\nMichel Goemans, Neil Olver, Thomas Rothvoss and Rico Zenklusen\nSTOC 2012\n\nUntil recently, LP relaxations have played a limited role in the design of approximation algorithms for the Steiner tree problem. In 2010, Byrka et al. presented a ln(4)+epsilon approximation based on a hypergraphic LP relaxation, but surprisingly, their analysis does not provide a matching bound on the integrality gap.\nWe take a fresh look at hypergraphic LP relaxations for the Steiner tree problem – one that heavily exploits methods and results from the theory of matroids and submodular functions – which leads to stronger integrality gaps, faster algorithms, and a variety of structural insights of independent interest. More precisely, we present a deterministic ln(4)+epsilon approximation that compares against the LP value and therefore proves a matching ln(4) upper bound on the integrality gap.\nSimilarly to Byrka et al., we iteratively fix one component and update the LP solution. However, whereas they solve an LP at every iteration after contracting a component, we show how feasibility can be maintained by a greedy procedure on a well-chosen matroid. Apart from avoiding the expensive step of solving a hypergraphic LP at each iteration, our algorithm can be analyzed using a simple potential function. This gives an easy means to determine stronger approximation guarantees and integrality gaps when considering restricted graph topologies. In particular, this readily leads to a 73/60 bound on the integrality gap for quasi-bipartite graphs.\nFor the case of quasi-bipartite graphs, we present a simple algorithm to transform an optimal solution to the bidirected cut relaxation to an optimal solution of the hypergraphic relaxation, leading to a fast 73/60 approximation for quasi-bipartite graphs. Furthermore, we show how the separation problem of the hypergraphic relaxation can be solved by computing maximum flows, providing a fast independence oracle for our matroids.\n\n#### Dynamic vs Oblivious Routing in Network Design\n\nConferenceJournalnetwork\nNavin Goyal, Neil Olver and Bruce Shepherd\nAlgorithmica 61(1): 161–173, 2011. Conference version: ESA 2009\n\nConsider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to dynamic routing, where routings may depend arbitrarily on the current demand. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of $\\Omega(\\log{n})$ more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in Chekuri (2007), and is tight up to constant factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns (Chekuri et al. 2007)." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.93288285,"math_prob":0.90288377,"size":16972,"snap":"2021-31-2021-39","text_gpt3_token_len":3384,"char_repetition_ratio":0.11981377,"word_repetition_ratio":0.007510327,"special_character_ratio":0.18907613,"punctuation_ratio":0.08428094,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9772217,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-26T05:37:58Z\",\"WARC-Record-ID\":\"<urn:uuid:9e79969e-46f0-4ef6-9828-e9a455dcdd72>\",\"Content-Length\":\"108572\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d85197f8-c655-4f0b-b234-cea158809160>\",\"WARC-Concurrent-To\":\"<urn:uuid:c827f044-98e1-4a3f-be03-fdcdd990295b>\",\"WARC-IP-Address\":\"208.113.160.109\",\"WARC-Target-URI\":\"https://nolver.net/home/pubtype/conference/\",\"WARC-Payload-Digest\":\"sha1:OBS6OPF6JEVEHAJJFAXOSRTHRBFTPAGW\",\"WARC-Block-Digest\":\"sha1:WSOPGKCLV5PBT5O4RB6GF3AMTVL6WHA5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046152000.25_warc_CC-MAIN-20210726031942-20210726061942-00707.warc.gz\"}"}
https://www.mail-archive.com/music-dsp@music.columbia.edu/msg02487.html
[ "# Re: [music-dsp] Time Varying BIBO Stability Analysis of Trapezoidal integrated optimised SVF v2\n\n```Hi Ross,\n\n```\nsince you opened this topic, I thought I'd try to share the intermediate results my findings, as much as I can remember them (that was a few years back). Most of them concern the continuous time case.\n```\n```\nFirst note regarding the continuous time case is that cutoff modulations do not affect the BIBO stability at all. More rigorously: - if the cutoff modulation is done by varying the gains *in front* (rather than behind) of *all* integrators in the system\n```- if the cutoff function w(t) is always positive\n- if the system is BIBO stable for some cutoff function w(t)\nthen the system is also BIBO stable for any other positive cutoff function\n\n```\nParticularly, if a linear system is BIBO-stable in time-invariant case (for the constant cutoff function), then it's also stable for varying cutoff.\n```\nThis is very easy to obtain from the state-space equation:\ndu/dt=w*F(u,x)\n```\nwhere u(t) is the state vector, x(t) is the input vector, w(t) is the cutoff scalar function and F(u,x,t) is the nonlinear time-varying version of A*u+B*x. Without reduction of generality we can assume w(t)=1 for the given stable case. Then, we simply rewrite the equation as\n```du/(w*dt)=F(u,x)\nand substitute the time parameter:\nd tau = w*dt\n```\nNow in \"tau\" time coordinates the modulated system is exactly the same as the unmodulated one in the \"t\" coordinates.\n```\nThe same doesn't seem to hold for the TPT discrete-time version, though.\n\n```\nIn a more general case for *linear* continuous time, IIRC, we have a sufficient (but it seems, not necessary) time-varying stability criterion: all eigenvalues of the matrix A+A^T must be \"uniformly negative\", that is they must be bounded by some negative number from above. It is essential to require this uniform negativity, otherwise the eigenvalues can get arbitrarily close to the self-oscillation case. This condition is simply obtained from the fact that in the absence of the input signal you want the absolute value of the state to decay with a relative speed, which is uniformly less that 1. This will make sure, that, whatever the bound of the input signal is, a large enough state will decay sufficiently fast, to win over the input vector B(t)*x(t). Indeed, ignoring the B*x term, we have\n```(d/dt) |u|^2=(d/dt)(u^T*u)=u'^T*u+u^T*u'=\n(A*u)^T*u+u^T*(A*u)=u^T*A^T*u+u^T*A*u=\nu^T*(A+A^T)*u<=|u|^2*max{lambda_i}\nwhere lambda_i are the eigenvalues of A+A^T.\nNow on the other hand\n(d/dt) |u|^2=2*|u|*(d/dt)|u|\nSo\n2*|u|*(d/dt)|u|<=|u|^2*max{lambda_i}\nand\n2*(d/dt)|u|<=|u|*max{lambda_i}\n\n```\nObviously, you don't have to satisfy the condition in the original state-space coordinates. Instead, you can satisfy it in any other coordinates, which corresponds to using P^T*A*P instead of A for some nonsingular matrix P.\n```\n```\nNow I didn't manage to get this condition satisfied for the continuous-time SVF. Reading your post, I admit, that I could have made a mistake there, but FWIW... First, I discarded the consideration of varying cutoff, as explained above and concentrated on the varying damping. Not managing to find a matrix P, I constructed an input signal, requiring the maximum possible growth of the state vector. The signal, IIRC was either sgn(s_1) or -sgn(s_1), where s_1 is the first of the state components (or it could have been s_2). Then I noticed that for low damping the state vector is moving in almost a circle, while for higher damping (but still with complex poles) is turns into an ellipse. This was exactly the problem: \"in principle\" the circle is having a bigger size, than the ellipse, but by switching the damping from low to high you could \"shoot\" the state point into a much \"higher orbit\". Much worse, in certain cases the system state can increase even in the full absence of the input signal!!! However, IIRC, I managed to show, that for a sufficiently large \"elliptic\" orbit (with high damping), (d/dt)|u|^2<=0 regardless of the current damping. Since we are already considering the \"worst possible\" input signal, the system state can't cross this boundary \"orbit\" to the outside.\n```\n```\nFor the discrete-time case the situation is more complicated, because we can't use the continuity of the state vector function. IIRC, I also didn't manage to build the \"worst-case\" signal, but there was the same problem of the state vector becoming larger in the absence of the input signal. That's why I was somewhat surprised that you simply managed to restrict the eigenvalues of the system matrix in some coordinates. Particularly suspicious is that your coordinate transformation matrix is \"built for the smallest damping\", while the more problematic case seems to occur \"at the larger damping\". But, as I said, I didn't finish that research and I could have been wrong. So just take my input FWIW.\n```\nRegards,\n\n--\nReaktor Application Architect\nNative Instruments GmbH\n+49-30-611035-0\n\nwww.native-instruments.com\n--\ndupswapdrop -- the music-dsp mailing list and website:\nsubscription info, FAQ, source code archive, list archive, book reviews, dsp" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.90876746,"math_prob":0.93916255,"size":5080,"snap":"2023-14-2023-23","text_gpt3_token_len":1318,"char_repetition_ratio":0.11130812,"word_repetition_ratio":0.0050314465,"special_character_ratio":0.23484252,"punctuation_ratio":0.1038835,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9895582,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-29T13:45:55Z\",\"WARC-Record-ID\":\"<urn:uuid:5dd76ae5-d832-4715-b74a-b4528befcf2d>\",\"Content-Length\":\"14336\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3fad7ba0-53eb-42f8-93c9-19d8a51f9a0e>\",\"WARC-Concurrent-To\":\"<urn:uuid:43b6584e-4730-47cb-b870-455c53c8dd4e>\",\"WARC-IP-Address\":\"72.52.77.8\",\"WARC-Target-URI\":\"https://www.mail-archive.com/music-dsp@music.columbia.edu/msg02487.html\",\"WARC-Payload-Digest\":\"sha1:APKHUMBRETC2OUYTYLDTH52VGSOHZZ4E\",\"WARC-Block-Digest\":\"sha1:PIFMRRAZEH64O4N6WDIPNM3HIFLV2K6Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948976.45_warc_CC-MAIN-20230329120545-20230329150545-00125.warc.gz\"}"}
https://physics.stackexchange.com/questions/246454/are-gravitational-force-and-gravitational-time-dilation-proportional
[ "# Are gravitational force and gravitational time dilation proportional?\n\nParticles in gravitational fields are subject to gravitational time dilation. The closer a particle is near a gravitational source, the slower is running its clock. I would like to know more about the relation between gravity and gravitational time dilation.\n\nIn order to get a rough impression I used Newton's gravity equation (which may be used for weak fields, and I found that gravity and time dilation are (approximately) proportional: Can this result be confirmed on the base of Einstein's field equation (maybe even for stronger fields)?\n\ndτ = proper time of a particle in the gravitation field of Earth, dt = proper time of an observer in infinity, rs = Schwarzschild radius of Earth, r = distance particle - center of Earth\n\nGravitational time dilation:\n\n$\\frac{dτ}{dt}=\\sqrt{1- \\frac{r_s}{r}} ≈ 1- \\frac{r_s}{2r}$\n\nTime dilation (difference):\n\n$1-\\frac{dτ}{dt} ≈ \\frac{r_s}{2r}= \\frac{GM}{c^2 r}$\n\nGravitational force (Newton's equation):\n\n$F=G \\frac{mM}{r^2}$\n\n\\begin{equation} \\frac{Gravitational\\:force}{Time\\:dilation\\:(difference)} ≈ \\frac{G\\frac{mM}{r^2}}{\\frac{GM}{c^2 r}}=\\frac{mc^2}{r}=\\frac{rest\\:energy\\:(of\\:the\\:particle\\:subject\\:to\\:time\\:dilation)}{distance\\:(of\\:the\\:particle)} \\end{equation}\n\n(As a result, time dilation would be approximately gravitaty, divided by the rest energy of the particle, multiplied by its distance.)\n\n• Hi Moonraker. If you haven't already done so, please take a minute to read the definition of when to use the homework-and-exercises tag, and the Phys.SE policy for homework-like problems. Mar 31, 2016 at 10:27\n• Hi @Qmechanic, thank you for your information, and I did read the page you indicated. - I don't know why you think that my question falls under this category. My question is clearly indicated in the title, and there is no other question: Is there some relation of proportionality between gravitational force and gravitational time dilation. I could even reformulate my question without the formulas I provided (if you wish so). I just need the information about Einstein field equations, nothing more. Mar 31, 2016 at 11:56\n• Also, for future reference, please don't delete and repost questions. Instead, if they're not well received, you should edit them to improve them. Mar 31, 2016 at 12:36\n• @David Z♦ : OK, I undeleted the former question. Thank you for this formal comment, I hope I fixed it. I would be keen on knowing your comment on the topic of my question? Sincerely Mar 31, 2016 at 13:23\n\nIf you have a look at my answer to Deriving a Schwarzschild radius using relativistic mass I discuss how the weak field approximation gives us an approximate metric for the Newtonian gravitational potential $\\phi$:\n\n$$ds^2 \\approx -\\left( 1 + \\frac{2\\phi}{c^2}\\right) c^2dt^2 + \\frac{1}{1 + 2\\phi/c^2}\\left(dx^2 + dy^2 + dz^2\\right)$$\n\nTo extract time dilation from this we take a stationary object, so $dx = dy = dz = 0$ and use the relationship between the line element and the proper time $ds^2 = -c^2d\\tau^2$ to get:\n\n$$\\frac{d\\tau}{dt} \\approx \\sqrt{ 1 + \\frac{2\\phi}{c^2}}$$\n\nTo clarify this, take two observers $A$ and $B$ with gravitational potential energies $\\phi_A$ and $\\phi_B$, then the equation tells us that the elapsed times recorded by $A$ and $B$ are related by:\n\n$$\\frac{dt_A}{dt_B} \\approx \\sqrt{ 1 + \\frac{2(\\phi_A - \\phi_B)}{c^2}}$$\n\nThis equation is only valid when $2\\Delta\\phi/c^2 \\ll 1$, in which case we can use the binomial expansion:\n\n$$\\frac{dt_A}{dt_B} \\approx 1 + \\frac{\\Delta\\phi}{c^2} + \\text{higher terms}$$\n\nand dropping the higher terms and rearranging:\n\n$$\\frac{dt_A - dt_B}{dt_B} \\approx \\frac{\\Delta\\phi}{c^2}$$\n\nAnd this is sort of what you describe. Remember that the potential energy $\\phi$ is the potential energy per unit mass, so if we multiply the top and bottom of the right side by the mass to get the total potential energy $\\Phi$ we get:\n\n$$\\frac{dt_A - dt_B}{dt_B} \\approx \\frac{\\Delta\\Phi}{mc^2}$$\n\nwhich is indeed the gravitational potential divided by the rest energy.\n\nBut this is an approximation that works (reliably) only in the weak field limit. As it happens the weak field expression works for any values of $r$ in the Schwarzschild metric, but as discussed in the linked question this is an accidental coincidence and can't be relied on.\n\n• Nice, interesting explanations, but you are far from answering my question! You confirmed that my rough calculation with Newton's equation yields approximately correct results for weak fields. I know this, even if I could not explain it with Schwarzschild metrics as you did. But my calculations (and yours also) induce the idea that gravitational force and gravitational time dilation are proportional, with a factor of proportionality equal to the rest energy of the particle divided by the distance. - Are they proportional or not? Mar 31, 2016 at 6:48\n• @Moonraker: I thought that was obvious from my final equation. In the weak field limit the relative time dilation is proportional to the gravitational potential. However this is only true in the weak field limit so it works for calculating the time dilation of geostationary satellites but not for calculating the time dilation near a black hole. Mar 31, 2016 at 7:08\n• My question is not for purposes of technological applications, but for exploring the nature of gravitational time dilation and gravity (even in stronger fields). Your final approximate equation does not include more insight than my final approximate equation, Newton's equation is appropriate for weak fields. Mar 31, 2016 at 8:09\n• I appreciate that you showed the Schwarzschild approximation, but there might be other insights deriving from Einstein's field equation which are putting some light on this supposed proportionality. Mass is producing gravity, and mass is producing gravitational time dilation - may be there is a direct relation between both of them?? Mar 31, 2016 at 8:09\n• @Moonraker: I have to confess that I don't understand what you are getting at. The linear proportionality is a weak field phenomenon and is an inevitable consequence of the fact that in the weak field limit GR must reproduce Newtonian gravity. Outside the weak field limit the time dilation is obviously related to the mass (more precisely the stress-energy tensor) but remember you can choose any coordinate system you want and the time dilation will depend on the coordinates you choose, so the relationship is a complicated one. Mar 31, 2016 at 8:22\n\nThey don't have to be related.\n\nFor instance if you have a hollow spherical shell of matter then the inside of the sphere is a flat spacetime region and it has the same time dilation as the shell.\n\nBut since the inside is flat, there is no gravitational force inside the shell. Yet there is time dilation." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8283579,"math_prob":0.9884254,"size":1346,"snap":"2022-05-2022-21","text_gpt3_token_len":371,"char_repetition_ratio":0.18554397,"word_repetition_ratio":0.0,"special_character_ratio":0.2600297,"punctuation_ratio":0.124497995,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9995983,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T18:16:06Z\",\"WARC-Record-ID\":\"<urn:uuid:ec400134-25ff-4a72-a18a-263f5f4bb3ba>\",\"Content-Length\":\"251582\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0dd01dcb-2331-4353-aba6-83d544d5e3f3>\",\"WARC-Concurrent-To\":\"<urn:uuid:a159a403-5a45-4811-a359-5637607d103c>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/246454/are-gravitational-force-and-gravitational-time-dilation-proportional\",\"WARC-Payload-Digest\":\"sha1:5QTNI6P2LHCNJPZI4OMCX7PDU4JRXSCI\",\"WARC-Block-Digest\":\"sha1:T7REEQOFZ3EXMX2MQLY565PM2LIPN6FO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662573189.78_warc_CC-MAIN-20220524173011-20220524203011-00171.warc.gz\"}"}
https://www.slideserve.com/yovela/sect-3-a-position-velocity-and-acceleration
[ "# Sect. 3-A Position , Velocity, and Acceleration - PowerPoint PPT Presentation", null, "Download Presentation", null, "Sect. 3-A Position , Velocity, and Acceleration\n\nSect. 3-A Position , Velocity, and Acceleration", null, "Download Presentation", null, "## Sect. 3-A Position , Velocity, and Acceleration\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. Sect. 3-APosition, Velocity, and Acceleration\n\n2. Position function - gives the location of an object at time t, usually s(t), x(t) or y(t) Velocity - The rate of change( derivative) of position, usually v(t) Acceleration - The rate of change ( derivative) of velocity usually a(t) Average velocity -\n\n3. 1) If find v(t) and a(t).\n\n4. 2) The position of a particle moving along the x - axis at time t is given by . Find the particles velocity and acceleration at t = 5. Velocity Acceleration\n\n5. Speed – The absolute value of velocity otherwise known as the magnitude of velocity\n\n6. Velocity Positive - the particle is moving to the right Negative - the particle is moving to the left Zero - the particle has momentarily stopped or is changing direction ( must have a sign change)\n\n7. 3) Find where the object changes direction if Find where v(t) = 0\n\n8. Acceleration and Velocity • If the sign of acceleration is the same as velocity, the speed of the particle is ______________ (the two are working together) • If the sign of the acceleration is opposite that of velocity, the speed of the particle is _________________ (the two are working against each other)\n\n9. 4) Given the same position function as #3 find the interval during which the particle is slowing down.\n\n10. 5) Given find the interval during which the particle is speeding up.\n\n11. Distance vs. Displacement • Displacement- change in position ( final position minus original position) • Distance- the total distance travelled by an object in the time interval even if duplicated\n\n12. Consider two intervals 6) Find the DISTANCE traveled by the particle whose position is given by on the interval (0,4). Distance NOT displacement!!\n\n13. 7) If • find the DISTANCE traveled by the particle on the interval (2,4). • Find the DISPLACEMENT on the interval (1,5)\n\n14. The graph shows the position function of a radio controlled car a) Was the car going faster at B or at C? b) When was the car stopped? c) At which point was the car’s velocity the greatest? d) At which point was the car’s speed decreasing?\n\n15. Homework PVA Worksheet and worksheet 3-A" ]
[ null, "https://www.slideserve.com/img/replay.png", null, "https://thumbs.slideserve.com/1_5651602.jpg", null, "https://www.slideserve.com/photo/32883.jpeg", null, "https://www.slideserve.com/img/output_cBjjdt.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.890393,"math_prob":0.96679294,"size":2006,"snap":"2020-34-2020-40","text_gpt3_token_len":441,"char_repetition_ratio":0.17482518,"word_repetition_ratio":0.08595989,"special_character_ratio":0.2442672,"punctuation_ratio":0.05978261,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.996886,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,1,null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T12:23:48Z\",\"WARC-Record-ID\":\"<urn:uuid:2d175c44-645b-48ef-956f-b6f97abe9967>\",\"Content-Length\":\"51392\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:61e5cc5a-22c2-416a-af11-cab92cb9b2a1>\",\"WARC-Concurrent-To\":\"<urn:uuid:9a78b3fb-6b1f-4786-b4a5-cde1387f1301>\",\"WARC-IP-Address\":\"35.162.74.143\",\"WARC-Target-URI\":\"https://www.slideserve.com/yovela/sect-3-a-position-velocity-and-acceleration\",\"WARC-Payload-Digest\":\"sha1:7Z47AZKDWDRQAIHWJAJXPRJSBYAHKYAG\",\"WARC-Block-Digest\":\"sha1:SDVG4XG766PHKPGHT7MJD4GRRMNYX44A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400197946.27_warc_CC-MAIN-20200920094130-20200920124130-00340.warc.gz\"}"}
http://de.git.xonotic.org/?p=xonotic/darkplaces.git;a=blobdiff;f=draw.h;h=3857e98e303f53a4f188079d6be0474ff1b8a943;hp=bbd964ed3d9839518be6f8c67a5faaccae177a83;hb=9d6f77621de650ffaaecb65a3485d51378632925;hpb=c045878e6948f00e52f17c9df6beefa2dfdfd868
[ "diff --git a/draw.h b/draw.h\nindex bbd964e..3857e98 100644 (file)\n--- a/draw.h\n+++ b/draw.h\n@@ -134,7 +134,15 @@ extern dp_fonts_t dp_fonts;\n#define STRING_COLOR_RGB_TAG_CHAR      'x'\n#define STRING_COLOR_RGB_TAG           \"^x\"\n\n-// all of these functions will set r_defdef.draw2dstage if not in 2D rendering mode (and of course prepare for 2D rendering in that case)\n+// prepare for 2D rendering (sets r_refdef.draw2dstage = 1 and calls R_ResetViewRendering2D)\n+void DrawQ_Start(void);\n+// resets r_refdef.draw2dstage to 0\n+void DrawQ_Finish(void);\n+// batch draw the pending geometry in the CL_Mesh_UI() model and reset the model,\n+// to be called by things like DrawQ_SetClipArea which make disruptive state changes.\n+void DrawQ_FlushUI(void);\n+// use this when changing r_refdef.view.* from e.g. csqc\n+void DrawQ_RecalcView(void);\n\n// draw an image (or a filled rectangle if pic == NULL)\nvoid DrawQ_Pic(float x, float y, cachepic_t *pic, float width, float height, float red, float green, float blue, float alpha, int flags);\n@@ -163,12 +171,6 @@ void DrawQ_SetClipArea(float x, float y, float width, float height);\nvoid DrawQ_ResetClipArea(void);\n// draw a line\nvoid DrawQ_Line(float width, float x1, float y1, float x2, float y2, float r, float g, float b, float alpha, int flags);\n-// resets r_refdef.draw2dstage\n-void DrawQ_Finish(void);\n-void DrawQ_RecalcView(void); // use this when changing r_refdef.view.* from e.g. csqc\n-// batch draw the pending geometry in the CL_Mesh_UI() model and reset the model,\n-// to be called by things like DrawQ_SetClipArea which make disruptive state changes.\n-void DrawQ_FlushUI(void);\n\nconst char *Draw_GetPicName(cachepic_t *pic);\nint Draw_GetPicWidth(cachepic_t *pic);" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6158914,"math_prob":0.87738246,"size":1466,"snap":"2019-43-2019-47","text_gpt3_token_len":414,"char_repetition_ratio":0.16142271,"word_repetition_ratio":0.21105528,"special_character_ratio":0.26398364,"punctuation_ratio":0.18039216,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96525776,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-14T09:20:46Z\",\"WARC-Record-ID\":\"<urn:uuid:2da7d3de-1a42-4de9-97df-943635897277>\",\"Content-Length\":\"9955\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4c43b2f6-a924-4a11-b835-64c2103d53f0>\",\"WARC-Concurrent-To\":\"<urn:uuid:70e7853f-5b1d-47cb-94e9-50dc3520a3ef>\",\"WARC-IP-Address\":\"46.38.241.138\",\"WARC-Target-URI\":\"http://de.git.xonotic.org/?p=xonotic/darkplaces.git;a=blobdiff;f=draw.h;h=3857e98e303f53a4f188079d6be0474ff1b8a943;hp=bbd964ed3d9839518be6f8c67a5faaccae177a83;hb=9d6f77621de650ffaaecb65a3485d51378632925;hpb=c045878e6948f00e52f17c9df6beefa2dfdfd868\",\"WARC-Payload-Digest\":\"sha1:HZGQ4XHNOXYAFBBA4ZWGAITG5QIMO7ME\",\"WARC-Block-Digest\":\"sha1:AR3FDDWIH4OX5AGCQTGI5VZFBJRZ67S3\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668334.27_warc_CC-MAIN-20191114081021-20191114105021-00268.warc.gz\"}"}
https://sanaulla.info/2013/04/08/arrays-sort-versus-arrays-parallelsort/?amp=1
[ "# Arrays.sort versus Arrays.parallelSort\n\nWe all have used Arrays.sort to sort objects and primitive arrays. This API used merge sort OR Tim Sort underneath to sort the contents as shown below:\n\n```public static void sort(Object[] a) {\nif (LegacyMergeSort.userRequested)\nlegacyMergeSort(a);\nelse\nComparableTimSort.sort(a);\n}\n```\n\nThis is all done sequentially, even though merge sort uses divide and conquer technique, its all done sequentially.\n\nCome Java 8, there is a new API introduced for sorting which is Arrays#parallelSort. This is does the sorting in parallel. Interesting right! Lets see how it does…\n\nArrays#parallelSort uses Fork/Join framework introduced in Java 7 to assign the sorting tasks to multiple threads available in the thread pool. This is called eating your own dog food. Fork/Join implements a work stealing algorithm where in a idle thread can steal tasks queued up in another thread.\n\n### An overview of Arrays#parallelSort:\n\nThe method uses a threshold value and any array of size lesser than the threshold value is sorted using the Arrays#sort() API (i.e sequential sorting). And the threshold is calculated considering the parallelism of the machine, size of the array and is calculated as:\n\n```private static final int getSplitThreshold(int n) {\nint p = ForkJoinPool.getCommonPoolParallelism();\nint t = (p > 1) ? (1 + n / (p << 3)) : n;\nreturn t < MIN_ARRAY_SORT_GRAN ? MIN_ARRAY_SORT_GRAN : t;\n}\n```\n\nOnce its decided whether to sort the array in parallel or in serial, its now to decide how to divide the array in to multiple parts and then assign each part to a Fork/Join task which will take care of sorting it and then another Fork/Join task which will take care of merging the sorted arrays. The implementation in JDK 8 uses this approach:\n– Divide the array into 4 parts.\n– Sort the first two parts and then merge them.\n– Sort the next two parts and then merge them.\nAnd the above steps are repeated recursively with each part until the size of the part to sort is not lesser than the threshold value calculated above.\n\n### Some interesting results:\n\nI tried to compare the time taken by the Arrays#sort and Arrays#parallelSort on a machine with 4 CPUs. The program which I used for this comparison is:\n\n```public class ArraysParallelDemo {\npublic static void main(String[] args) throws FileNotFoundException {\nList<Double> arraySource = new ArrayList<>();\n\ngetSystemResourceAsStream(\"java8demo/large_array_input\"));\nString[] strNums = line.split(\",\");\nfor ( String strN : strNums){\n}\n}\n\nSystem.out.println(arraySource.size());\n\nDouble [] myArray = new Double;\nmyArray = arraySource.toArray(myArray);\nlong startTime = System.currentTimeMillis();\nArrays.sort(myArray);\nlong endTime = System.currentTimeMillis();\nSystem.out.println(\"Time take in serial: \"+\n(endTime-startTime)/1000.0);\n\nDouble [] myArray2 = new Double;\nmyArray2 = arraySource.toArray(myArray);\nstartTime = System.currentTimeMillis();\nArrays.parallelSort(myArray2);\nendTime = System.currentTimeMillis();\nSystem.out.println(\"Time take in parallel: \"+\n(endTime-startTime)/1000.0);\n\n}\n}\n```\n\nThere is a similar implementation for Lists as well and lot of the operations on Lists have a parallel equivalent." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7464922,"math_prob":0.78813267,"size":3373,"snap":"2023-14-2023-23","text_gpt3_token_len":726,"char_repetition_ratio":0.111605816,"word_repetition_ratio":0.03258656,"special_character_ratio":0.2265046,"punctuation_ratio":0.14451827,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9847679,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-01T21:38:02Z\",\"WARC-Record-ID\":\"<urn:uuid:26377539-710a-485d-b527-578107397c88>\",\"Content-Length\":\"53188\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7075767-c967-4f51-8e54-fb1d3f84ebba>\",\"WARC-Concurrent-To\":\"<urn:uuid:40561e0f-809e-46b6-b557-3fced980521d>\",\"WARC-IP-Address\":\"192.0.78.180\",\"WARC-Target-URI\":\"https://sanaulla.info/2013/04/08/arrays-sort-versus-arrays-parallelsort/?amp=1\",\"WARC-Payload-Digest\":\"sha1:YQJ5S4V63Q3FGQX7NIMGQYQNJFGJW7GX\",\"WARC-Block-Digest\":\"sha1:X6YX5DVR5BRHQINTHDUNMYZJKMBGIWAR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224648209.30_warc_CC-MAIN-20230601211701-20230602001701-00344.warc.gz\"}"}
http://maths-statistics-tutor.com/simple_linear_regression_pasw_spss.php
[ "# Performing simple linear regression in PASW (SPSS)\n\nWhen do we do simple linear regression?\nWe run simple linear regression when we want to access the relationship between two continuous variables.\n\nExample Scenario\nIn a statistics course, we want to see if there is any relationship between study time and scores in the mid-semester exam.\n\nIn this example, our null hypothesis is that there is no relationship between study time and exam scores. Our alternative hypothesis is that the more time students study, the higher the exam score.\n\nIn the data, the first column is exam scores and the second column is study time. The dataset can be obtained here.", null, "Before we perform the actual regression analysis, we can explore the relationship with a scatter plot.", null, "It appears that the more time students study, the higher the exam scores and the relationship looks linear. We now perform the regression analysis to see if there is an actual relationship between study time and exam scores. (We cannot make any definite conclusion until we do an appropriate statistical analysis.\n\nStep 1\nSelect \"Analyze -> Regression -> Linear\".", null, "A new window pops out.", null, "Step 2\nFrom the list on the left, select the variable \"Exam score\" as \"Dependent\" and the variable \"Hours\" as the \"Independent(s)\". Click \"OK\".", null, "Step 3\nThe results now pop out in the \"Output\" window.", null, "Step 4\nWe can now interpret the result.", null, "From B in the third table, since the p-value is 0, the relationship between study hours and exam scores is significant. From A in the second table, the correlation coefficient, R, is 0.827. Therefore, we can conclude that study hours is positively correlated with exam score and the relationship is very strong (R is positive and is very closed to 1). From C in the last table, we can conclude that on average, for every one hour a student study, he gets 2.391 more marks in the exam.", null, "© Maths-Statistics-Tutor.com 2010 Web Development Team." ]
[ null, "http://maths-statistics-tutor.com/img/simple_linear_regression/1.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/scatterplot.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/2.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/3.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/4.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/5.jpg", null, "http://maths-statistics-tutor.com/img/simple_linear_regression/6.jpg", null, "http://maths-statistics-tutor.com/img/contact_maths_statistics_button.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9271326,"math_prob":0.9097722,"size":1813,"snap":"2019-13-2019-22","text_gpt3_token_len":386,"char_repetition_ratio":0.15312327,"word_repetition_ratio":0.067961164,"special_character_ratio":0.21511307,"punctuation_ratio":0.10985915,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99525565,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-19T07:37:23Z\",\"WARC-Record-ID\":\"<urn:uuid:901b6ad3-64e2-4b86-96c9-5253e00ef5dc>\",\"Content-Length\":\"5787\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6ceb28e9-9fe3-4190-9834-f90e6cfd3ec0>\",\"WARC-Concurrent-To\":\"<urn:uuid:dd41053b-2ffb-4243-951b-5356f0d52717>\",\"WARC-IP-Address\":\"97.74.141.1\",\"WARC-Target-URI\":\"http://maths-statistics-tutor.com/simple_linear_regression_pasw_spss.php\",\"WARC-Payload-Digest\":\"sha1:QR24DQK3OYSZJZPFOFLFWL32YU7MOXJO\",\"WARC-Block-Digest\":\"sha1:J4BL2ZFK6HAFTARRPQXELGH4Y5BTQHYV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912201922.85_warc_CC-MAIN-20190319073140-20190319095140-00205.warc.gz\"}"}
http://beastie.cs.ua.edu/ACP-C/index_20.html
[ "", null, "", null, "", null, "Lists Contents\n\n# Lists\n\nYou can download the functions defined or used in this chapter with the following commands:\n\n``` wget troll.cs.ua.edu/ACP-C/ilist.c //integer-valued nodes\nwget troll.cs.ua.edu/ACP-C/ilist.h\nwget troll.cs.ua.edu/ACP-C/rlist.c //real-valued nodes\nwget troll.cs.ua.edu/ACP-C/rlist.h\nwget troll.cs.ua.edu/ACP-C/slist.c //string-valued nodes\nwget troll.cs.ua.edu/ACP-C/slist.h\nwget troll.cs.ua.edu/ACP-C/olist.c //'object'-valued nodes\nwget troll.cs.ua.edu/ACP-C/olist.h\nwget troll.cs.ua.edu/ACP-C/employeeList.c //employee linked list demo\n```\n\n## The List data structure\n\nWe could stop at this point and just use nodes and their operations to make true lists. But just as constructors, accessors, and mutators free us from being concerned how nodes and records are structured, we can design some list (sometimes called linked list) operators that free us from some of the details of the nodes themselves. If we do our design and implementation properly, a reader of our code will have few clues that lists are build from nodes.\n\nThe first task is to decide what will represent an empty list. The null pointer will work well for this role.\n\n``` Node *\nnewEmptyList(void)\n{\nreturn 0;\n}\n```\n\nNext, we define join, a function that will be used to add a value to a list, returning the new list. We will use our integer-valued nodes from the previous chapter:\n\n``` Node *\njoin(int value,Node *items)\n{\nreturn newNode(value,items);\n}\n```\n\nThe join function takes a value and a list as arguments and returns a new node that glues the two arguments together. The result is a list one value larger than the list that is passed in. Note that join is non-destructive with regards to the original list; if we want to modify the original list, we must reassign the original list with the return value of join:\n\n``` items = join(value,items);\n```\n\nWe can see from the definition of an empty list and from join that a list is either 0 (the null pointer) or a node. Two accessor functions are often defined for lists, head and tail. The head function returns the value stored in the first node in the list, while the tail returns the chain of nodes that follows the first node:\n\n``` int head(Node *items) { return getNodeValue(items); }\nNode *tail(Node *items) { return getNodeNext(items); }\n```\n\nTwo mutator functions are also commonly defined:\n\n``` void setHead(Node *items,int v) { setNodeValue(items,v); }\nvoid setTail(Node *items,Node *n) { setNodeNext(items,n); }\n```\n\nYou may be wondering at this point why we bother to distinguish lists and nodes. One reason is we can improve lists by keeping some more information around; we will save that improvement for later. Another reason is it is vitally important to practice the concept of abstraction. Modern software systems exhibit a large number of abstraction layers. With our lists, we can see for layers of abstractions: variables, which abstract locations in memory, structures, which abstract collections of variables, nodes, which abstract structures with two components, and lists, which abstracts a chain of `nodes`. Each level of abstraction frees us from thinking about the details of the underlying layers. We emphasize abstraction over and over, because it is so very important.\n\n### The join operator\n\nLet us now look at the join operation more closely. Here is a rewrite of join that uses a temporary variable, n, to hold the new node that will join the given value and list together:\n\n``` Node *\njoin(int v,Node *items)\n{\nNode *n = newEmptyNode(); //step 1\nsetNodeValue(n,v); //step 2\nsetNodeNext(n,items); //step 3\nreturn n;\n}\n\n```\n\nFirst, let us create an empty list to which we will join a value:\n\n``` a = newEmptyList();\n```\n\nGraphically, the situation looks like this:", null, "Now, we call join to join the value of 13 to the list a.\n\n``` a = join(13,a);\n```\n\nAt the very start of the join function, the formal parameters v and items have been set to the value 13 and a, respectively. The situation looks like this:", null, "The variables v and items, since they are local to the function join, are shown in blue35. After step 1, `n = newEmptyNode()`, we have:", null, "As with items and v, the variable n is shown in blue as it is a local variable. After step 2, `setNodeValue(v,None)`, the node n has its value set to v. the variable n. The situation changes to:", null, "After step 3, `setNodeNext(n,items)`, the next pointer of n, which is null, is changed to the value of items, which is also null. So the situation remains the same as before. Finally, n is returned and the variable a is reassigned to have the value of n. The variables v, items, and n go out of scope and disappear, leaving:", null, "If we add a second value to the list a, as in:\n\n``` a = join(7,a);\n```\n\nat the start of the join function, we have:", null, "After creating node n (step 1) and setting its value pointer (step 2), we have:", null, "Setting n's next pointer to items yields:", null, "At this point, we return the value of n and assign it to a:", null, "From this last drawing, we can see that list a now includes the value 7 at the front of the list, as intended. As before, at this point the variables local to join, are no longer in scope.\n\n### Chaining calls to join\n\nAs seen in the previous section, the join function is used to build a list:\n\n``` a = 0;\na = join(13,a);\na = join(7,a);\na = join(42,a);\n```\n\nThe above code builds the following list:", null, "An alternative way to build the exact same list is to chain together the series of calls to join:\n\n``` a = join(42,join(7,join(13,0)));\n```\n\nBoth methods are rather tedious for larger arrays, so we will make use of a list constructor that takes an array of integers and returns a list of those integers. This code:\n\n``` int numbers[] = {42,7,13};\nNode *a = arrayToList(numbers,sizeof(numbers)/sizeof(int));\n```\n\nproduces the same list. A first attempt at defining arrayToList might look like this:\n\n``` Node *\narrayToList(int *array,int size)\n{\nint i;\nNode *items = 0; //start items as the empty list\nfor (i = 0; i < size; ++i)\nitems = join(array[i],items);\nreturn items;\n}\n```\n\nUnfortunately, this produces a list whose values are found in the reverse order from that of the array. Why this is so is answered by the question, \"What is the last value joined to the growing list and where did it end up in the list?\". Obviously, the last value joined was the last value in the array and it ended up as the first value in the list, since join places its first argument at the head of the list. By a similar logic, the next-to-the-last value in the array ended up in the second position in the list, and so on.\n\nWe can fix this deficiency by defining a function that creates a new list in the reverse order of a given list. The code mimics our arrayToList function:\n\n``` Node *\nreverse(Node *a)\n{\nNode *items = 0;\nwhile (a != 0)\n{\na = tail(a);\n}\nreturn items;\n}\n```\n\nAgain, the last value in the incoming list a is placed in the first position of the new list items.\n\nThe arrayToList function becomes:\n\n``` Node *\narrayToList(int *array,int size)\n{\nint i;\nNode *items = 0; //start items as the empty list\nfor (i = 0; i < size; ++i)\n{\nitems = join(array[i],items);\n}\nNode *rev = reverse(items);\nfreeList(items);\nreturn rev;\n}\n```\n\nThis revised version of arrayToList is a bit inefficient in that the values to be placed in the list are traversed twice, once by accessing every value in the array (the for loop) and once by accessing every value in reverse's incoming list. The arrayToList functions found in the list modules mentioned in the start of this chapter cleverly make a single traversal. See if you can figure out how they work.\n\n### Reading a list from a file\n\nConsider a file of integers that we wish to read into a list. As always, we use the read pattern:\n\n``` do the initial read\n{\n}\n```\n\nConcretely, we have:\n\n``` Node *\n{\nint v;\nNode *items;\n\nitems = 0; //items points to an empty list\nfscanf(fp,\"%d\",&v);\nwhile (!feof(fp))\n{\nitems = join(v,items); //update items\nfscanf(fp,\"%d\",&v);\n}\nreturn items;\n}\n```\n\nLike the arrayToList function in the previous subsection, the readIntegers function also reverses the order of the integers as found in the file. If order must be maintained, one can reverse items before returning or use the same trick the version of arrayToList in the ilist module uses.\n\n### Displaying a list\n\nTo display a list, we need to walk the list. A walk of a list is comprised of visiting every node in the list from front to back. Typically, a loop is used to implement a walk. Here is a display function for a list of integer-valued nodes:\n\n``` void\ndisplayList(Node *items)\n{\nwhile (items != 0)\n{\nprintf(\"{%d}\",v);\nitems = tail(items); //take a step\n}\nprintf(\"\\n\");\n}\n```\n\nWith this function in place, we can see if join is really working. Here is some code that tests both join and display:\n\n``` //test (compile with ilist.c)\n#include \"ilist.h\"\nint numbers[] = {42,7,13};\nNode *a = arrayToList(numbers,sizeof(numbers)/sizeof(int));\ndisplayList(a);\n```\n\nRunning this code yields the following output, as expected:\n\n``` {42}{7}{13}\n```\n\n## Lists of other values\n\nWe can make lists of any kind of value. The modules rlist.c and slist.c contain analogs to the functions in ilist.c, except they work with real numbers (`double`) and strings (`char *`), respectively.\n\nAnother module, the olist.c module, allows for lists of pointers to arbitrary structures (or any pointers, other than function pointers). Consider the employee record structure from the chapter on structures. One might read a file of employee records, storing them into a linked list, this way:\n\n``` #include \"employee.h\"\n#include \"olist.h\"\n...\nNode *\n{\nNode *employees = 0; //zero is the empty list\nwhile (!feof(fp))\n{\nemployees = join(e,Employees);\n}\nreturn employees;\n}\n```\n\nA careful inspection of the olist module reveals that the value in a node has type `void *`. A variable of this type can store any pointer (except a function pointer) safely. However, once stored, the pointer loses any knowledge of the kind of thing to which it points (i.e. the kind of thing found at the address stored in the pointer). Another way to describe this loss of information is to say the pointer becomes generic. Once the pointer is genericized, it is up to the programmer to convert it back to the kind of pointer it once was. For example, this code fails:\n\n``` Node *emps = readEmployeeList(fp);\n```\n\nbecause the code writer has not converted the generic pointer returned by olist's head function into an Employee pointer. This code, on the other hand, succeeds:\n\n``` Node *emps = readEmployeeList(fp);\nEmployee *e = head(emps); //generic pointer converted to Employee pointer\nchar *name = e->name;\n```\n\nThe latter two lines can be combined into a single line with a cast:\n\n``` Node *emps = readEmployeeList(fp);\nchar *name = ((Employee *) head(emps))->name;\n```\n\nOne can also use the accessor function for the name field in the Employee structure:\n\n``` Node *emps = readEmployeeList(fp);\nThis gives the compiler the information that the generic pointer returned by `head(emps)` is really a pointer to an Employee structures, since getEmployeeName accepts Employee pointers.", null, "", null, "", null, "Lists Contents" ]
[ null, "http://beastie.cs.ua.edu/ACP-C/previous.png", null, "http://beastie.cs.ua.edu/ACP-C/up.png", null, "http://beastie.cs.ua.edu/ACP-C/next.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list1.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list2.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list3.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list4.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list5.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list6.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list7.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list8.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list9.png", null, "http://beastie.cs.ua.edu/ACP-C/pic-list10.png", null, "http://beastie.cs.ua.edu/ACP-C/previous.png", null, "http://beastie.cs.ua.edu/ACP-C/up.png", null, "http://beastie.cs.ua.edu/ACP-C/next.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8331778,"math_prob":0.92395395,"size":11230,"snap":"2020-45-2020-50","text_gpt3_token_len":2688,"char_repetition_ratio":0.14671299,"word_repetition_ratio":0.037506603,"special_character_ratio":0.24407837,"punctuation_ratio":0.14597602,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9633421,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"im_url_duplicate_count":[null,null,null,null,null,null,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-27T12:39:28Z\",\"WARC-Record-ID\":\"<urn:uuid:f99f3c0b-26ba-4409-b05b-18c7ca367d72>\",\"Content-Length\":\"17120\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fbc30bd8-85e6-419f-85a7-a0e44b6b8734>\",\"WARC-Concurrent-To\":\"<urn:uuid:6320d8cc-f7a4-4792-9fa4-5a542f3f769a>\",\"WARC-IP-Address\":\"130.160.143.106\",\"WARC-Target-URI\":\"http://beastie.cs.ua.edu/ACP-C/index_20.html\",\"WARC-Payload-Digest\":\"sha1:OAKLLQ3JGEUW3QETXJ2Z4OZ5DASR7RJP\",\"WARC-Block-Digest\":\"sha1:VRYCOYN637A4YGKDVGR5VPILDM6QWQLX\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107894175.55_warc_CC-MAIN-20201027111346-20201027141346-00530.warc.gz\"}"}
https://abdulfatir.com/blog/2020/Langevin-Monte-Carlo/
[ "Langevin Monte Carlo is a class of Markov Chain Monte Carlo (MCMC) algorithms that generate samples from a probability distribution of interest (denoted by $\\pi$) by simulating the Langevin Equation. The Langevin Equation is given by\n\n$\\lambda\\frac{dX_t}{dt} = -\\frac{\\partial V(x)}{\\partial x} + \\eta(t), \\tag{1}\\label{eq:langevin}$\n\nwhere $X_t$ is the position of a particle in a potential $V(x)$ and $\\eta(t)$ is a noise term. The dynamics in Eq. ($\\ref{eq:langevin}$) is also commonly written as the following Stochastic Differential Equation (SDE)\n\n$\\mathrm{d}X_t = \\underset{\\text{drift term}}{\\underbrace{-\\nabla V(x)\\mathrm{d}t}} + \\underset{\\text{diffusion term}}{\\underbrace{\\sqrt{2}\\mathrm{d}B_t}} \\tag{2}\\label{eq:itodiff}$\n\nwhich represents an Itô diffusion, where $\\mathrm{d}B_t$ denotes the time derivative of standard Brownian motion.\n\nIt can be shown that the SDE in Eq. ($\\ref{eq:itodiff}$) has a unique invariant measure (or simply, a steady-state distribution) that does not change along the trajectory ($X_t$) of the particle. This means that if $X_0$ is distributed according to some probability density function $p_\\infty$, then $X_t$ is also distributed according to $p_\\infty$ for all $t \\geq 0$. If we set the potential $V$ in Eq. ($\\ref{eq:itodiff}$) cleverly such that $p_\\infty = \\pi$, then we can simulate the SDE (Eq. $\\ref{eq:itodiff}$) to generate samples from $\\pi$.\n\n### The steady-state distribution: choosing the potential\n\nThe Fokker-Plank equation is a partial differential equation (PDE) that describes the evolution of a probability distribution over time under the effect of drift forces and random (or noise) forces. The equivalent Fokker-Plank equation for the SDE in Eq. ($\\ref{eq:itodiff}$) is given by\n\n$\\frac{\\partial p(x,t)}{\\partial t} = \\frac{\\partial}{\\partial x}\\left[\\frac{\\partial V(x)}{\\partial x}p(x,t)\\right] + \\frac{\\partial^2p(x,t)}{\\partial x^2}. \\tag{3}\\label{eq:fpe}$\n\nThe steady-state solution of the Fokker-Plank equation is given by $\\frac{\\partial p(x,t)}{\\partial t} = 0$. If $p_\\infty$ is the steady-state distribution, we have\n\n$\\frac{\\partial p(x,t)}{\\partial t} = \\frac{\\partial}{\\partial x}\\left[\\frac{\\partial V(x)}{\\partial x}p_\\infty(x) + \\frac{\\partial p_\\infty(x)}{\\partial x}\\right] = \\frac{\\partial}{\\partial x}J(x) = 0, \\tag{4}\\label{eq:steadystate}$\n\nwhere $J(x)$ denotes the probability “flux”. Eq. ($\\ref{eq:steadystate}$) implies that $J(x)$ must be a constant; however, $p_\\infty(x)$ and $\\frac{\\partial p_\\infty(x)}{\\partial x}$ must also satisfy certain boundary conditions. Specifically, the boundary condition that $J(x) = 0$ at infinity must be satisfied. Since $J(x) = 0$ at infinity and $J(x)$ is a constant, it must be equal to 0 everywhere. This leaves us with\n\n$J(x) = \\frac{\\partial V(x)}{\\partial x}p_\\infty(x) + \\frac{\\partial p_\\infty(x)}{\\partial x} = 0, \\tag{5}\\label{eq:zeroflux}$\n\nwhich has the solution\n\n$p_\\infty(x) \\propto \\exp(-V(x)). \\tag{6}\\label{eq:gibbs}$\n\nEq. ($\\ref{eq:gibbs}$) represents a Gibbs distribution. This means that we can sample from energy-based models (EBMs) of the form $\\pi(x) = \\frac{\\exp[-E(x)]}{Z}$, by setting $V(x) = E(x)$ in Eq. ($\\ref{eq:itodiff}$). We can also write the distribution $\\pi(x)$ as $\\exp[\\log\\pi(x)]$, which means that we can set $V(x) = -\\log\\pi(x)$. It must be noted that we do not really need to know the normalization constant $Z$ for this to work because Eq. ($\\ref{eq:itodiff}$) requires $\\nabla\\log\\pi(x)$ and $\\nabla Z = 0$ since $Z$ is a constant.\n\n### Simulating the SDE\n\nHaving derived the form of the potential $V(x)$, we are now interested in simulating the following SDE to sample from its steady state distribution, i.e., $\\pi(x)$,\n\n$\\mathrm{d}X_t = \\nabla \\log\\pi(x)\\mathrm{d}t + \\sqrt{2}\\mathrm{d}B_t. \\tag{7}\\label{eq:finalsde}$\n\nThe SDE can be discretized using a numerical method such as the Euler-Maruyama method. The Euler-Maruyama approximation of Eq. ($\\ref{eq:finalsde}$) can be written as\n\n$X_{t + \\tau} - X_{t} = \\tau\\nabla \\log\\pi(x) + \\sqrt{2}(B_{t+\\tau}-B_{t}), \\tag{8}\\label{eq:eulerapprox1}$\n\nwhere $\\tau$ is the step-size and $(B_{t+\\tau}-B_{t}) \\sim \\mathcal{N}(0,\\tau)$. This allows us to write Eq. ($\\ref{eq:eulerapprox1}$) as\n\n$X_{t + \\tau} = X_{t} + \\tau\\nabla \\log\\pi(x) + \\sqrt{2\\tau}\\xi, \\tag{9}\\label{eq:eulerapprox2}$\n\nwhere $\\xi \\sim \\mathcal{N}(0,1)$. The time-step $\\tau$ can also be changed over time.\n\nEq. ($\\ref{eq:eulerapprox2}$) gives us a method to sample from a probability distribution $\\pi(x)$ by setting an initial seed $X_0$ and simulating the dynamics which, after a burn-in phase, will generate samples from $\\pi(x)$. This algorithm is known as the Unadjusted Langevin Algorithm (ULA) which requires $\\nabla \\log\\pi(x)$ to be $L$-Lipschitz for stability.\n\nThe ULA always accepts the new sample proposed by Eq. ($\\ref{eq:eulerapprox2}$). Metropolis-adjusted Langevin Algorithm (MALA), on the other hand, uses the Metropolis-Hastings algorithm to accept or reject the proposed sample. Since $\\xi \\sim \\mathcal{N}(0,1)$, $X_{t + \\tau} \\sim \\mathcal{N}(X_{t} + \\tau\\nabla \\log\\pi(x),2\\tau)$ in Eq. ($\\ref{eq:eulerapprox2}$). This means that the proposal distribution is given by\n\n$q(x'|x) \\propto \\exp\\left(-\\frac{\\|x'-x-\\tau\\nabla \\log\\pi(x)\\|^2}{2\\cdot2\\tau}\\right).$\n\nThe sample ($\\tilde{X}_{k+1}$) proposed by Eq. ($\\ref{eq:eulerapprox2}$) is accepted with the following acceptance probability\n\n$\\alpha := \\min\\left(1, \\frac{\\pi(\\tilde{X}_{k+1})q(X_k|\\tilde{X}_{k+1})}{\\pi(X_{k})q(\\tilde{X}_{k+1}|X_k)}\\right).$\n\n### Visualizing Langevin Monte Carlo Sampling\n\nI set out to visualize these MCMC algorithms using matplotlib.animation to see how the distribution evolves over time. Unfortunately, writing to an MP4 file using matplotlib.animation is painfully slow and I could not find a simple way to speed it up. To solve this issue, I wrote a shell script to parallelize the generation of the chunks of the video and then combined them into one long video. The following video shows how samples are generated using MALA from a heart-shaped density given by\n\n$\\pi(\\mathbf{x}=\\begin{bmatrix}x_1 & x_2\\end{bmatrix}^\\top) \\propto \\exp\\left(-\\frac{0.8x_1^2 + \\left(x_2-\\sqrt{x_1^2}\\right)^2}{2^2}\\right).$\n\nThe code used to generate the video above can be found here.\n\n Working with the Langevin and Fokker-Planck equations (notes).\n Chapter 4, Stochastic Processes and Applications, Grigorios A. Pavliotis (book).\n Wikipedia articles (a, b, c, d)." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7829211,"math_prob":0.9999244,"size":6411,"snap":"2021-31-2021-39","text_gpt3_token_len":1999,"char_repetition_ratio":0.13532074,"word_repetition_ratio":0.014616322,"special_character_ratio":0.29620963,"punctuation_ratio":0.10064412,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000043,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-26T16:11:46Z\",\"WARC-Record-ID\":\"<urn:uuid:80a01242-54a8-42a5-90a9-18f8964c51e7>\",\"Content-Length\":\"17113\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3ad38086-9949-4ccf-9502-8b4a39a443d1>\",\"WARC-Concurrent-To\":\"<urn:uuid:3539600e-22fc-496d-b720-174365c8ac3c>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"https://abdulfatir.com/blog/2020/Langevin-Monte-Carlo/\",\"WARC-Payload-Digest\":\"sha1:7THIRARCXQYKEXGN3G7GKPEIFMMEC372\",\"WARC-Block-Digest\":\"sha1:VX47I46YXOHOJHAMUXZYA75EJK66JFUB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057882.56_warc_CC-MAIN-20210926144658-20210926174658-00375.warc.gz\"}"}
https://whatisconvert.com/152-ounces-in-pounds
[ "# What is 152 Ounces in Pounds?\n\n## Convert 152 Ounces to Pounds\n\nTo calculate 152 Ounces to the corresponding value in Pounds, multiply the quantity in Ounces by 0.0625 (conversion factor). In this case we should multiply 152 Ounces by 0.0625 to get the equivalent result in Pounds:\n\n152 Ounces x 0.0625 = 9.5 Pounds\n\n152 Ounces is equivalent to 9.5 Pounds.\n\n## How to convert from Ounces to Pounds\n\nThe conversion factor from Ounces to Pounds is 0.0625. To find out how many Ounces in Pounds, multiply by the conversion factor or use the Mass converter above. One hundred fifty-two Ounces is equivalent to nine point five Pounds.", null, "## Definition of Ounce\n\nThe ounce (abbreviation: oz) is a unit of mass with several definitions, the most popularly used being equal to approximately 28 grams. The size of an ounce varies between systems. Today, the most commonly used ounces are the international avoirdupois ounce (equal to 28.3495231 grams) and the international troy ounce (equal to 31.1034768 grams).\n\n## Definition of Pound\n\nThe pound or pound-mass (abbreviations: lb, lbm, lbm, ℔) is a unit of mass with several definitions. Nowadays, the most common is the international avoirdupois pound which is legally defined as exactly 0.45359237 kilograms. A pound is equal to 16 ounces.\n\n### Using the Ounces to Pounds converter you can get answers to questions like the following:\n\n• How many Pounds are in 152 Ounces?\n• 152 Ounces is equal to how many Pounds?\n• How to convert 152 Ounces to Pounds?\n• How many is 152 Ounces in Pounds?\n• What is 152 Ounces in Pounds?\n• How much is 152 Ounces in Pounds?\n• How many lb are in 152 oz?\n• 152 oz is equal to how many lb?\n• How to convert 152 oz to lb?\n• How many is 152 oz in lb?\n• What is 152 oz in lb?\n• How much is 152 oz in lb?" ]
[ null, "https://whatisconvert.com/images/152-ounces-in-pounds", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8942339,"math_prob":0.98864263,"size":1731,"snap":"2019-51-2020-05","text_gpt3_token_len":484,"char_repetition_ratio":0.17892298,"word_repetition_ratio":0.09003215,"special_character_ratio":0.28249568,"punctuation_ratio":0.123595506,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9981872,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T13:57:17Z\",\"WARC-Record-ID\":\"<urn:uuid:c675fb98-9279-4a09-bbc1-68ba0fc05c19>\",\"Content-Length\":\"26625\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7ee8bd07-7e6a-49ee-b7fc-3d3d30d17a1d>\",\"WARC-Concurrent-To\":\"<urn:uuid:7c056e67-e459-4714-a315-14fa0e9a8107>\",\"WARC-IP-Address\":\"104.31.71.53\",\"WARC-Target-URI\":\"https://whatisconvert.com/152-ounces-in-pounds\",\"WARC-Payload-Digest\":\"sha1:LIWKDSHS4GWGVKQUHE32KVUMXEFOK3ZV\",\"WARC-Block-Digest\":\"sha1:YQNAZZ5QSEHNFV6RNWNZ3DXLPOGFRILY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540565544.86_warc_CC-MAIN-20191216121204-20191216145204-00193.warc.gz\"}"}
https://discourse.mc-stan.org/t/possible-to-fit-this-time-series-model-in-brms/18168
[ "# Possible to fit this time series model in brms?\n\nElection forecasting has, in recent years, come to rely on models like those described in Jackman (2005):\n\ny_{i} \\sim \\mathrm{Normal}(\\mu_{i}, \\sigma_{i}) \\\\ \\mu_{i} = \\alpha_{t[i]} +\\delta_{j[i]} \\\\ \\alpha_{t} \\sim \\mathrm{Normal}(\\alpha_{t-1}, \\omega), t = 2, ..., T\n\nHere, poll y is modelled as the function of some grand mean \\alpha that varies over each day in the data and a set of house effects, \\delta, due to persistent biases present in each polling company’s methods.\n\nImportantly, \\alpha_{t} is itself modelled as a function of \\alpha_{t-1}. I know that brms can handle autoregressive elements, but can it do so for anything other than the dependent variable?\n\nIt’s worth noting also that often there are missing days in the data too.\n\nHola,\n\nWell for those kind of models you can use atsar package. Still have some struggle with the documentation and performance but is a good start. If you look a bit in the repository you find the stan code , and tou can play a bit with it to get your model fit\n\nHope that helps you :)\n\n1 Like" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8990357,"math_prob":0.9653378,"size":742,"snap":"2022-27-2022-33","text_gpt3_token_len":206,"char_repetition_ratio":0.1097561,"word_repetition_ratio":0.0,"special_character_ratio":0.2897574,"punctuation_ratio":0.13071896,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9722333,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-26T02:02:14Z\",\"WARC-Record-ID\":\"<urn:uuid:f5e63783-3bb0-48ea-abfd-4b22df818ba1>\",\"Content-Length\":\"21457\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6aab2c83-82f3-4647-ae11-97066deedfe8>\",\"WARC-Concurrent-To\":\"<urn:uuid:165f3672-02bd-494f-a576-b1f290b30744>\",\"WARC-IP-Address\":\"64.62.250.111\",\"WARC-Target-URI\":\"https://discourse.mc-stan.org/t/possible-to-fit-this-time-series-model-in-brms/18168\",\"WARC-Payload-Digest\":\"sha1:3KDA5D4LDUNOQJYCEKP5KE623YRQTHTC\",\"WARC-Block-Digest\":\"sha1:PA6VWIRCY3FV5MPXOHJVVT6VKYLUP6DD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103036363.5_warc_CC-MAIN-20220626010644-20220626040644-00584.warc.gz\"}"}
https://codingtube.tech/2021/09/17/java/java-array/
[ "# Array in java\n\nAn array in java is a data a structure used to process a collection of data that is all of the same type\n\nOther definition about Array in java\n\nAn array is a flexible structure for storing a sequence of values all of the same type.\n\nA structure that holds multiple values of the same type.\n\n• An array behaves behaves like a numbered numbered list of variables variables with a uniform naming mechanism\n• It has a part that does not change: the name of the array\n• It has a part that can change: an integer in square brackets\n\nExample\n\nscore , score , score , score , score , score, score, score, score, score\n\n## Creating and Accessing Arrays\n\n• An array that beheaves like this collection of variables, all of type double, can be created using one statement as follows\n\ndouble[] [ ]; score = new double;\n\n• Or using two statements:\n\ndouble[] score;\nscore = new double;\n\n• The individual variables that together make up the array are called indexed variables\n• They can also be called subscripted variables or elements of the array\n• The number in square brackets is called an index or subscript\n• In Java, indices must be numbered starting with 0, and nothing else\n\nscore , score, score , score , score , score, score, score, score, score\n\n• The number of indexed variables in an array is called the length or size of the array\n• When an array is created, the length of the array is given in square brackets after the array type\n• The indexed variables are then numbered starting with 0, and ending with the integer that is one less than the length of the array\n\nscore, score, score, score, score;\n\n• A variable may be used in place of the integer\n\nExample\n\ndouble[] score = new double;\n\n## Declaring and Creating an Array\n\n• An array is declared and created in almost the same way that objects are declared and created\n\nBaseType[] ArrayName = new BaseType[size];\n\n• The size may be given as an expression that evaluates to a nonnegative integer, for example, an int variable\n\nchar[] line = new char;\nPerson[] specimen = new Person;\n\n## Array Traversal in java\n\nProcessing each array element sequentially from the first to the last\n\n```for (int i = 0; i < <array>.length; i++) {\n<do something with array [i]>;\n}\n```\n\nA Complete Array Program in java\n\n``` import java.util.*;\npublic class Temperature1 {\npublic static void main(String[] args) {\nScanner console = new Scanner(System.in);\nSystem.out.print(\"How many days' temperatures? \");\nint numDays = console.nextInt();\nint sum = 0;\nfor (int i = 1; i <= numDays; i++) {\nSystem.out.print(\"Day \" + i + \"'s high temp: \");\nint next = console.nextInt();\nsum += next;\n}\ndouble average = (double) sum / numDays;\nSystem.out.println();\nSystem.out.println(\"Average = \" + average);\n}\n}\n\n```\n\n## Buffer Overruns\n\nOne of the earliest and still most common sources of computer security problems is a buffer overrun (also known as a buffer overflow). A buffer overrun is similar to an array index out of bounds exception. It occurs when a program writes data beyond the bounds of the buffer set aside for that data.\n\nBuffer overruns are often written as array code. You might wonder how such a malicious program could be written if the computer checks the bounds when you access an array. The answer is that older programming languages like C and C++ do not check bounds when you access an array. By the time Java was designed in the early 1990s, the danger of buffer overruns was clear and the designers of the language decided to include array-bounds checking so that Java would be more secure. Microsoft included similar bounds checking when it designed the language C# in the late 1990s\n\n## The For-Each Loop in java Array\n\nJava 5 introduced a new loop construct that simplifies certain array loops. It is known as the enhanced for loop, or the for-each loop. It can be used whenever you find yourself wanting to examine each value in an array.\n\nThe foreach loop, or enhanced for statement, as Java calls it, is used to enumerate the values in a collection of values\n\n```int sum= 0;\nfor (int v : b) {\nsum= sum + v;\n}\n```\n\nExample\n\n```public class ArrayExample {\npublic static void main(String[] args) {\nint[] numbers = {2, 4, 6, 8, 10};\nfor (int n: numbers) {\nSystem.out.println(n);\n}\n}\n}\n```\n\noutput\n\n2\n4\n6\n8\n10\n\n## Iterate over Java String Array using For-Each\n\n```public class ArrayExample {\npublic static void main(String[] args) {\nString names[] = {\"apple\", \"banana\", \"cherry\", \"mango\"};\nfor(String name: names) {\nSystem.out.println(\"Hello \" + name + \"!\");\n}\n}\n}\n\n```\n\nOutput\n\nHello apple!\nHello banana!\nHello cherry!\nHello mango!\n\n## Limitations of Arrays\n\nsome general limitations of arrays:\n\n• You can’t change the size of an array in the middle of program execution\n• You can’t compare arrays for equality using a simple == test. Remember that arrays are objects, so if you ask whether one array is == to another array, you are asking whether they are the same object, not whether they store the same values\n• You can’t print an array using a simple print or println statement. You will get odd output when you do so\n\nThe first limitation is more difficult to overcome. Because an array is allocated as a contiguous block of memory, it is not easy to make it larger. To make an array bigger, you’d have to construct a new array that is larger than the old one and copy values from the old to the new array. Java provides a class called ArrayList that does this growing operation automatically. It also provides methods for inserting values in and deleting values from the middle of a list\n\nMultidimensional Arrays\n\nArrays of more than one dimension are called multidimensional arrays\n\nRectangular Two-Dimensional Arrays\n\nThe most common use of a multidimensional array is a two-dimensional array of a certain width and height. For example, suppose that on three separate days you took a series of five temperature readings. You can define a two-dimensional array that has three rows and five columns as follows\n\ndouble[][] temps = new double;\n\nExample\n\n```public class Main {\npublic static void main(String[] args) {\nint[][] myNumbers = { {1, 2, 3, 4}, {5, 6, 7} };\nfor (int i = 0; i < myNumbers.length; ++i) {\nfor(int j = 0; j < myNumbers[i].length; ++j) {\nSystem.out.println(myNumbers[i][j]);\n}\n}\n}\n}\n\n```\n\nOutput\n\n1\n2\n3\n4\n5\n6\n7" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8188023,"math_prob":0.9036463,"size":6294,"snap":"2023-40-2023-50","text_gpt3_token_len":1513,"char_repetition_ratio":0.12384738,"word_repetition_ratio":0.047402006,"special_character_ratio":0.25961232,"punctuation_ratio":0.12123678,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9794123,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-05T21:52:30Z\",\"WARC-Record-ID\":\"<urn:uuid:e0e9709b-0f22-4d87-88cc-0e1d24aa57c8>\",\"Content-Length\":\"141248\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e952dcfe-a48b-4c85-a52f-a773a48226ba>\",\"WARC-Concurrent-To\":\"<urn:uuid:a60ef9d2-77a2-4b16-844a-52c74481d923>\",\"WARC-IP-Address\":\"172.67.195.44\",\"WARC-Target-URI\":\"https://codingtube.tech/2021/09/17/java/java-array/\",\"WARC-Payload-Digest\":\"sha1:RSBI2U6TRAYFSIZ267U3EBMAHGSXC5W6\",\"WARC-Block-Digest\":\"sha1:PCVKXFOJAEFCRBATO7AZW6AJWSERN6IJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100568.68_warc_CC-MAIN-20231205204654-20231205234654-00104.warc.gz\"}"}
http://serdis.dis.ulpgc.es/~lalvarez/research/demos/ColorStereoFlow/index.html
[ "3-D Geometry reconstruction using a color image\nstereo pair and partial differential equations\nby\nL.Alvarez and J.Sánchez\n\nIn this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a\ncolor image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next,  we\npropose a new model for the disparity estimation based on an energie functional. We look for the local minima of\nthe energy using the associated Euler-Lagrange partial differential equation. This model is a generalization to color\nimage of the model developed by L.Alvarez, R.Deriche, J.Sánchez and J.Weickert in the paper Dense Disparity Map\nEstimation Respecting Image Discontinuities with some changes in the strategy to avoid the irrelevant local minima.\nWe present some numerical experiences of \\$3-D\\$ reconstruction, using this method for some real stereo pairs.\n\nFor more details see the paper 3-D Geometry reconstruction using a color image stereo pair and partial\ndifferential equations\n\nNext we present several experiments to illustrate the method", null, "Figure 1. We present an stereo pair of the face of Javier Sánchez, one of author\nof this work, and 4 views of the 3-D reconstruction using the proposed method. If\nyou click on the image you will see a movie to ilustrate the 3-D reconstruction.", null, "Figure 2. We present an stereo pair of the face of Julio Esclarín, a member of the Comp.\nScience Depart. at the University of Las Palmas, and 4 views of the 3-D reconstruction\nusing the proposed method. If you click on the image you will see a movie to\nilustrate the 3-D reconstruction.", null, "Figure 3. We present an stereo pair of an outdoor scene of the laboratory Instituto Universitario de\nCiencias y Tecnologías Cibernéticas de la Universidad de Las Palmas de G.C., and 4 views of\nthe 3-D reconstruction using the proposed method. If you click on the image you will see a movie to\nilustrate the 3-D reconstruction.\n\nlalvarez@dis.ulpgc.es / updated March 17, 2000" ]
[ null, "http://serdis.dis.ulpgc.es/~lalvarez/research/demos/ColorStereoFlow/JavierColor.JPG", null, "http://serdis.dis.ulpgc.es/~lalvarez/research/demos/ColorStereoFlow/JulioColor.JPG", null, "http://serdis.dis.ulpgc.es/~lalvarez/research/demos/ColorStereoFlow/InstitutoColor.JPG", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.73967755,"math_prob":0.74841255,"size":1595,"snap":"2019-13-2019-22","text_gpt3_token_len":382,"char_repetition_ratio":0.13073538,"word_repetition_ratio":0.20930232,"special_character_ratio":0.19623825,"punctuation_ratio":0.09508197,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9530805,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T20:19:14Z\",\"WARC-Record-ID\":\"<urn:uuid:3eeb6d60-7f92-4e45-8237-65304e03d2a4>\",\"Content-Length\":\"3962\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ef92232e-aa30-4c17-bb18-7eb7649fa871>\",\"WARC-Concurrent-To\":\"<urn:uuid:b265eb5a-ebdd-42c6-b526-ba1d2853dcd3>\",\"WARC-IP-Address\":\"193.145.147.54\",\"WARC-Target-URI\":\"http://serdis.dis.ulpgc.es/~lalvarez/research/demos/ColorStereoFlow/index.html\",\"WARC-Payload-Digest\":\"sha1:TIIDNCKKA7Q4BSTXQ24AJ4KZ5LILTQKI\",\"WARC-Block-Digest\":\"sha1:GPRSNMIEI4SDA6VNT6ELJKKXDJ4BY7VI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202572.29_warc_CC-MAIN-20190321193403-20190321215403-00475.warc.gz\"}"}
https://tutorialspoint.dev/algorithm/mathematical-algorithms/modulo-2-binary-division
[ "# Cyclic Redundancy Check and Modulo-2 Division\n\nCRC or Cyclic Redundancy Check is a method of detecting accidental changes/errors in communication channel.\n\nCRC uses Generator Polynomial which is available on both sender and receiver side. An example generator polynomial is of the form like x3 + x + 1. This generator polynomial represents key 1011. Another example is x2 + 1 that represents key 101.\n\n```n : Number of bits in data to be sent\nfrom sender side.\nk : Number of bits in the key obtained\nfrom generator polynomial. ```\n\nSender Side (Generation of Encoded Data from Data and Generator Polynomial (or Key)):\n\n1. The binary data is first augmented by adding k-1 zeros in the end of the data\n2. Use modulo-2 binary division to divide binary data by the key and store remainder of division.\n3. Append the remainder at the end of the data to form the encoded data and send the same\n4. .\n\nReceiver Side (Check if there are errors introduced in transmission)\nPerform modulo-2 division again and if remainder is 0, then there are no errors.\n\nIn this article we will focus only on finding the remainder i.e. check word and the code word.\n\nModulo 2 Division:\nThe process of modulo-2 binary division is the same as the familiar division process we use for decimal numbers. Just that instead of subtraction, we use XOR here.\n\n• In each step, a copy of the divisor (or data) is XORed with the k bits of the dividend (or key).\n• The result of the XOR operation (remainder) is (n-1) bits, which is used for the next step after 1 extra bit is pulled down to make it n bits long.\n• When there are no bits left to pull down, we have a result. The (n-1)-bit remainder which is appended at the sender side.\n\nIllustration:\n\nExample 1 (No error in transmission):\n\n```Data word to be sent - 100100\nKey - 1101 [ Or generator polynomial x3 + x2 + 1]\n\nSender Side:", null, "Therefore, the remainder is 001 and hence the encoded\ndata sent is 100100001.", null, "Therefore, the remainder is all zeros. Hence, the\ndata received has no error. ```\n\nExample 2: (Error in transmission)\n\n```Data word to be sent - 100100\nKey - 1101\n\nSender Side:", null, "Therefore, the remainder is 001 and hence the\ncode word sent is 100100001.\n\nLet there be error in transmission media", null, "Since the remainder is not all zeroes, the error\nis detected at the receiver side.\n\nImplementation\nBelow is Python implementation for generating code word from given binary data and key.\n\n`# Returns XOR of 'a' and 'b' `\n`# (both of same length) `\n`def` `xor(a, b): `\n` `\n`    ``# initialize result `\n`    ``result ``=` `[] `\n` `\n`    ``# Traverse all bits, if bits are `\n`    ``# same, then XOR is 0, else 1 `\n`    ``for` `i ``in` `range``(``1``, ``len``(b)): `\n`        ``if` `a[i] ``=``=` `b[i]: `\n`            ``result.append(``'0'``) `\n`        ``else``: `\n`            ``result.append(``'1'``) `\n` `\n`    ``return` `''.join(result) `\n` `\n` `\n`# Performs Modulo-2 division `\n`def` `mod2div(divident, divisor): `\n` `\n`    ``# Number of bits to be XORed at a time. `\n`    ``pick ``=` `len``(divisor) `\n` `\n`    ``# Slicing the divident to appropriate `\n`    ``# length for particular step `\n`    ``tmp ``=` `divident[``0` `: pick] `\n` `\n`    ``while` `pick < ``len``(divident): `\n` `\n`        ``if` `tmp[``0``] ``=``=` `'1'``: `\n` `\n`            ``# replace the divident by the result `\n`            ``# of XOR and pull 1 bit down `\n`            ``tmp ``=` `xor(divisor, tmp) ``+` `divident[pick] `\n` `\n`        ``else``:   ``# If leftmost bit is '0' `\n`            ``# If the leftmost bit of the dividend (or the `\n`            ``# part used in each step) is 0, the step cannot `\n`            ``# use the regular divisor; we need to use an `\n`            ``# all-0s divisor. `\n`            ``tmp ``=` `xor(``'0'``*``pick, tmp) ``+` `divident[pick] `\n` `\n`        ``# increment pick to move further `\n`        ``pick ``+``=` `1`\n` `\n`    ``# For the last n bits, we have to carry it out `\n`    ``# normally as increased value of pick will cause `\n`    ``# Index Out of Bounds. `\n`    ``if` `tmp[``0``] ``=``=` `'1'``: `\n`        ``tmp ``=` `xor(divisor, tmp) `\n`    ``else``: `\n`        ``tmp ``=` `xor(``'0'``*``pick, tmp) `\n` `\n`    ``checkword ``=` `tmp `\n`    ``return` `checkword `\n` `\n`# Function used at the sender side to encode `\n`# data by appending remainder of modular divison `\n`# at the end of data. `\n`def` `encodeData(data, key): `\n` `\n`    ``l_key ``=` `len``(key) `\n` `\n`    ``# Appends n-1 zeroes at end of data `\n`    ``appended_data ``=` `data ``+` `'0'``*``(l_key``-``1``) `\n`    ``remainder ``=` `mod2div(appended_data, key) `\n` `\n`    ``# Append remainder in the original data `\n`    ``codeword ``=` `data ``+` `remainder `\n`    ``print``(``\"Remainder : \"``, remainder) `\n`    ``print``(``\"Encoded Data (Data + Remainder) : \"``, `\n`          ``codeword) `\n` `\n`# Driver code `\n`data ``=` `\"100100\"`\n`key ``=` `\"1101\"`\n`encodeData(data, key) `\n\nOutput:\nRemainder : 001\nEncoded Data (Data + Remainder) : 100100001\n\nNote that CRC is mainly designed and used to protect against common of errors on communication channels and NOT suitable protection against intentional alteration of data (See reasons here)\nReferences:\nhttps://en.wikipedia.org/wiki/Cyclic_redundancy_check\n\n```" ]
[ null, "https://tutorialspoint.dev/image/rational1.jpg", null, "https://tutorialspoint.dev/image/rational2.jpg", null, "https://tutorialspoint.dev/image/rational1.jpg", null, "https://tutorialspoint.dev/image/rational4.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.79121685,"math_prob":0.8645169,"size":4585,"snap":"2021-43-2021-49","text_gpt3_token_len":1207,"char_repetition_ratio":0.12137088,"word_repetition_ratio":0.05966587,"special_character_ratio":0.2791712,"punctuation_ratio":0.10660487,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99865013,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,4,null,2,null,4,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T02:38:46Z\",\"WARC-Record-ID\":\"<urn:uuid:d6b3fce3-6131-4594-8ebc-04e3a04f9e8a>\",\"Content-Length\":\"38609\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b711104a-5417-44ed-a8ad-5c31c20db9db>\",\"WARC-Concurrent-To\":\"<urn:uuid:0d1b7e16-4c85-464d-9560-08771f8c4050>\",\"WARC-IP-Address\":\"172.67.169.89\",\"WARC-Target-URI\":\"https://tutorialspoint.dev/algorithm/mathematical-algorithms/modulo-2-binary-division\",\"WARC-Payload-Digest\":\"sha1:WEU6VZ2WUW43CKCBM4UINOLVGE2STMDB\",\"WARC-Block-Digest\":\"sha1:RVNQCSMXVGU5SQCZITL6DLYKIUHXZDQI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585380.70_warc_CC-MAIN-20211021005314-20211021035314-00394.warc.gz\"}"}
http://songcharts.tk/calculate-average-daily-range-forex-606653.html
[ "Calculate average daily range forex", null, "Average True Range Spreadsheet & Tutorial - Invest Excel\n\nAre you looking for an ADR indicator for MT4? Today, I'm going to show you what is, in my opinion, the best average daily range indicator for MetaTrader 4.", null, "Multi Range Calculator Metatrader 4 Indicator\n\nThe Average True Range The average range is also a good indicator to use for filtering which consists of news, opinions, daily and weekly forex analysis,", null, "5 Day Average Daily Range — Indicator by IamTheDudeMan\n\nHow to Calculate the Daily Range for Forex. we’re going to teach you all about the daily range, how to calculate the daily range, (Average Directional Movement)", null, "What Is Forex? - BabyPips.com\n\nDiscover how average true range is used as a stop-loss indicator in trading strategies, and learn how to calculate it in Excel. This volatility indicator is used to", null, "Average Daily Range Pro Calculator Metatrader 4 Indicator", null, "Average True Range (ATR) | Measure Market - FOREX.com\n\nHow to calculate ADR (Average Daily Range) This will give you the average daily range. Forex Average Pips: 250-300/month. Email: i_ipun[at]yahoo.com. Edward Revy,", null, "How to Use ATR in a Forex Strategy - Forex Trading News\n\nAverage Daily Range Pro Calculator. Scam or not - Click here to find out.", null, "Average True Range (ATR) - TradingView Wiki\n\nIf you are trading any kind of intraday forex system, then it's always a good idea to be fully aware of the average daily range of the pair(s) you are trading.", null, "Currencies Average daily range - Forex Market Hours\n\nAverage Daily Range Calculator . You can install and use the ADR Calculator with the MetaTrader 4.0 trading platform provided by any Forex broker.", null, "How to Trade Using the Average True Range Indicator\n\nHome Forex Blog Forex Tips – Be Wary of Average Daily Ranges. Forex Tips – Be Wary of Average Daily Ranges. where should you calculate the ADR range,", null, "How to Calculate the Daily Range for Forex | Investoo.com\n\n2019-03-12 · You can calculate the average high-low range on a piece of paper, The next day, the price opens gap up, but the daily range is the same \\$2.", null, "Forex Volatility - Mataf\n\nHow do we calculate the Average Daily Range? By taking the difference of the high and low of the trading day, you calculate the daily range. But you must be", null, "32# ADR (Average Day Range) Strategy Trading System. How to calculate ADR (Average Daily Range) Forex Indicator Average Range.", null, "CompassFX | Average Daily Range Calculator - ADR\n\nThe average true range indicator is an In order to calculate the average true range, you take the average of each true range value over a fixed period of", null, "Daily Range Calculator Metatrader 4 Indicator - fxtsp.com\n\nForex Volatility. Add our content on The volatility calculated on this page is called Average true range let's calculate the volatility of the Euro dollar", null, "The Average Daily Range Of The Major Forex Currency Pairs\n\n2018-07-04 · Forex, also known as Position Size Calculator; Check out the graph of the average daily trading volume for the forex market,", null, "How to Use the Average Daily Range When Trading Forex\n\nThe indicator I am referring to is called Average Daily Range How to Calculate ADR. The calculation of the daily range of a Average Daily Range of a Forex", null, "Foreign Exchange Volatility | Currency Movement | Forex\n\n0 Average Daily Range Pro Calculator Metatrader 4 Indicator. This indicator measures the average daily range (volatility) for the following time periods: 5 days", null, "I am working with daily data and 21 trading days corresponds to approximately one month. In column G we will calculate the AVERAGE of column F (true range).", null, "How to Analyze the Average Trading Range - dummies\n\n2008-09-23 · 100 pip movements and daily average movement. uses the average daily range of the past 10 days to calculate entry/exit and SL (look on the Forex Systems", null, "Calculating Average True Range (ATR) in Excel - Macroption\n\n2013-10-28 · How to Use ATR in a Forex Strategy. Average True Range Talking Points: Forex traders can use ATR to gauge market Get daily market analysis from our", null, "Measuring Volatility with Average True Range - DailyFX\n\nThis is an outside day that would use Method 1 to calculate and the first 14-day ATR is the average of the daily TR The Average True Range indicator can", null, "Average Daily Range 2010 - Currency Forecasts\n\nLearn about Average True Range and how to identify it on a forex chart.", null, "", null, "" ]
[ null, "https://c.mql5.com/31/36/average-daily-range-screen-9179.png", null, "http://www.billlions.com/wp-content/uploads/2016/03/ADR-bad-low-adr-200x200.png", null, "http://www.forex-tsd.com/attachments/metatrader-4/138268d1338419678-average-day-range-indicator-adr-daily-adr.png", null, "https://www.panduantrading.com/assets/uploads/2017/10/Average-Daily-Range-Pro-Calculator-Indicator-816x424.jpg", null, "http://forexwinners.ru/wp-content/uploads/2014/01/Average-Daily-Range-Pro-Calculator-660x330.jpg", null, "https://media.giphy.com/media/l0HefOZVMXvIHC5ry/giphy.gif", null, "http://investexcel.net/wp-content/uploads/2012/04/Average-True-Range-Excel.png", null, "https://www.panduantrading.com/assets/uploads/2017/09/Daily-Average-Range-cpy-04.jpg", null, "http://www.billlions.com/wp-content/uploads/2016/03/ADR-bad-low-adr.png", null, "http://forex-indicators.net/files/indicators/truerange.png", null, "http://www.dolphintrader.com/wp-content/uploads/2014/01/average-daily-range-pro-indicator-mt4.png", null, "http://www.fxtsp.com/wp-content/uploads/2010/02/100-daily-range_calculator-metatrader-4-indicator.gif", null, "http://www.compassfx.com/images/adr_pro_2_lg.jpg", null, "http://forexwinners.net/wp-content/uploads/2013/05/Range.jpg", null, "http://mt4indicators.com/wp-content/uploads/2015/03/ADR_TheGreedyPig-640x439.png", null, "https://c.mql5.com/3/145/brentcrud-d1-fx-choice-limited.png", null, "https://i.ytimg.com/vi/15mvligjgoo/maxresdefault.jpg", null, "https://forex-station.com/download/file.php", null, "http://www.forex-indikatoren.com/wp-content/uploads/2017/04/average-daily-range.png", null, "http://www.billlions.com/wp-content/uploads/2016/03/ADR-good-high-adr-500x500.png", null, "https://c.mql5.com/forextsd/forum/63/hroutput01.jpg", null, "http://www.investoo.com/wp-content/uploads/2015/05/Screen-Shot-2015-05-11-at-14.37.23.png", null, "https://c.mql5.com/forextsd/forum/63/mp_mtf_pj9100_001com.jpg", null, "http://forexzz.com/wp-content/uploads/2015/11/adr-calc.png", null, "https://c.mql5.com/forextsd/forum/150/12-03-2015_6-34-59_am.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8285965,"math_prob":0.91635424,"size":4918,"snap":"2019-26-2019-30","text_gpt3_token_len":1086,"char_repetition_ratio":0.25600326,"word_repetition_ratio":0.057692308,"special_character_ratio":0.21207808,"punctuation_ratio":0.0706278,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97916216,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null,null,null,3,null,3,null,null,null,3,null,3,null,3,null,3,null,7,null,4,null,3,null,null,null,3,null,3,null,null,null,null,null,null,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-26T20:00:24Z\",\"WARC-Record-ID\":\"<urn:uuid:d28bf4ea-56a1-409e-a6f0-0fb9bb7b21a1>\",\"Content-Length\":\"18618\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5b576b8-edc7-4dca-8422-787f179e2a99>\",\"WARC-Concurrent-To\":\"<urn:uuid:008efc97-4790-4aa5-a659-0a153068b03d>\",\"WARC-IP-Address\":\"104.24.118.121\",\"WARC-Target-URI\":\"http://songcharts.tk/calculate-average-daily-range-forex-606653.html\",\"WARC-Payload-Digest\":\"sha1:3BDW5QHQA5GS66YEB2Q5KPPAFHYK3NX4\",\"WARC-Block-Digest\":\"sha1:LR3RG5OYKZDTORX6WFI2E5BNLXYIU7BT\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560628000545.97_warc_CC-MAIN-20190626194744-20190626220744-00368.warc.gz\"}"}
https://huaibei.home.focus.cn/gonglue/5e84e6b4a91042e1.html
[ "|\n\n# 安装厨房推拉门 节省厨房空间\n\n安装厨房推拉门不但可以节省家居空间，还能起到一定的装饰效果，因此，厨房推拉门现在越来越受到人们的欢迎。那么，如何安装厨房推拉门呢？首先要根据房屋结构、空间大小和使用功能来设计。这可不是一件简单的事哦，下面就让我们来带您详细的了解一下。", null, "安装厨房推拉门\n\n1、上滑道安装\n\n上滑道安装时必须按门洞宽度和开启方向的要求将其同门梁或雨蓬梁进行固定一般以门洞宽度的中心为基准两分固定时要注意以下要点滑道同雨蓬梁或门梁连接处的左右标高一致滑道相对于门洞中心尺寸一致。滑道中心线与彩板外墙或砖墙外边的尺寸一致且其尺寸为门扇厚度的一半外加20mm的间隙如为彩板外墙尚需另加20mm的包边宽度。\n\n2、门扇安装\n\n门扇及滑轮系统由公司在车间内加工成型。上滑道安装结束后随即将滑轮成对放入滑道滑槽内然后用人工或其它吊装工具将门扇竖直运到其下方并将门扇上焊接的螺杆套入滑轮上的螺栓孔内用双螺帽临时紧固。同理将另一门扇先行挂起。\n\n3、门扇调整\n\n门扇均已挂好后将二个门扇均推到门洞中心位置并将其贴紧按室外地坪标高的要求将门扇下扁钢调到地坪上表面0～10mm同时调整两门扇连接处的缝隙到最小且侧边垂直于地面。标高调整用松紧上面的螺帽进行。门扇全部调整结束后将滑轮上的止推销用开口销固定在滑轮上。\n\n4、门上限位器\n\n安装门扇全部调整完后将门扇分别全部关闭和推开根据其位置将上滑道底部或内部用角钢上限位器焊接在距离滑轮边10mm的地方使门扇的开启区域限制在其有效范围内。角钢与滑轮接触处要求设置不小于20mm的硬质橡胶垫作为缓冲。", null, "5、导饼和门下限位器安装\n\n导饼和门下限位器安装要求同土建配合进行其要点是导饼中心线定位可按门扇下扁钢的实际位置进行定位导饼露出地面为10～15mm间距为500mm。下限位器定位时以将门扇推到距外边10～20mm位置外埋入砼中或砼施工完后用膨胀螺栓固定。\n\n6、门五金配件安装\n\n厨房推拉门的五金配件常用的有门拉手、锁扣可在门安装调整全部结束且无误后进行按各工程所先用的五金配件的安装要求分别进行应注意所的配件的平面位置和标高要求均在同一位置以影响美观。\n\n`声明：本文由入驻焦点开放平台的作者撰写，除焦点官方账号外，观点仅代表作者本人，不代表焦点立场错误信息举报电话： 400-099-0099，邮箱：jubao@vip.sohu.com，或点此进行意见反馈，或点此进行举报投诉。`", null, "A B C D E F G H J K L M N P Q R S T W X Y Z\nA - B - C - D - E\n• A\n• 鞍山\n• 安庆\n• 安阳\n• 安顺\n• 安康\n• 澳门\n• B\n• 北京\n• 保定\n• 包头\n• 巴彦淖尔\n• 本溪\n• 蚌埠\n• 亳州\n• 滨州\n• 北海\n• 百色\n• 巴中\n• 毕节\n• 保山\n• 宝鸡\n• 白银\n• 巴州\n• C\n• 承德\n• 沧州\n• 长治\n• 赤峰\n• 朝阳\n• 长春\n• 常州\n• 滁州\n• 池州\n• 长沙\n• 常德\n• 郴州\n• 潮州\n• 崇左\n• 重庆\n• 成都\n• 楚雄\n• 昌都\n• 慈溪\n• 常熟\n• D\n• 大同\n• 大连\n• 丹东\n• 大庆\n• 东营\n• 德州\n• 东莞\n• 德阳\n• 达州\n• 大理\n• 德宏\n• 定西\n• 儋州\n• 东平\n• E\n• 鄂尔多斯\n• 鄂州\n• 恩施\nF - G - H - I - J\n• F\n• 抚顺\n• 阜新\n• 阜阳\n• 福州\n• 抚州\n• 佛山\n• 防城港\n• G\n• 赣州\n• 广州\n• 桂林\n• 贵港\n• 广元\n• 广安\n• 贵阳\n• 固原\n• H\n• 邯郸\n• 衡水\n• 呼和浩特\n• 呼伦贝尔\n• 葫芦岛\n• 哈尔滨\n• 黑河\n• 淮安\n• 杭州\n• 湖州\n• 合肥\n• 淮南\n• 淮北\n• 黄山\n• 菏泽\n• 鹤壁\n• 黄石\n• 黄冈\n• 衡阳\n• 怀化\n• 惠州\n• 河源\n• 贺州\n• 河池\n• 海口\n• 红河\n• 汉中\n• 海东\n• I\n• J\n• 晋中\n• 锦州\n• 吉林\n• 鸡西\n• 佳木斯\n• 嘉兴\n• 金华\n• 景德镇\n• 九江\n• 吉安\n• 济南\n• 济宁\n• 焦作\n• 荆门\n• 荆州\n• 江门\n• 揭阳\n• 金昌\n• 酒泉\n• 嘉峪关\nK - L - M - N - P\n• K\n• 开封\n• 昆明\n• 昆山\n• L\n• 廊坊\n• 临汾\n• 辽阳\n• 连云港\n• 丽水\n• 六安\n• 龙岩\n• 莱芜\n• 临沂\n• 聊城\n• 洛阳\n• 漯河\n• 娄底\n• 柳州\n• 来宾\n• 泸州\n• 乐山\n• 六盘水\n• 丽江\n• 临沧\n• 拉萨\n• 林芝\n• 兰州\n• 陇南\n• M\n• 牡丹江\n• 马鞍山\n• 茂名\n• 梅州\n• 绵阳\n• 眉山\n• N\n• 南京\n• 南通\n• 宁波\n• 南平\n• 宁德\n• 南昌\n• 南阳\n• 南宁\n• 内江\n• 南充\n• P\n• 盘锦\n• 莆田\n• 平顶山\n• 濮阳\n• 攀枝花\n• 普洱\n• 平凉\nQ - R - S - T - W\n• Q\n• 秦皇岛\n• 齐齐哈尔\n• 衢州\n• 泉州\n• 青岛\n• 清远\n• 钦州\n• 黔南\n• 曲靖\n• 庆阳\n• R\n• 日照\n• 日喀则\n• S\n• 石家庄\n• 沈阳\n• 双鸭山\n• 绥化\n• 上海\n• 苏州\n• 宿迁\n• 绍兴\n• 宿州\n• 三明\n• 上饶\n• 三门峡\n• 商丘\n• 十堰\n• 随州\n• 邵阳\n• 韶关\n• 深圳\n• 汕头\n• 汕尾\n• 三亚\n• 三沙\n• 遂宁\n• 山南\n• 商洛\n• 石嘴山\n• T\n• 天津\n• 唐山\n• 太原\n• 通辽\n• 铁岭\n• 泰州\n• 台州\n• 铜陵\n• 泰安\n• 铜仁\n• 铜川\n• 天水\n• 天门\n• W\n• 乌海\n• 乌兰察布\n• 无锡\n• 温州\n• 芜湖\n• 潍坊\n• 威海\n• 武汉\n• 梧州\n• 渭南\n• 武威\n• 吴忠\n• 乌鲁木齐\nX - Y - Z\n• X\n• 邢台\n• 徐州\n• 宣城\n• 厦门\n• 新乡\n• 许昌\n• 信阳\n• 襄阳\n• 孝感\n• 咸宁\n• 湘潭\n• 湘西\n• 西双版纳\n• 西安\n• 咸阳\n• 西宁\n• 仙桃\n• 西昌\n• Y\n• 运城\n• 营口\n• 盐城\n• 扬州\n• 鹰潭\n• 宜春\n• 烟台\n• 宜昌\n• 岳阳\n• 益阳\n• 永州\n• 阳江\n• 云浮\n• 玉林\n• 宜宾\n• 雅安\n• 玉溪\n• 延安\n• 榆林\n• 银川\n• Z\n• 张家口\n• 镇江\n• 舟山\n• 漳州\n• 淄博\n• 枣庄\n• 郑州\n• 周口\n• 驻马店\n• 株洲\n• 张家界\n• 珠海\n• 湛江\n• 肇庆\n• 中山\n• 自贡\n• 资阳\n• 遵义\n• 昭通\n• 张掖\n• 中卫\n\n1室1厅1厨1卫1阳台\n\n1\n2\n3\n4\n5\n\n0\n1\n2\n\n1\n\n1\n\n0\n1\n2\n3", null, "", null, "", null, "报名成功，资料已提交审核", null, "A B C D E F G H J K L M N P Q R S T W X Y Z\nA - B - C - D - E\n• A\n• 鞍山\n• 安庆\n• 安阳\n• 安顺\n• 安康\n• 澳门\n• B\n• 北京\n• 保定\n• 包头\n• 巴彦淖尔\n• 本溪\n• 蚌埠\n• 亳州\n• 滨州\n• 北海\n• 百色\n• 巴中\n• 毕节\n• 保山\n• 宝鸡\n• 白银\n• 巴州\n• C\n• 承德\n• 沧州\n• 长治\n• 赤峰\n• 朝阳\n• 长春\n• 常州\n• 滁州\n• 池州\n• 长沙\n• 常德\n• 郴州\n• 潮州\n• 崇左\n• 重庆\n• 成都\n• 楚雄\n• 昌都\n• 慈溪\n• 常熟\n• D\n• 大同\n• 大连\n• 丹东\n• 大庆\n• 东营\n• 德州\n• 东莞\n• 德阳\n• 达州\n• 大理\n• 德宏\n• 定西\n• 儋州\n• 东平\n• E\n• 鄂尔多斯\n• 鄂州\n• 恩施\nF - G - H - I - J\n• F\n• 抚顺\n• 阜新\n• 阜阳\n• 福州\n• 抚州\n• 佛山\n• 防城港\n• G\n• 赣州\n• 广州\n• 桂林\n• 贵港\n• 广元\n• 广安\n• 贵阳\n• 固原\n• H\n• 邯郸\n• 衡水\n• 呼和浩特\n• 呼伦贝尔\n• 葫芦岛\n• 哈尔滨\n• 黑河\n• 淮安\n• 杭州\n• 湖州\n• 合肥\n• 淮南\n• 淮北\n• 黄山\n• 菏泽\n• 鹤壁\n• 黄石\n• 黄冈\n• 衡阳\n• 怀化\n• 惠州\n• 河源\n• 贺州\n• 河池\n• 海口\n• 红河\n• 汉中\n• 海东\n• I\n• J\n• 晋中\n• 锦州\n• 吉林\n• 鸡西\n• 佳木斯\n• 嘉兴\n• 金华\n• 景德镇\n• 九江\n• 吉安\n• 济南\n• 济宁\n• 焦作\n• 荆门\n• 荆州\n• 江门\n• 揭阳\n• 金昌\n• 酒泉\n• 嘉峪关\nK - L - M - N - P\n• K\n• 开封\n• 昆明\n• 昆山\n• L\n• 廊坊\n• 临汾\n• 辽阳\n• 连云港\n• 丽水\n• 六安\n• 龙岩\n• 莱芜\n• 临沂\n• 聊城\n• 洛阳\n• 漯河\n• 娄底\n• 柳州\n• 来宾\n• 泸州\n• 乐山\n• 六盘水\n• 丽江\n• 临沧\n• 拉萨\n• 林芝\n• 兰州\n• 陇南\n• M\n• 牡丹江\n• 马鞍山\n• 茂名\n• 梅州\n• 绵阳\n• 眉山\n• N\n• 南京\n• 南通\n• 宁波\n• 南平\n• 宁德\n• 南昌\n• 南阳\n• 南宁\n• 内江\n• 南充\n• P\n• 盘锦\n• 莆田\n• 平顶山\n• 濮阳\n• 攀枝花\n• 普洱\n• 平凉\nQ - R - S - T - W\n• Q\n• 秦皇岛\n• 齐齐哈尔\n• 衢州\n• 泉州\n• 青岛\n• 清远\n• 钦州\n• 黔南\n• 曲靖\n• 庆阳\n• R\n• 日照\n• 日喀则\n• S\n• 石家庄\n• 沈阳\n• 双鸭山\n• 绥化\n• 上海\n• 苏州\n• 宿迁\n• 绍兴\n• 宿州\n• 三明\n• 上饶\n• 三门峡\n• 商丘\n• 十堰\n• 随州\n• 邵阳\n• 韶关\n• 深圳\n• 汕头\n• 汕尾\n• 三亚\n• 三沙\n• 遂宁\n• 山南\n• 商洛\n• 石嘴山\n• T\n• 天津\n• 唐山\n• 太原\n• 通辽\n• 铁岭\n• 泰州\n• 台州\n• 铜陵\n• 泰安\n• 铜仁\n• 铜川\n• 天水\n• 天门\n• W\n• 乌海\n• 乌兰察布\n• 无锡\n• 温州\n• 芜湖\n• 潍坊\n• 威海\n• 武汉\n• 梧州\n• 渭南\n• 武威\n• 吴忠\n• 乌鲁木齐\nX - Y - Z\n• X\n• 邢台\n• 徐州\n• 宣城\n• 厦门\n• 新乡\n• 许昌\n• 信阳\n• 襄阳\n• 孝感\n• 咸宁\n• 湘潭\n• 湘西\n• 西双版纳\n• 西安\n• 咸阳\n• 西宁\n• 仙桃\n• 西昌\n• Y\n• 运城\n• 营口\n• 盐城\n• 扬州\n• 鹰潭\n• 宜春\n• 烟台\n• 宜昌\n• 岳阳\n• 益阳\n• 永州\n• 阳江\n• 云浮\n• 玉林\n• 宜宾\n• 雅安\n• 玉溪\n• 延安\n• 榆林\n• 银川\n• Z\n• 张家口\n• 镇江\n• 舟山\n• 漳州\n• 淄博\n• 枣庄\n• 郑州\n• 周口\n• 驻马店\n• 株洲\n• 张家界\n• 珠海\n• 湛江\n• 肇庆\n• 中山\n• 自贡\n• 资阳\n• 遵义\n• 昭通\n• 张掖\n• 中卫", null, "", null, "• 手机", null, "• 分享\n• 设计\n免费设计\n• 计算器\n装修计算器\n• 入驻\n合作入驻\n• 联系\n联系我们\n• 置顶\n返回顶部" ]
[ null, "https://t1.focus-img.cn/sh740wsh/zx/duplication/5f12c893-6579-4423-ba0f-ea94e20e5d70.JPEG", null, "https://t1.focus-img.cn/sh740wsh/zx/duplication/648aa9ac-bfc2-4a4e-bec2-2a643c530a06.JPEG", null, "data:image/png;base64,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", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAACwElEQVRYR+3XT0gUURwH8N97s5qiuEqEilb7lPWwO0g0S3WQsoMlWdHB9hB0kEiJwIjyFkIXCyQqD4V2CBI6bEGBCJZEf/BQsAMhdnAG3XVVVDr4B8XZ0ZlfTLXkbK2z7rogNHvcN+/3PvP9/VjeEkTkYAd9iA2y6IadkNW42gnZCVklYLX+/85Q2Odzu4JBeUckNOHxnNVUNUAovc0k6c5mqIy3bMLjOamp6itAzDYghNIOJsvtiVAZBUW83lpNUfoQIDcGIAA6l5d3aN/w8Nd/oTIGivD8kXVFGQDE/A0YJBx3ySVJz9JKaKalZVdpd3fUaiBj65M8f3BtdXUQAJymPZRerZDl7rRmKOz1nsZo9BHk5JxiIyMjVqgQz/OgKO8QcffGZ4nDcZONjj6w2r9py8IeT6Ouqr2AmEUA5mhh4fH9oiglKjohCFX6wsJ7BCg2YTiunUlShxXm59AnuqBFqqsPaCsrXxDgz42SkOlsp7O2XBRD8cWnBIGpi4sfALFs4xql9K5Llm8lg9kUZCyOV1XdA027ZnpbgHBOUdGx0mBwOvb9jM9XpszPf0QAl+lgjntYIUk3ksVYgowHQm73Y9T1y6aihMhZJSW1e4eG5iZraorXZmeNZNwmOKVPmCxf2QomKdBv1FPU9YtxqG+OggL/+tJSABC9cZheJstNW8UkDYKeHhrq7HyOut4Y1z7NNGO/folfsra2C9DcrGcOZFRubXWE+vtfIMCZRAcRgD7W0HAeurrWU8Ekn1Csut+fHRLF1whwIv5AAvCWCcI5CATUVDFbBwHAd78/d1kU+xHgaOxgAvApXxAa9gQCq+lgUgIZm+br6vIXxsffIMBhQsjnQsbqiwYHl9PFpAwyNk7V1zvXxsbuZ1VWXi8fGFjcDkxaoO0C/DWL9n97i2gzdkFLtaU2yCo5OyGrhH4AtD5LNJ/vw8QAAAAASUVORK5CYII=", null, "https://huaibei.home.focus.cn/gonglue/5e84e6b4a91042e1.html", null, "https://t1.focus-res.cn/front-pc/module/loupan-baoming/images/yes.png", null, "https://t1.focus-res.cn/front-pc/module/loupan-baoming/images/qrcode.png", null, "data:image/png;base64,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", null, "https://t.focus-res.cn/home-front/pc/img/qrcode.d7cfc15.png", null, "data:image/png;base64,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", null ]
{"ft_lang_label":"__label__zh","ft_lang_prob":0.92394084,"math_prob":0.45310748,"size":870,"snap":"2020-24-2020-29","text_gpt3_token_len":1029,"char_repetition_ratio":0.045034643,"word_repetition_ratio":0.0,"special_character_ratio":0.11034483,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999534,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,1,null,1,null,null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T04:58:14Z\",\"WARC-Record-ID\":\"<urn:uuid:d6a112d3-9be7-4db2-9e42-5f4887521f9a>\",\"Content-Length\":\"144452\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f981bdff-d582-44ff-b2cb-c64c4702e42c>\",\"WARC-Concurrent-To\":\"<urn:uuid:3d13e39c-8e2d-4921-ab6c-7aa4e488aa11>\",\"WARC-IP-Address\":\"42.63.21.227\",\"WARC-Target-URI\":\"https://huaibei.home.focus.cn/gonglue/5e84e6b4a91042e1.html\",\"WARC-Payload-Digest\":\"sha1:EANU4SAAWLC4RELX6WQDBNN2EEG62LCU\",\"WARC-Block-Digest\":\"sha1:AK73IRAD77U4WCYQ3VPIAWRYE7LOOQKR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347401260.16_warc_CC-MAIN-20200529023731-20200529053731-00169.warc.gz\"}"}
https://www.geeksforgeeks.org/spacing-between-boxplots-in-ggplot2-in-r/?ref=rp
[ "# Spacing between boxplots in ggplot2 in R\n\n• Last Updated : 18 Jul, 2021\n\nIn this article, we are going to see how to add space between the boxplots in ggplot2 using R programming language.\n\nDataset in use: Crop_recommendation\n\n### Method 1: Using width between boxplot\n\nHere we will use width attributes to define space between the boxplot. In this the value is passed to the attribute.\n\nSyntax: geom_boxplot(width)\n\nProgram:\n\n## R\n\n `library``(ggplot2)`` ` `# loading data set and storing it in ds variable``df <- ``read.csv``(``\"Crop_recommendation.csv\"``, header = ``TRUE``)`` ` `# create a boxplot by using geom_boxplot() function``# of ggplot2 package``plot = ``ggplot``(data=df,``              ``mapping=``aes``(``                ``x=label, y=temperature))+``geom_boxplot``(width = 0.5)``plot `\n\nOutput:", null, "### Method 2: Using position_dodge\n\nHere we will use position_dodge to define the vertical position of a geom while adjusting the horizontal position. position_dodge() requires the grouping variable to be specified position.\n\nSyntax:\n\ngeom_boxplot( position = position_dodge(width))\n\nProgram:\n\n## Python3\n\n `library(ggplot2)`` ` `# loading data set and storing it in ds variable``df <``-` `read.csv(``\"Crop_recommendation.csv\"``, header ``=` `TRUE)`` ` `# create a boxplot by using geom_boxplot() function``# of ggplot2 package``plot``=` `ggplot(data``=``df,``             ``mapping``=``aes(x``=``label, ``                         ``y``=``temperature))``+``geom_boxplot(width``=``0.1``, position ``=` `position_dodge(width``=``0.5``))``plot`\n\nOutput:", null, "My Personal Notes arrow_drop_up" ]
[ null, "https://media.geeksforgeeks.org/wp-content/uploads/20210701115856/Capture-660x574.PNG", null, "https://media.geeksforgeeks.org/wp-content/uploads/20210701115856/Capture-660x574.PNG", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.55585873,"math_prob":0.9469237,"size":1367,"snap":"2022-40-2023-06","text_gpt3_token_len":359,"char_repetition_ratio":0.14966984,"word_repetition_ratio":0.16346154,"special_character_ratio":0.24725677,"punctuation_ratio":0.12719299,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98836446,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,8,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T01:38:33Z\",\"WARC-Record-ID\":\"<urn:uuid:6fcee1b3-8048-4ebb-9fdb-1d0d663001f2>\",\"Content-Length\":\"130244\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d646942c-b111-4d9c-9dcc-2c0c15485603>\",\"WARC-Concurrent-To\":\"<urn:uuid:faf74eae-b92b-4b96-a4e8-975cc5a2207d>\",\"WARC-IP-Address\":\"104.97.85.137\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/spacing-between-boxplots-in-ggplot2-in-r/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:75ZL7CIDIHGY4MS7CWQT2IIZRIHY4WQA\",\"WARC-Block-Digest\":\"sha1:RCRLCNYHHOXTRFS4OQBHQVMKRI7LZ3CV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337446.8_warc_CC-MAIN-20221003231906-20221004021906-00314.warc.gz\"}"}
https://www.wilsonware.com/electronics/series_parallel_circuits.htm
[ "Series/Parallel Circuits Click one of the buttons above to move to that topic.\n Your browser does not support Java Applets Circuits consisting of both series and parallel elements are series-parallel circuits. RESISTANCE IN SERIES-PARALLEL CIRCUITS Equivalent circuits are used to find series-parallel resistance. REDRAWING CIRCUITS FOR CLARITY Circuits can be redrawn to make current flow understandable. Steps for Redrawing the Circuit for Clarity Trace the current paths in the circuit. Label the nodes (junctions) in the circuit. Recognize points that are the same voltage Visualize a rearrangement Redraw into a simpler form REDRAWING A SERIES-PARALLEL CIRCUIT Start with the negative terminal of the voltage source and follow the current flow through the components. SERIES-PARALLEL CIRCUIT ANALYSIS Reduce all parallel circuits to series-equivalent resistances. Combine all the branches containing more than one resistance in series into a single resistance. Redraw the resulting equivalent circuit and determine the equivalent resistance of the whole circuit. When the series-parallel circuit has been simplified, solve for the total current, voltage, or power, as required. To obtain a complete solution for the series-parallel circuit, find the individual component values by using the values obtained in the equivalent circuit and applying them to the original circuit. Solve for individual voltage, current, or power, as required. WHEATSTONE BRIDGE A series parallel circuit which is useful for rectifiers and measuring instruments is a bridge. A wheatstone bridge is a special measuring instrument. Balancing the bridge One of the resistances can be adjusted until there is zero current flow between the junction at the middle of each parallel branch. TROUBLESHOOTING SERIES-PARALLEL CIRCUITS Troubleshooting often involves isolating the circuit into smaller parallel or series elements." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.81210154,"math_prob":0.9598569,"size":1043,"snap":"2019-51-2020-05","text_gpt3_token_len":233,"char_repetition_ratio":0.14051972,"word_repetition_ratio":0.0,"special_character_ratio":0.1581975,"punctuation_ratio":0.055555556,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9726689,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-08T21:36:15Z\",\"WARC-Record-ID\":\"<urn:uuid:6da7a5c8-8197-488b-a25c-9bf5b29afd1f>\",\"Content-Length\":\"8595\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3d160e2-183d-4ec4-ba4a-0ef0e0d69a6d>\",\"WARC-Concurrent-To\":\"<urn:uuid:9264f813-70e6-429a-9450-9bf33376a29d>\",\"WARC-IP-Address\":\"173.236.159.173\",\"WARC-Target-URI\":\"https://www.wilsonware.com/electronics/series_parallel_circuits.htm\",\"WARC-Payload-Digest\":\"sha1:J3CTCTVM6UR2A6VSZVFGPZ24OSVNYGGJ\",\"WARC-Block-Digest\":\"sha1:7HCIXJIJZ66PE3Q5IMG3PM47VBQ6UM3F\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540514893.41_warc_CC-MAIN-20191208202454-20191208230454-00517.warc.gz\"}"}
https://www.nationaltrustcollections.org.uk/results?ObjectType=saucer+dish
[ "## You searched , Object Type: “saucer dish”\n\nShow me:\nand\n\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 8 items Explore\n• Explore\n• Explore\n• Explore\n• 12 items Explore\n• Explore\n• Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 32 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• 4 items Explore\n• Explore\n• Explore\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• 4 items\n• 8 items Explore\n• 3 items Explore\n• 5 items Explore\n• Explore\n• 8 items Explore\n• Explore\n• 5 items Explore\n• Explore\n• 8 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 6 items Explore\n• 2 items Explore\n• 3 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 7 items Explore\n• Explore\n• 1 items Explore\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 9 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 11 items Explore\n• Explore\n• Explore\n• 3 items Explore\n• Explore\n• 1 items Explore\n• Explore\n• 2 items Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 3 items Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 3 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 1 items\n• Explore\n• 1 items Explore\n• 1 items Explore\n• Explore\n• Explore\n• 4 items\n• Explore\n• 4 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• 2 items Explore\n• Explore\n• Explore\n• Explore\n• 5 items Explore\n• 2 items Explore\n• Explore\n• 2 items Explore\n• Explore\n• 13 items Explore\n• Explore\n• Explore\n• Explore\n• 1 items Explore\n• Explore\n• Explore\n• Explore\n• Explore\n• Explore" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.59503293,"math_prob":0.980798,"size":598,"snap":"2022-27-2022-33","text_gpt3_token_len":181,"char_repetition_ratio":0.13636364,"word_repetition_ratio":0.0,"special_character_ratio":0.17892976,"punctuation_ratio":0.23333333,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98579216,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T16:56:22Z\",\"WARC-Record-ID\":\"<urn:uuid:7ead4c3e-9240-402f-8859-b3cb47f94748>\",\"Content-Length\":\"224610\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:caecfe72-4daa-49e3-b3b1-2c7710649941>\",\"WARC-Concurrent-To\":\"<urn:uuid:89d95be6-d01b-49f6-af79-0635459ee89a>\",\"WARC-IP-Address\":\"13.93.104.16\",\"WARC-Target-URI\":\"https://www.nationaltrustcollections.org.uk/results?ObjectType=saucer+dish\",\"WARC-Payload-Digest\":\"sha1:ECC5LUZKAUEAJJ65WNJBRGCYSWPY5A6G\",\"WARC-Block-Digest\":\"sha1:XW3GKGT64IXB43OI6E3AGEY23R4LAR6A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103850139.45_warc_CC-MAIN-20220630153307-20220630183307-00760.warc.gz\"}"}
https://www.tutorialspoint.com/antenna_theory/antenna_theory_short_dipole.htm
[ "# Antenna Theory - Short Dipole\n\nA short dipole is a simple wire antenna. One end of it is open-circuited and the other end is fed with AC source. This dipole got its name because of its length.\n\n### Frequency range\n\nThe range of frequency in which short dipole operates is around 3KHz to 30MHz. This is mostly used in low frequency receivers.\n\n## Construction & Working of Short Dipole\n\nThe Short dipole is the dipole antenna having the length of its wire shorter than the wavelength. A voltage source is connected at one end while a dipole shape is made, i.e., the lines are terminated at the other end.", null, "The circuit diagram of a short dipole with length L is shown. The actual size of the antenna does not matter. The wire that leads to the antenna must be less than one-tenth of the wavelength. That is\n\n$$L < \\frac{\\lambda}{10}$$\n\nWhere\n\n• L is the length of the wire of the short dipole.\n\n• λ is the wavelength.\n\nAnother type of short dipole is infinitesimal dipole, whose length is far less than its wave length. Its constructiion is similar to it, but uses a capacitor plate.\n\n## Infinitesimal Dipole\n\nA dipole whose length is far less than wavelength is infitesimal dipole. This antenna is actually impractical. Here, the length of the dipole is less than even fiftith part of the wavelength.\n\nThe length of the dipole, Δl << λ. Where, λ is the wavelength.\n\n$$\\Delta l = \\frac{\\lambda}{50}$$\n\nHence, this is the infinitely small dipole, as the name implies.\n\nAs the length of these dipoles is very small, the current flow in the wire will be dI. These wires are generally used with capacitor plates on both sides, where low mutual coupling is needed. Because of the capacitor plates, we can say that uniform distribution of current is present. Hence the current is not zero here.\n\nThe capacitor plates can be simply conductors or the wire equivalents. The fields radiated by the radial currents tend to cancel each other in the far field so that the far fields of the capacitor plate antenna can be approximated by the infinitesimal dipole.\n\nThe radiation pattern of a short dipole and infinitesimal dipole is similar to a half wave dipole. If the dipole is vertical, the pattern will be circular. The radiation pattern is in the shape of “figure of eight” pattern, when viewed in two-dimensional pattern.\n\nThe following figure shows the radiation pattern of a short dipole antenna, which is in omni-directional pattern.", null, "The following are the advantages of short dipole antenna −\n\n• Ease of construction, due to small size\n\n• Power dissipation efficiency is higher\n\nThe following are the disadvantages of short dipole antenna −\n\n• High resistive losses\n• High power dissipation\n• Low Signal-to-noise ratio" ]
[ null, "https://www.tutorialspoint.com/antenna_theory/images/short_dipole.jpg", null, "https://www.tutorialspoint.com/antenna_theory/images/omni_directional_pattern.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9326892,"math_prob":0.9785012,"size":2695,"snap":"2021-43-2021-49","text_gpt3_token_len":604,"char_repetition_ratio":0.17428465,"word_repetition_ratio":0.023913043,"special_character_ratio":0.20667903,"punctuation_ratio":0.09770115,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958464,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,10,null,10,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-24T06:42:29Z\",\"WARC-Record-ID\":\"<urn:uuid:6abb5479-7dc7-4543-82a8-de3b06d10822>\",\"Content-Length\":\"33039\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36b2bca0-3a63-417d-8cc9-db6c2afa20b6>\",\"WARC-Concurrent-To\":\"<urn:uuid:637f8715-b48e-45a5-bf95-590a40847ced>\",\"WARC-IP-Address\":\"72.21.91.42\",\"WARC-Target-URI\":\"https://www.tutorialspoint.com/antenna_theory/antenna_theory_short_dipole.htm\",\"WARC-Payload-Digest\":\"sha1:GVQEIPHUVN2XTWX3J2KFEZNZNSIAE7GZ\",\"WARC-Block-Digest\":\"sha1:V73FEDYTWWOY3BTYKK3BWFVGRGEJKHOF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585911.17_warc_CC-MAIN-20211024050128-20211024080128-00237.warc.gz\"}"}
https://panotbook.com/theory-of-consumer-behaviour/
[ "# Theory Of Consumer Behaviour NCERT Textbook PDF\n\nTheory Of Consumer Behaviour NCERT Class 12 Economics Chapter 2 Solutions‘ PDF Quick download link is given at the bottom of this article. You can see the PDF demo, size of the PDF, page numbers, and direct download Free PDF of ‘Ncert Class 12 Economics Chapter 2 Exercise Solution’ using the download button.\n\n## Theory Of Consumer Behaviour NCERT Textbook With Solutions Book PDF Free Download\n\n### Chapter 2: Theory Of Consumer Behaviour\n\nA consumer usually decides his demand for a commodity on the basis of utility (or satisfaction) that he derives from it.\n\nWhat is utility? The utility of a commodity is its want-satisfying capacity. The more the need of a commodity or the stronger the desire to have it, the greater is the utility derived from the commodity.\n\nThe utility is subjective. Different individuals can get different levels of utility from the same commodity.\n\nFor example, someone who likes chocolates will get much higher utility from chocolate than someone who is not so fond of chocolates, Also, a utility that one individual gets from the commodity can change with change in place and time.\n\nFor example, utility from the use of a room heater will depend upon whether the individual is in Ladakh or Chennai (place) or whether it is summer or winter (time).\n\nCardinal utility analysis assumes that level of utility can be expressed in numbers. For example, we can measure the utility derived from a shirt and say, this shirt gives me 50 units of utility.\n\nBefore discussing further, it will be useful to have a look at two important measures of utility.\nMeasures of Utility Total Utility: Total utility of a fixed quantity of a commodity (TU) is the total satisfaction derived from consuming the given amount of some commodity x.\n\nMore of commodity x provides more satisfaction to the consumer. TU depends on the quantity of the commodity consumed. Therefore, TUn refers to total utility derived from consuming n units of a commodity x.\n\nMarginal Utility: Marginal utility (MU) is the change in total utility due to consumption of one additional unit of a commodity.\n\nFor example, suppose 4 bananas give us 28 units of total utility and 5 bananas give us 30 units of total utility.\n\nClearly, consumption of the 5th banana has caused the total utility to increase by 2 units (30 units minus 28 units). Therefore, the marginal utility of the 5th banana is 2 units.\n\nCardinal utility analysis is simple to understand, but suffers from a major drawback in the form of quantification of utility in numbers. In real life, we never express utility in the form of numbers.\n\nAt the most, we can rank various alternative combinations in terms of having more or less utility. In other words, the consumer does not measure utility in numbers, though she often ranks\nvarious consumption bundles. This forms the starting point of this topic – Ordinal Utility Analysis.\n\nIt may be mentioned that the law of Diminishing Marginal Rate of Substitution causes an indifference curve to be convex to the origin.\n\nThis is the most common shape of an indifference curve. But in case of goods being perfect substitutes4, the marginal rate of substitution does not diminish. It remains the same.\n\n### NCERT Solutions Class 12 Economics Chapter 2 Theory Of Consumer Behaviour\n\n1. What do you mean by the budget set of a consumer?\n\nA budget set of a consumer is a bundle of two or more goods in certain quantities and combinations that is desirable and affordable for the consumer based on their price range. A budget set is also called as an opportunity set.\n\n2. What is budget line?\n\nA budget line is a graphical representation of a consumer’s constraints when buying a combination of two or more products with a given budget.\n\nA budget line will shift whenever there is a change in the prices, preferences or income. It is also called a consumption possibility line. Here, it is assumed that the customer spends the entire income on the bundle of products.\n\n3. Explain why the budget line is downward sloping.\n\nWith a limited income, the customer can increase the consumption of one good only by decreasing the consumption of the other good. This is why a budget line is downward sloping.\n\nNCERT Class 12 Economics Textbook Chapter 2 Theory Of Consumer Behaviour With Answer PDF Free Download" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9078818,"math_prob":0.7860563,"size":4394,"snap":"2022-40-2023-06","text_gpt3_token_len":920,"char_repetition_ratio":0.14419134,"word_repetition_ratio":0.01212938,"special_character_ratio":0.20232135,"punctuation_ratio":0.09079903,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.954195,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-27T01:44:40Z\",\"WARC-Record-ID\":\"<urn:uuid:0a154a75-eead-4854-9c02-3046bf187aec>\",\"Content-Length\":\"144294\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7fe3d3b0-896a-4333-a2ab-ca85d6039ff0>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf8a87e4-8558-4666-8868-bca2074da1b6>\",\"WARC-IP-Address\":\"172.67.216.252\",\"WARC-Target-URI\":\"https://panotbook.com/theory-of-consumer-behaviour/\",\"WARC-Payload-Digest\":\"sha1:MKDMRFYAJGWTTDJYOGGH52S2KPMEMJ2D\",\"WARC-Block-Digest\":\"sha1:7ZFZLJDEKQ45ID2WUGAYTWQCVRQRGSX3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334974.57_warc_CC-MAIN-20220927002241-20220927032241-00602.warc.gz\"}"}
https://onlinecalculator.guru/calculus/derivative-calculator/
[ "# Derivative Calculator\n\nFree Derivative Calculator helps you to find the differentiation of the given function, with steps shown. Make your calculations easier and faster by giving the input function and tap on the calculate button to get the output as derivative of the function in no time.\n\nDerivative Calculator: Struggling to calculate the derivative of a function? Then, here is the solution for your problem. Differentiation can be calculated easily by using the differentiation rules. You can understand and learn about the entire concept from here and also get the simple steps to solve the questions. Our handy calculator does all the required calculations and displays the exact output along with all the steps of calculations in fraction of seconds.\n\n## Find Derivative of Function\n\nHere are the easy steps that should be followed while finding the derivative. The steps are along the lines:\n\n• Take any function to calculate the derivative.\n• Have a look at the basic formulas or rules that are useful to solve the differentiation.\n• Apply those rules and solve the function easily.\n\n### Important Derivative Rules\n\nBelow mentioned are the some important derivate rules that are used while solving the derivative of any function. Have a look at them.\n\n1. d/dx (a) = 0 (where a is a constant)\n2. d/dx (x) = 1\n3. d/dx (xn) = nxn-1 [power rule]\n4. d/dx (ex) = ex [exponent rule]\n5. d/dx (log x) = 1/x\n6. d/dx (ax) = ax logx\n7. d/dx (f+g) = d/dx (f) + d/dx (g)\n8. d/dx (f-g) = d/dx (f) - d/dx (g)\n9. d/dx (ay) = a dy/dx\n10. (f.g)' = f'g + g'f [product rule]\n11. (f/g)' = (f'g - g'f) / (g2) [quotient rule]\n12. d/dx (f(g(x) = f'(g(x))g'(x) [chain rule]\n13. For Trigonometric Functions:\n• d/dx sin(x) = cos(x)\n• d/dx cos(x) = -sin(x)\n• d/dx tan(x) = sec2(x)\n• d/dx cot(x) = -cosec2(x)\n\nExample\n\nQuestion: Solve derivative of 6 / √z3 + 1 / (8z4) - 1 / (3z10)\n\nSolution:\n\nGiven function is 6 / √z3 + 1 / (8z4) - 1 / (3z10)\n\nd/ dz ( 6 / √z3 + 1 / (8z4) - 1 / (3z10)) = ?\n\n= d/ dz ( 6 z-3/2 + 1/8 (z-4) - 1/3 (z-10)\n\n= d/ dz (6 z-3/2) + d/ dz (1/8 (z-4)) - d/ dz (1/3 (z-10))\n\nApply the power rule i.e d/ dx xn = nxn-1\n\n= 6 (-3/2) z-3/2 - 1 + 1/8 (-4) z-4-1 -1/3(-10) z-10-1\n\n= -9z-5/2 - 1/2 z-5 + 10/3 z-11\n\nd/ dz ( 6 / √z3 + 1 / (8z4) - 1 / (3z10)) = -9z-5/2 - 1/2 z-5 + 10/3 z-11\n\nOnlinecalculator.guru has different algebra concepts calculators which are free to use & easy to understand and you can make any of your calculations easy & quick.", null, "### FAQs on Derivative Calculator\n\n1. What is derivative formula?\n\nDerivative is the fundamental tool of calculus. The derivative of a function of a real variable measures the sensitivity to change a quantity which is determined by another quantity. Derivative formula is\n\nf1(x) = lim△x→0 ([f(x) + △x) - f(x)] / △x\n\n2. What is the purpose of derivatives?\n\nDerivatives are the financial contracts whose value is linked to the value of an underlying asset.\n\n3. How do you find the derivative on a calculator?\n\nEnter the input function in the calculator and hit on the calculate button which is provided next to that input box to get the output instantly.\n\n4. Find the derivative of f(x). Where f(x) = 6x3 - 9x + 4?\n\nf'(x) = 6.3 x3-1 -9(1) + 0\n\n= 18 x2 -9" ]
[ null, "https://onlinecalculator.guru/static/images/Calculus/Derivative-Calculator.jpeg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87717915,"math_prob":0.999403,"size":2335,"snap":"2022-27-2022-33","text_gpt3_token_len":705,"char_repetition_ratio":0.16559416,"word_repetition_ratio":0.10022779,"special_character_ratio":0.32462525,"punctuation_ratio":0.0720339,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998353,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-06T04:05:40Z\",\"WARC-Record-ID\":\"<urn:uuid:b2bc48b7-feb2-4443-acda-c70d70ca26fc>\",\"Content-Length\":\"48488\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fe31960e-ab20-4873-82c1-1e039dd8b3f2>\",\"WARC-Concurrent-To\":\"<urn:uuid:5fc8ce14-882e-4fc1-9a90-751caa0444e5>\",\"WARC-IP-Address\":\"104.26.4.233\",\"WARC-Target-URI\":\"https://onlinecalculator.guru/calculus/derivative-calculator/\",\"WARC-Payload-Digest\":\"sha1:WUT4G3UVKULOQ4W5SHFSESI2AIZLEQKU\",\"WARC-Block-Digest\":\"sha1:VW34LN44GY6AMTQMWBGVREIBV5CGYN3S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104660626.98_warc_CC-MAIN-20220706030209-20220706060209-00087.warc.gz\"}"}
https://programmer.group/5e1f0182b5552.html
[ "# Common features of vue. Form, calculated properties, custom, listener, filter, lifecycle\n\nKeywords: Vue Attribute\n\n## Form operation\n\n### Form scope modifier\n\n1. Number: converts the form value to a number\n```data:{\ninputmsg:'123'\n}\n<input type=text v-model.number=\"inputmsg\">//The value of this form is output as data\n```\n1. trim: remove spaces at the beginning and end of the form\n```data:{\ninputmsg:' 123 '\n}\n<input type=text v-model.trim=\"inputmsg\">//The value of this form is' 123 ', without spaces\n```\n1. lazy: switch input event to change event (trigger only when cursor is lost)\n```data:{\ninputmsg:123\n}\n<input type=text v-model.lazy=\"inputmsg\">//When the form is input, the data in the corresponding data will not change immediately, but will change when the mouse leaves\n```\n\n### input single line text box\n\n```data:{\ninputmsg:'Single line text'\n}\n<input type=text v-model=\"inputmsg\">//This binds the input values in both directions\n```\n\n### textarea multiline text box\n\n```data:{\ntextareamsg:'Single line text'\n}\n<textarea type=text v-model=\"textarea\"></textarea>//In this way, the value of textarea is bound in both directions\n```\n\n### select drop-down list\n\n1. single election\n\n```data:{\nselect:1//Variable corresponds to the item selected by default, single variable definition\n}\n<select v-model=\"select\">//Bind data in both directions on select\n<option value=\"0\">0</option>//Each option is distinguished by value, which is also used to associate the corresponding binding variables.\n<option value=\"1\">1</option>\n<option value=\"2\">2</option>\n<option value=\"3\">3</option>\n</select>\n```\n\n1. more choices\n\n```data:{\nselect:['0']//If select is multiple, you need to define an array. The value in the array corresponds to the value item in the selected option\n}\n<select v-model=\"select\" multipel='true'>//Bind data in two directions on select. The multipel property sets select to multi select\n<option value=\"0\">0</option>//Each option is distinguished by value, which is also used to associate the corresponding binding variables.\n<option value=\"1\">1</option>\n<option value=\"2\">2</option>\n<option value=\"3\">3</option>\n</select>\n```\n\n```data:{\nmsg: 1 //The variable corresponds to the item selected by default,\n}\n//male<input type=\"radio\" name=\"sex\" value=\"0\" v-model=\"msg\">//The radio boxes of the same group are bound to the same variable, and value is used as the distinction\n```\n\n### checkbox check box\n\n```data:{\narr:[\"2\",'1'] //The data bound to the check box is an array. The values in the array correspond to the option to select the corresponding check box.\n}\n//eat<input type=\"checkbox\" name=\"checkbox\" value=\"1\" v-model=\"arr\">//The radio boxes of the same group are bound to the same variable, and value is used as the distinction\n//drink<input type=\"checkbox\" name=\"checkbox\" value=\"2\" v-model=\"arr\">\n//play<input type=\"checkbox\" name=\"checkbox\" value=\"3\" v-model=\"arr\">\n//Happy<input type=\"checkbox\" name=\"checkbox\" value=\"4\" v-model=\"arr\">\n```\n\n## directive custom instruction\n\n1. Global custom instruction\nDefine the custom instruction outside the vue instance, which can be used by all components.\n```Vue.directive('focus',{//Focus is the name of the user-defined instruction. You need to add V - to the reference. Such as: v-focus\ninserted:function(el,binding){//inserted is the hook function of the user-defined instruction, el is the element calling the instruction, and it is the native html element. binding parameter, which can be left blank, as follows\n//inserted:function(el){//inserted is the hook function of the custom instruction, el is the element of the calling instruction, and is the native html element\nel.focus();//Focus of attention\nconsole.log(binding)//Parameters can be output\n}\n})\n//Quote\ndata:{\nmsg:123\n}\n<input type='text' v-focus=\"msg\">\n<input type='text' v-focus >\n```\n1. Local custom instruction\n**The local custom instruction is defined in the directives parameter in the vue instance; it can only be used in its own components; * * as follows:\n```const vm = Vue({\ndata:{}\ndirectives:{//Custom instructions. Others are the same as global instructions.\nfocus:{\ninserted:function(el,binding){//inserted is the hook function of the user-defined instruction, el is the element calling the instruction, and it is the native html element. binding parameter, which can be left blank, as follows\n//inserted:function(el){//inserted is the hook function of the custom instruction, el is the element of the calling instruction, and is the native html element\nel.focus();//Focus of attention\nconsole.log(binding)//Parameters can be output\n}\n}\n}\n})\n//Same usage as global instruction\n```\n\n## Calculated calculation properties\n\nThe calculated attributes can depend on the data, and the data does not need to be re rendered. Based on data rendering in data\nAdd the computed parameter to the vue instance;\n\n```data:{msg:123}\ncomputed: {\ncomputed1: function(){//computed1 is the name of the calculation attribute, and the reference can directly refer to the name. Just like variables in data.\nreturn this.msg.split('').reverse().join('')//The calculation property needs to return the calculation result by return.\n}\n}\n//Quote\n<div>{{computed1}}</div>//The result is 321\n```\n```\tDifference between computed and methods methods methods.\ncomputed: there will be a cache. When the data in the data remains unchanged, it will not be re rendered.\nmethods: there is no cache, and the function will be called again every time.\n```\n\n## watch listener\n\n```\t**Handle some asynchronous and expensive events**\nAdd the watch parameter to the vue instance\n```\n```data:{\nfirstname:123,\nlastname:453,\nfullname:'123 453'\n},\nwatch:{\nfirstname: function(val){//Firstname is the data in the data to be monitored, val is the latest value of firstname\nthis.fullname = val+' '+this.lastname;//When the monitored variable changes, perform the corresponding operation.\n},\nlastname: function(val){//lastname is the data in the data to be monitored, val is the latest value of lastname\nthis.fullname = this.firstname+' '+val;//When the monitored variable changes, perform the corresponding operation.\n},\n}\n```\n\n## Filter filter\n\nData formatting, such as capitalization of the initial of a string.\n\n### Definition\n\nGlobal definition. It is defined outside the vue instance, similar to the custom instruction, and can be used by all components. as\n\n```//The filter can carry parameters, starting from the second bit, such as\n//**Vue.filter('filtername',function(value,arg1, arg2){//arg is the parameter passed by the filter**\nVue.filter('filtername',function(value){//filtername is the name of the filter, and value is the data that calls the filter.\nreturn value.charAt(0).toUpperCase()+value.slice(1)\n//The first letter in charAt(0) data, toUpperCase to uppercase, toLowerCase to lowercase, slice from the second bit\n})\n```\n\nLocal filter. Add the filters parameter in the Vue instance to define the filter in the parameter, which is only valid in this component. as\n\n```data:{msy:asd},\nfilters:{\n//The filter can carry parameters, starting from the second bit, such as\n//**filtername: function(value,arg1, arg2){//arg is the parameter passed by the filter**\nfiltername: function(value){\nreturn value.charAt(0).toUpperCase()+value.slice(1)\n}\n}\n```\n\n### usage\n\n```//It can be directly used in interpolation expressions, such as:\n//Usage of parameter passing, < div > {MSG | filtername (arg1,arg2)}} < / div >\n<div>{{msg | filtername}} </div>\n//The filter supports multiple functions, such as:\n<div>{{msg | filtername1 | filtername2}} </div>\n//It can also be used in property binding, such as:\n//The usage of parameter passing, < div: id = \"MSG | filtername (arg1, arg2)\" >\n<div :id=\"msg | filtername\"> </div>\n```\n\n## life cycle\n\nThese methods are the same as method and data.\n\n### Main stage\n\n```**Mount (initialize related properties)**\n```\n1. beforeCreate / / called after instance initialization, before data observation and event configuration\n2. Created / / called immediately after the instance is created.\n3. beforeMout / / called before the mount starts\n4. mouted //el is replaced by the newly created vm.\\$el. After mounting it to an instance, the hook is called. The function indicates that the initialization is complete. usage\n```mounted: function(){\n//operation\n}\n```\n\nUpdate (change operation of element or component)\n6. beforeUpdate / / called when updating data, which occurs before virtual DOM patching\n7. updated / / if the virtual DOM is re rendered and patched due to data update, the hook will be called after that\nDestroy (destroy related properties)\n\n1. Call before beforeDestroy / / instance destruction\n2. After destroyed / / instance destruction, call", null, "", null, "Published 8 original articles, praised 0, visited 83\n\nPosted by OuchMedia on Wed, 15 Jan 2020 04:11:00 -0800" ]
[ null, "https://programmer.group/images/article/2c1bfabe4c2aec9bea98d6e28b7cde8e.jpg", null, "https://programmer.group/images/article/d1358d4695d8660de2972cc1f6e682b2.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.66331667,"math_prob":0.8154635,"size":8433,"snap":"2019-51-2020-05","text_gpt3_token_len":1904,"char_repetition_ratio":0.14153518,"word_repetition_ratio":0.21903959,"special_character_ratio":0.2490217,"punctuation_ratio":0.12975098,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9597582,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T04:30:51Z\",\"WARC-Record-ID\":\"<urn:uuid:78bf6a78-b478-4029-97a5-054984e4da47>\",\"Content-Length\":\"37280\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:abed7c0a-8f8b-4db1-b5fc-3cfce44ec94f>\",\"WARC-Concurrent-To\":\"<urn:uuid:4d226776-5d9d-4e51-bbdf-fb0a3cce2b6f>\",\"WARC-IP-Address\":\"174.137.48.86\",\"WARC-Target-URI\":\"https://programmer.group/5e1f0182b5552.html\",\"WARC-Payload-Digest\":\"sha1:HFNE4QJNLR5OLSYV4Q6YJAXX7CTZZ56U\",\"WARC-Block-Digest\":\"sha1:ZXXPGKEDWGPWNJH6KYZUAMQQ6XRDDSIC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251773463.72_warc_CC-MAIN-20200128030221-20200128060221-00114.warc.gz\"}"}
https://ask.learncbse.in/t/write-an-equation-that-defines-the-exponential-function-with-base-b-0/63854
[ "", null, "# Write an equation that defines the exponential function with base b > 0\n\na) Write an equation that defines the exponential function with base b > 0.\nb) What is the domain of this function?\nc) If b≠1, what is the range of this function?" ]
[ null, "https://ask.learncbse.in/images/discourse-logo-sketch.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.78614044,"math_prob":0.9943439,"size":238,"snap":"2020-34-2020-40","text_gpt3_token_len":60,"char_repetition_ratio":0.16239317,"word_repetition_ratio":0.47619048,"special_character_ratio":0.24789916,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99780345,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-19T05:32:35Z\",\"WARC-Record-ID\":\"<urn:uuid:9233c191-9562-43e4-b994-5bff6c5f6324>\",\"Content-Length\":\"9846\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:00cfa83d-e606-44b5-ab38-4dfb7c94a1a0>\",\"WARC-Concurrent-To\":\"<urn:uuid:ee68321c-0044-49b5-bdbf-f9bfcbfe9da4>\",\"WARC-IP-Address\":\"46.165.252.193\",\"WARC-Target-URI\":\"https://ask.learncbse.in/t/write-an-equation-that-defines-the-exponential-function-with-base-b-0/63854\",\"WARC-Payload-Digest\":\"sha1:YEZ5NFN5XA7NNZYYDKHSRQ3MGBCZQWLR\",\"WARC-Block-Digest\":\"sha1:WPY3VO3FR2JL5BOT25XVSBTGPG4CAF2N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400190270.10_warc_CC-MAIN-20200919044311-20200919074311-00207.warc.gz\"}"}
http://forums.wolfram.com/mathgroup/archive/2004/Aug/msg00367.html
[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Hypergeometric function\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg50188] Hypergeometric function\n• From: jujio77 at yahoo.com (Scott)\n• Date: Thu, 19 Aug 2004 06:28:24 -0400 (EDT)\n• Sender: owner-wri-mathgroup at wolfram.com\n\n```I have a finite alternating series of hypergeometric (2F1) functions.\nThese functions have complex parameters. When I sum the series I get\nlarger and larger values. My question is this, does anyone know how\nprecise Mathematica is when calculating a hypergeometric fn\nnumerically ie, how many sig figs are correct?\n\nI have done various transformations on the hypergeometric fn and then\nsummed the series. Each time I arrive at the same result.\n\nThanks for any replies,\nScott\n\n```\n\n• Prev by Date: Label of Max[list]\n• Next by Date: GUIKit FileDialog Widget\n• Previous by thread: Re: Label of Max[list]\n• Next by thread: Re: Hypergeometric function" ]
[ null, "http://forums.wolfram.com/mathgroup/images/head_mathgroup.gif", null, "http://forums.wolfram.com/mathgroup/images/head_archive.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/2.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/4.gif", null, "http://forums.wolfram.com/mathgroup/images/search_archive.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.87248087,"math_prob":0.6923184,"size":700,"snap":"2019-51-2020-05","text_gpt3_token_len":180,"char_repetition_ratio":0.14224137,"word_repetition_ratio":0.0,"special_character_ratio":0.24285714,"punctuation_ratio":0.15789473,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98666364,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-14T02:12:33Z\",\"WARC-Record-ID\":\"<urn:uuid:156fa0ad-9842-4fbc-b6e0-5a174657c7e4>\",\"Content-Length\":\"44118\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5d6a5b5f-a990-4508-b588-7e24c15da9bd>\",\"WARC-Concurrent-To\":\"<urn:uuid:39e7496f-a6c1-4c85-99a1-d0c60e5e6dec>\",\"WARC-IP-Address\":\"140.177.205.73\",\"WARC-Target-URI\":\"http://forums.wolfram.com/mathgroup/archive/2004/Aug/msg00367.html\",\"WARC-Payload-Digest\":\"sha1:RG27RKXJX34L4A5FEEFXC7IWHP6KY2TB\",\"WARC-Block-Digest\":\"sha1:BCDVSPSMLENWKJ57BQ2FIYUCQQVJFHPP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540579703.26_warc_CC-MAIN-20191214014220-20191214042220-00461.warc.gz\"}"}
https://embed.tutorhub.com/question/algebra--34
[ "Lesson hub\n\n## Can't find the answer? Try online tutoring", null, "We have the UK’s best selection of online tutors, when and for how long you need them.\n\nGetting 1-on-1 support is cheaper than you might think.\n\n### Participating users\n\nWelcome to our free-to-use Q&A hub, where students post questions and get help from other students and tutors.\n\nYou can ask your own question or look at similar Pure Mathematics questions.\n\nHi @luisxxi, thanks for taking your time to help me on this question. But as I've mentioned in my post, I need help on the 3rd part. I was able to manage the first two parts myself.\n\nAny help on this is highly appreciates.\n\nMany thanks!\n\nIn the first part you must transform the equation so that it fits you:\n\n((a+b+c)/a)+((a+b+c)/b)+((a+b+c)/c)>=9\n\n1+(b/a)+(c/a)+(a/b)+1+(c/b)+(a/c)+(b/c)+1>=9\n\nrearranging\n\n(a/b+b/a) + (a/c+c/a) + (b/c+c/b) + 3 >=9\n\nand you must develop the following remarkable product:\n\n(a-b)^2=a^2-2ab+b^2 if a=b then a^2-2ab+b^2=0\n\n=> a^2+b^2=2ab => (a^2+b^2)/ab=2 => a/b+b/a=2\n\nthe important thing here is that you make the assumption a = b and\n\na=c and b=c\n\nWith that assumption you have the problem done", null, "" ]
[ null, "https://embed.tutorhub.com/assets/illustrations/illus-heads-e1667e6e7e628149ebf8bed3dc859983.png", null, "https://embed.tutorhub.com/assets/illustrations/illus-bg01-2a7e8f558a27aa8d1a956b542ff02787.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8546527,"math_prob":0.90375054,"size":731,"snap":"2019-26-2019-30","text_gpt3_token_len":206,"char_repetition_ratio":0.09903714,"word_repetition_ratio":0.0,"special_character_ratio":0.30779755,"punctuation_ratio":0.084337346,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99892116,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-17T16:50:53Z\",\"WARC-Record-ID\":\"<urn:uuid:2ac2beaa-14c5-426a-ae62-68b1c239e2cf>\",\"Content-Length\":\"21120\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8cdab0df-3eb3-48c2-b7a6-c7c6e884391b>\",\"WARC-Concurrent-To\":\"<urn:uuid:23ed532a-27bf-4954-9b32-b7d810681657>\",\"WARC-IP-Address\":\"134.213.155.185\",\"WARC-Target-URI\":\"https://embed.tutorhub.com/question/algebra--34\",\"WARC-Payload-Digest\":\"sha1:OABSK2KBTW7JN7MATRH52QTLEC4ITY5F\",\"WARC-Block-Digest\":\"sha1:RXPVIWTFWBKTEH2EOV3L2GYWYFNKXCF5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525355.54_warc_CC-MAIN-20190717161703-20190717183703-00536.warc.gz\"}"}
https://codereview.stackexchange.com/questions/212825/discrete-event-simulation-for-production-defects/213209
[ "# Discrete event simulation for production defects\n\nI have one machine, which produces parts. In machine_failure_rate% it produces faulty parts which need to be produced again. Thus, we end up with a simple queuing problem. Can the following code be futher functionalized? I have the feeling, I can get rid of time_parts, but all I have in mind deteriorates the code as I need further lookups in the production_df data frame to look for \"what was produced / what needs to be produced now?\". The following script is running:\n\ninput_rate <- 1/60 # input rate [1/min, 1/input_rate corresponds to interarrival time in min]\nn <- 1000 # number of parts\ndt <- 1 # timestep = time to transfer faulty parts back to production. [min]\n\nmachine_production_rate <- 1/40 # production rate [1/min]\nmachine_failure_rate <- 0.2 # machine failure rate\n\n# Sum all interarrival times\nset.seed(123456)\nt_event <- cumsum(rpois(n, 1/input_rate))\n\n# Create initial list of tasks. Produces parts will be cut off.\ntime_parts <- data.frame(id = c(1:n),\nt = t_event,\nstringsAsFactors = FALSE)\n\n# ========= Functions ==========================================================\ncreate_machine <- function(failure_rate, production_rate) {\nmachine <- list()\nmachine$failure_rate <- failure_rate machine$production_rate <- production_rate\nmachine$is_occupied <- FALSE return(machine); } update_machine <- function(ind_production_df, machine, production_df) { if (machine$is_occupied) {\nif (production_df$po_start[ind_production_df] + 1/machine$production_rate <= t) {\nmachine$is_occupied <- FALSE } } return(machine) } production_summary <- function(production_df, machine, input_rate) { no_of_failures <- sum(production_df$no_failures)\ntotal_production_time <- max(production_df$po_start) + 1/machine$production_rate\nuptime <- (no_of_failures + n)/machine$production_rate print(paste0(\"Estimated machine$failure_rate \",\nround(no_of_failures/(no_of_failures + n), 2),\n\" [theory \", round(machine$failure_rate, 2), \"]\")) print(paste0(\"Up-time \", uptime, \", of total time \", total_production_time, \". Auslastung \", round(uptime/total_production_time, 2), \" [theory \", round(input_rate/machine$production_rate*1/(1 - machine$failure_rate), 2), \"]\")) } # ========= DE simulation ====================================================== machine <- create_machine(machine_failure_rate, machine_production_rate) production_df <- data.frame(id = time_parts$id,\ntime = time_parts$t, production_start = rep(0, nrow(time_parts)), no_failures = rep(0, nrow(time_parts)), stringsAsFactors = FALSE) t <- 0 while (length(time_parts$t) > 0) {\nind_production_df <- which(production_df$id == time_parts$id)\n\nmachine <- update_machine(ind_production_df, machine, production_df)\n\nif (!machine$is_occupied & time_parts$t <= t) {\n# A machine is available and a part needs to be produced\nmachine$is_occupied <- TRUE production_df$po_start[ind_production_df] <- t\nif (runif(1) < machine$failure_rate) { # bad part time_parts$t <- time_parts$t + dt time_parts <- time_parts[sort(time_parts$t, index.return = TRUE)$ix, ] production_df$no_failures[ind_production_df] <-\nproduction_df$no_failures[ind_production_df] + 1 t <- t + min(time_parts$t, dt)\n} else {\n# good part\nif (production_df$po_start[ind_production_df] + 1/machine$production_rate >= t &&\nnrow(time_parts) >= 2) {\ntime_parts <- time_parts[2:(nrow(time_parts)), ]\n} else {\ntime_parts <- time_parts[FALSE, ]\n}\nt <- t + 1/machine$production_rate machine$is_occupied <- FALSE\n}\n} else {\n# machine is occupied or no part needs to be produced\nt <- t + min(time_parts$t, dt) } } # ========= Results ============================================================ production_summary(production_df, machine, input_rate) Backround: I think about a generalisation (more machines, more input-sources, more complex rules how/when/... parts a produces). I fear that I will end up with tons of unreadable and unmaintainable code-lines if I proceed like this. Edit: I think t <- t + min(time_parts$t, dt) is a bug and the correct version is t <- min(time_parts$t, t + dt). It only worked because the time difference dt was always the minimum. In the last case you could speed up using t <- max(time_parts$t, t + dt) as there is nothing to do in the time inbetween.\n\n• Could you explain what \"po_start\" represents - is this the time at which production starts for a given part? – Russ Hyde Feb 5 at 9:22\n• Yes, it means, when the production really starts - due to a queue, this can be delayed in contrast to the original t_event. I also made a tiny edit to the post... – Christoph Feb 5 at 9:48\n• I've been working on this, but can't post my code from work. I can restructure the code and get the same result but I was wondering whether there might be an error. Within your code t <- t + min(time_parts$t, dt). The contents of time_parts are the earliest-time a given part can be made and the current time must increase at each iteration, shouldn't you update current time to max(t + dt, time_parts$t)? – Russ Hyde Feb 6 at 10:02\n• @RussHyde No, I don't think so: if I increase t, I should take the earliest point in time where something can change. This is save. It might be, that sometimes a max would speed up... I am curious about your results :-) – Christoph Feb 6 at 15:39\n\nThis was a pretty difficult challenge - principally because R doesn't have a built-in priority queue data-structure, but also because the priority-queue-like data-frame (time_parts) was wrapped around the results-storing data-frame (production_df) and the main while loop contains code at a few different levels of abstraction.\n\n# Idiomatic R\n\nI did some simple stuff first: pulled all your functions to the start of the script, reformatted some code/comments.\n\nThere was a couple of things I changed for idiomatic reasons:\n\nwhich(production_df$id == time_parts$id)\n# -->\nmatch(time_parts$id, production_df$id)\n\n# time_parts[2:(nrow(time_parts)), ] # and\n# time_parts[FALSE, ] # when time_parts has only one row\n# can both be replaced with\ntime_parts[-1, ]\n# (which is the idiomatic way to drop the first row) so this allowed us to remove an if-else clause\n\n# You don't need to do rep(some_value, n) when you're adding a\n# constant column to a data-frame at construction:\nproduction_df <- data.frame(id = time_parts$id, time = time_parts$t,\nproduction_start = rep(0, nrow(time_parts)),\nno_failures = rep(0, nrow(time_parts)),\nstringsAsFactors = FALSE)\n# -->\nproduction_df <- data.frame(id = time_parts$id, time = time_parts$t,\nproduction_start = 0,\nno_failures = 0,\nstringsAsFactors = FALSE)\n\n# order(...) does the same thing as sort(..., index.return)$ix sort(time_parts$t, index.return = TRUE)$ix # --> order(time_parts$t)\n\n# nrow(x) is more idiomatic than length(x$some_column) while(length(time_parts$t) > 0){\n# -->\nwhile(nrow(time_parts) > 0) {\n# but I subsequently replaced this newer line as well\n\n\n# Explicit data-classes\n\nI converted your create_machine function so that it returns an object of class \"Machine\"; this wasn't really necessary.\n\ncreate_machine <- function(failure_rate, production_rate) {\nstructure(\nlist(\nfailure_rate = failure_rate,\nproduction_rate = production_rate,\nis_occupied = FALSE\n),\nclass = \"Machine\"\n)\n}\n\n\nI added a create_part function that similarly returns a Part object. There was a lot of repeats of 1 / machine$production_rate in your code; I replaced these with a call to part$production_duration. Also I thought your test to see whether a produced part was a failure should be associated with the produced part object (part$is_failure); with this, the while-loop logic becomes more explicit: create_part <- function(machine) { structure( list( is_failure = runif(1) < machine$failure_rate,\nproduction_duration = 1 / machine$production_rate ), class = \"Part\" ) } # then we can use this in the while-loop part <- create_part(machine) if (part$is_failure) {\n# bad part logic\n...\n} else {\n# good part logic\n...\n}\n\n\n# Restructuring the while loop\n\nI wanted to push that while-loop into a function - the less work you do in the global environment, the better.\n\nSince you want to extract data from production_df for your report, the function should return the production_df. During the while-loop, you access production_df, time_parts, t, dt (which I renamed dt_recovery based on your comments), n and machine. So we might want to pass all of those into that function. But we can compute some of those from the others:\n\n• n is the nrow of production_df,\n\n• t isn't needed outside of the while loop and\n\n• the data that initialises time_parts also initialises production_df.\n\nThe only thing we need to initialise both time_parts and production_df is the arrival-times or times at which the parts were ordered (which I renamed t_ordered).\n\nSo, we can put that while-loop into a function that takes arguments t_ordered, dt_recovery, machine.\n\nrun_event_simulation <- function(t_ordered, machine, dt_recovery) {\nn_parts <- length(t_ordered)\n\n# results data-frame\nproduction_df <- data.frame(\nid = seq(n_parts),\nt_ordered = t_ordered,\nt_started = 0,\nt_completed = 0,\nno_failures = 0,\nstringsAsFactors = FALSE\n)\n\ntime_parts <- ... # define in terms of production_df\n\n# while-loop logic\n\n# return the updated production_df\n\n\nI added the column t_completed into production_df so that you can more easily compute total_production_time from production_df in your report (this allows you to generalise the production rates)\n\n# in production_summary\n...\ntotal_production_time <- max(production_df$t_completed) ... # A functional priority queue The really big step: R doesn't have a native priority-queue, and it would be pretty hard to encode using the S3 or S4 classes since you can't update by reference in those classes. There is a priority-queue defined in the package liqueueR, but I've no experience of that. So I just wrote a simpler version of the priority queue (as an S3 class): this allows you to • peek: extract the element in the queue with the lowest priority value (without mutating the queue) • delete_min: remove that element with the lowest priority value from the queue and return the resulting queue • add: add a new element to the queue according to it's priority, returning the resulting queue • and provides a couple of helper methods (is_empty, nrow) However, this doesn't provide a pop_element(queue): typically, pop_element removes the leading element from the queue and returns that element. That is, it returns the leading element and updates the queue through a side-effect. This side-effect is problematic in R, so I didn't include a pop_element function. To achieve pop_element you have to peek and then delete_min. # Priority Queue class create_priority_queue <- function(x, priority_column) { structure( list( # note that we only order once - see add for how this is possible queue = x[order(x[[priority_column]]), ] ), class = \"PriorityQueue\", priority_column = priority_column ) } # generic methods for Priority Queue is_empty <- function(x, ...) UseMethod(\"is_empty\") peek <- function(x, ...) UseMethod(\"peek\") delete_min <- function(x, ...) UseMethod(\"delete_min\") add <- function(x, ...) UseMethod(\"add\") nrow <- function(x, ...) UseMethod(\"nrow\") nrow.default <- function(x, ...) { base::nrow(x) } # implemented methods for Priority Queue nrow.PriorityQueue <- function(x, ...) { nrow(x$queue)\n}\nis_empty.PriorityQueue <- function(x, ...) {\nnrow(x) == 0\n}\npeek.PriorityQueue <- function(x, ...) {\nx$queue[1, ] } delete_min.PriorityQueue <- function(x, ...) { x$queue <- x$queue[-1, ] x } add.PriorityQueue <- function(x, new_element, ...) { priority_column <- attr(x, \"priority_column\") # split the existing values by comparison of their priorities to # those of the new-element lhs <- which(x$queue[[priority_column]] <= new_element[[priority_column]])\nrhs <- setdiff(seq(nrow(x)), lhs)\nx$queue <- rbind(x$queue[lhs, ], new_element, x$queue[rhs, ]) x } Then I replaced your time_parts data-frame with a PriorityQueue: # inside run_event_simulation ... # Create initial list of tasks. Once produced, a part will be removed from the # queue. product_queue <- create_priority_queue( data.frame( id = production_df$id,\nt = production_df$t_ordered ), \"t\" ) ... I added a few other helpers. The final code looks like this: # ---- classes # Priority Queue class create_priority_queue <- function(x, priority_column) { structure( list( queue = x[order(x[[priority_column]]), ] ), class = \"PriorityQueue\", priority_column = priority_column ) } # A machine for producing Parts create_machine <- function(failure_rate, production_rate) { structure( list( failure_rate = failure_rate, production_rate = production_rate, is_occupied = FALSE ), class = \"Machine\" ) } # A manufactured part create_part <- function(machine) { structure( list( is_failure = runif(1) < machine$failure_rate,\nproduction_duration = 1 / machine$production_rate ), class = \"Part\" ) } # methods for Priority Queue is_empty <- function(x, ...) UseMethod(\"is_empty\") peek <- function(x, ...) UseMethod(\"peek\") delete_min <- function(x, ...) UseMethod(\"delete_min\") add <- function(x, ...) UseMethod(\"add\") nrow <- function(x, ...) UseMethod(\"nrow\") nrow.default <- function(x, ...) { base::nrow(x) } nrow.PriorityQueue <- function(x, ...) { nrow(x$queue)\n}\n\nis_empty.PriorityQueue <- function(x, ...) {\nnrow(x) == 0\n}\n\npeek.PriorityQueue <- function(x, ...) {\nx$queue[1, ] } delete_min.PriorityQueue <- function(x, ...) { x$queue <- x$queue[-1, ] x } add.PriorityQueue <- function(x, new_element, ...) { priority_column <- attr(x, \"priority_column\") lhs <- which(x$queue[[priority_column]] <= new_element[[priority_column]])\nrhs <- setdiff(seq(nrow(x)), lhs)\nx$queue <- rbind(x$queue[lhs, ], new_element, x$queue[rhs, ]) x } # ---- functions update_machine <- function(machine, ind_production_df, production_df, current_time) { if (machine$is_occupied) {\nif (\nproduction_df$t_started[ind_production_df] + 1 / machine$production_rate <= current_time\n) {\nmachine$is_occupied <- FALSE } } return(machine) } should_produce_part <- function(machine, earliest_production_time, current_time) { !machine$is_occupied &&\nearliest_production_time <= current_time\n}\n\nincrement_failures <- function(df, i) {\ndf[i, \"no_failures\"] <- 1 + df[i, \"no_failures\"]\ndf\n}\n\n# ---- format results\n\nproduction_summary <- function(production_df, machine, input_rate) {\nn_parts <- nrow(production_df)\nno_of_failures <- sum(production_df$no_failures) total_production_time <- max(production_df$t_completed)\nuptime <- (no_of_failures + n_parts) / machine$production_rate print(paste0( \"Estimated machine$failure_rate \",\nround(no_of_failures / (no_of_failures + n_parts), 2),\n\" [theory \", round(machine$failure_rate, 2), \"]\" )) print(paste0( \"Up-time \", uptime, \", of total time \", total_production_time, \". Auslastung \", round(uptime / total_production_time, 2), \" [theory \", round( input_rate / machine$production_rate * 1 / (1 - machine$failure_rate), 2 ), \"]\" )) } # ---- discrete-event simulation # run_event_simulation <- function(t_ordered, machine, dt_recovery) { n_parts <- length(t_ordered) # results data-frame production_df <- data.frame( id = seq(n_parts), t_ordered = t_ordered, t_started = 0, t_completed = 0, no_failures = 0, stringsAsFactors = FALSE ) # Create initial list of tasks. Once produced, a part will be removed from the # queue. product_queue <- create_priority_queue( data.frame( id = production_df$id,\nt = production_df$t_ordered ), \"t\" ) t <- 0 while (!is_empty(product_queue)) { queued_part <- peek(product_queue) ind_production_df <- match( queued_part$id, production_df$id ) machine <- update_machine(machine, ind_production_df, production_df, t) if ( should_produce_part(machine, earliest_production_time = queued_part$t,\ncurrent_time = t)\n) {\n# A machine is available and a part needs to be produced\n\n# - pop the scheduled part from the queue; add it back if it's production\n# fails\nproduct_queue <- delete_min(product_queue)\n\nmachine$is_occupied <- TRUE production_df$t_started[ind_production_df] <- t\npart <- create_part(machine)\n\nif (part$is_failure) { # bad part - add it back to the schedule queued_part$t <- queued_part$t + dt_recovery product_queue <- add(product_queue, queued_part) production_df <- increment_failures(production_df, ind_production_df) t <- t + min(peek(product_queue)$t, dt_recovery)\n} else {\n# good part\nt <- t + part$production_duration production_df$t_completed[ind_production_df] <- t\nmachine$is_occupied <- FALSE } } else { # machine is occupied or no part needs to be produced t <- t + min(peek(product_queue)$t, dt_recovery)\n}\n}\nproduction_df\n}\n\n# ---- script\nset.seed(123456)\n\n# Input rate [1/min, 1/input_rate corresponds to interarrival time in min]\ninput_rate <- 1 / 60\n\n# Number of parts\nn_parts <- 1000\n\n# timestep = time to transfer faulty parts back to production. [min]\ndt_recovery <- 1\n\n# Production rate [1/min]\nmachine_production_rate <- 1 / 40\n\n# Machine failure rate\nmachine_failure_rate <- 0.2\n\n# Sum all interarrival times\nt_ordered <- cumsum(rpois(n_parts, 1 / input_rate))\n\nmachine <- create_machine(machine_failure_rate, machine_production_rate)\n\n# ---- results\n\nproduction_df <- run_event_simulation(\nt_ordered, machine, dt_recovery\n)\n\nproduction_summary(production_df, machine, input_rate)\n\n\nWhy aren't S3 queues easy?\n\n(This is actually quite hard to explain). Well, the pop method on a priority-queue returns an element from the queue and moves the queue on by one step. (In R) Updating the queue might look like new_queue <- old_queue[-1] and obtaining the returned element might look like returned_element <- old_queue. So a pop function might look like\n\npop <- function(q) {\n# extract the head\nel <- q\n\n# In a reference-based language you could update the queue\n# using a side-effect like q.drop()\n# But in R, this creates a new queue: and if it isn't returned\n# explicitly, it is thrown away at the end of the pop function\nnew_q <- q[-1]\n\n# return the element that's at the head of the original queue\nel\n}\n\n# calling_env\nmy_q <- create_queue(...)\n\nBut the queue has not been altered by that pop. Now we could rewrite that function to do something dangerous like q <<- q[-1] and that would update the q in the calling environment. I consider this dangerous because q might not exist in the calling environment and that introduces side-effects, which are much harder to reason about.\n• @Christoph there was a couple of things I didn't feel comfortable restructuring. I couldn't work out why update_machine works the way it does: it seems to look into the future before it decides what to do now. It makes more sense to me for is_occupied to be set to FALSE at the end of each while-loop iteration. – Russ Hyde Feb 12 at 13:08\n• Updated. But it's pretty difficult to explain. I'm not particularly interested in stochastic simulation at present. I did have a look at your simmer documentation. Can you confirm that when you mclapply() over different simulation chains, different seeds are used for each chain? – Russ Hyde Feb 18 at 9:53\n• To your function pop <- function(q): why don't you just return(list(el=el, new_q=new_q)? Then you could work within one line r <- pop(q); el <- r$el; q <- r$new_q; rm(r);? But I still understand your comment that calling by reference would be smart... – Christoph Aug 7 at 14:35" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6955043,"math_prob":0.93471247,"size":13697,"snap":"2019-35-2019-39","text_gpt3_token_len":3417,"char_repetition_ratio":0.19696195,"word_repetition_ratio":0.22419028,"special_character_ratio":0.2833467,"punctuation_ratio":0.16697164,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99092984,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T19:11:03Z\",\"WARC-Record-ID\":\"<urn:uuid:482fa957-edad-457a-a654-b22f759ae883>\",\"Content-Length\":\"169350\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:904caa97-99aa-40ce-ae61-3315aee0bc18>\",\"WARC-Concurrent-To\":\"<urn:uuid:e53548eb-a6a5-4123-9726-93e2ec672b5e>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://codereview.stackexchange.com/questions/212825/discrete-event-simulation-for-production-defects/213209\",\"WARC-Payload-Digest\":\"sha1:KVHAEXAEJOIJ7GQNODSHCO3RWZDSN4JK\",\"WARC-Block-Digest\":\"sha1:2W5DPLNZJABJUYA6UTJVSJLFGBLJT46K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574058.75_warc_CC-MAIN-20190920175834-20190920201834-00170.warc.gz\"}"}
https://www.colorhexa.com/2b28f8
[ "# #2b28f8 Color Information\n\nIn a RGB color space, hex #2b28f8 is composed of 16.9% red, 15.7% green and 97.3% blue. Whereas in a CMYK color space, it is composed of 82.7% cyan, 83.9% magenta, 0% yellow and 2.7% black. It has a hue angle of 240.9 degrees, a saturation of 93.7% and a lightness of 56.5%. #2b28f8 color hex could be obtained by blending #5650ff with #0000f1. Closest websafe color is: #3333ff.\n\n• R 17\n• G 16\n• B 97\nRGB color chart\n• C 83\n• M 84\n• Y 0\n• K 3\nCMYK color chart\n\n#2b28f8 color description : Bright blue.\n\n# #2b28f8 Color Conversion\n\nThe hexadecimal color #2b28f8 has RGB values of R:43, G:40, B:248 and CMYK values of C:0.83, M:0.84, Y:0, K:0.03. Its decimal value is 2828536.\n\nHex triplet RGB Decimal 2b28f8 `#2b28f8` 43, 40, 248 `rgb(43,40,248)` 16.9, 15.7, 97.3 `rgb(16.9%,15.7%,97.3%)` 83, 84, 0, 3 240.9°, 93.7, 56.5 `hsl(240.9,93.7%,56.5%)` 240.9°, 83.9, 97.3 3333ff `#3333ff`\nCIE-LAB 35.61, 68.322, -98.377 18.695, 8.807, 89.516 0.16, 0.075, 8.807 35.61, 119.774, 304.78 35.61, -9.035, -129.307 29.677, 60.512, -158.067 00101011, 00101000, 11111000\n\n# Color Schemes with #2b28f8\n\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #f5f828\n``#f5f828` `rgb(245,248,40)``\nComplementary Color\n• #288df8\n``#288df8` `rgb(40,141,248)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #9328f8\n``#9328f8` `rgb(147,40,248)``\nAnalogous Color\n• #8df828\n``#8df828` `rgb(141,248,40)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #f89328\n``#f89328` `rgb(248,147,40)``\nSplit Complementary Color\n• #28f82b\n``#28f82b` `rgb(40,248,43)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #f82b28\n``#f82b28` `rgb(248,43,40)``\n• #28f5f8\n``#28f5f8` `rgb(40,245,248)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #f82b28\n``#f82b28` `rgb(248,43,40)``\n• #f5f828\n``#f5f828` `rgb(245,248,40)``\n• #0a07cd\n``#0a07cd` `rgb(10,7,205)``\n• #0b07e6\n``#0b07e6` `rgb(11,7,230)``\n• #130ff7\n``#130ff7` `rgb(19,15,247)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #4341f9\n``#4341f9` `rgb(67,65,249)``\n• #5c59fa\n``#5c59fa` `rgb(92,89,250)``\n• #7472fa\n``#7472fa` `rgb(116,114,250)``\nMonochromatic Color\n\n# Alternatives to #2b28f8\n\nBelow, you can see some colors close to #2b28f8. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #2859f8\n``#2859f8` `rgb(40,89,248)``\n• #2848f8\n``#2848f8` `rgb(40,72,248)``\n• #2836f8\n``#2836f8` `rgb(40,54,248)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #3c28f8\n``#3c28f8` `rgb(60,40,248)``\n• #4e28f8\n``#4e28f8` `rgb(78,40,248)``\n• #5f28f8\n``#5f28f8` `rgb(95,40,248)``\nSimilar Colors\n\n# #2b28f8 Preview\n\nText with hexadecimal color #2b28f8\n\nThis text has a font color of #2b28f8.\n\n``<span style=\"color:#2b28f8;\">Text here</span>``\n#2b28f8 background color\n\nThis paragraph has a background color of #2b28f8.\n\n``<p style=\"background-color:#2b28f8;\">Content here</p>``\n#2b28f8 border color\n\nThis element has a border color of #2b28f8.\n\n``<div style=\"border:1px solid #2b28f8;\">Content here</div>``\nCSS codes\n``.text {color:#2b28f8;}``\n``.background {background-color:#2b28f8;}``\n``.border {border:1px solid #2b28f8;}``\n\n# Shades and Tints of #2b28f8\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #01000d is the darkest color, while #f9f9ff is the lightest one.\n\n• #01000d\n``#01000d` `rgb(1,0,13)``\n• #010120\n``#010120` `rgb(1,1,32)``\n• #020233\n``#020233` `rgb(2,2,51)``\n• #030246\n``#030246` `rgb(3,2,70)``\n• #040359\n``#040359` `rgb(4,3,89)``\n• #05046c\n``#05046c` `rgb(5,4,108)``\n• #06047f\n``#06047f` `rgb(6,4,127)``\n• #070592\n``#070592` `rgb(7,5,146)``\n• #0805a5\n``#0805a5` `rgb(8,5,165)``\n• #0906b8\n``#0906b8` `rgb(9,6,184)``\n• #0907cb\n``#0907cb` `rgb(9,7,203)``\n• #0a07de\n``#0a07de` `rgb(10,7,222)``\n• #0b08f1\n``#0b08f1` `rgb(11,8,241)``\n• #1815f7\n``#1815f7` `rgb(24,21,247)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\n• #3e3bf9\n``#3e3bf9` `rgb(62,59,249)``\n• #504ef9\n``#504ef9` `rgb(80,78,249)``\n• #6361fa\n``#6361fa` `rgb(99,97,250)``\n• #7674fa\n``#7674fa` `rgb(118,116,250)``\n• #8987fb\n``#8987fb` `rgb(137,135,251)``\n• #9b9afc\n``#9b9afc` `rgb(155,154,252)``\n``#aeadfc` `rgb(174,173,252)``\n• #c1c0fd\n``#c1c0fd` `rgb(193,192,253)``\n• #d4d3fe\n``#d4d3fe` `rgb(212,211,254)``\n• #e6e6fe\n``#e6e6fe` `rgb(230,230,254)``\n• #f9f9ff\n``#f9f9ff` `rgb(249,249,255)``\nTint Color Variation\n\n# Tones of #2b28f8\n\nA tone is produced by adding gray to any pure hue. In this case, #8f8e92 is the less saturated color, while #2b28f8 is the most saturated one.\n\n• #8f8e92\n``#8f8e92` `rgb(143,142,146)``\n• #86869a\n``#86869a` `rgb(134,134,154)``\n• #7e7da3\n``#7e7da3` `rgb(126,125,163)``\n• #7675ab\n``#7675ab` `rgb(118,117,171)``\n• #6d6cb4\n``#6d6cb4` `rgb(109,108,180)``\n• #6564bc\n``#6564bc` `rgb(101,100,188)``\n• #5d5bc5\n``#5d5bc5` `rgb(93,91,197)``\n• #5453cd\n``#5453cd` `rgb(84,83,205)``\n``#4c4ad6` `rgb(76,74,214)``\n• #4442de\n``#4442de` `rgb(68,66,222)``\n• #3c39e7\n``#3c39e7` `rgb(60,57,231)``\n• #3331ef\n``#3331ef` `rgb(51,49,239)``\n• #2b28f8\n``#2b28f8` `rgb(43,40,248)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #2b28f8 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.5199653,"math_prob":0.72056174,"size":3673,"snap":"2019-35-2019-39","text_gpt3_token_len":1703,"char_repetition_ratio":0.12237667,"word_repetition_ratio":0.011111111,"special_character_ratio":0.5567656,"punctuation_ratio":0.23809524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9823716,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-17T09:02:23Z\",\"WARC-Record-ID\":\"<urn:uuid:626ecd54-f6c4-4d0d-822b-dd38728f40ff>\",\"Content-Length\":\"36256\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:30a7cb98-c643-4bab-af4c-85525f90d586>\",\"WARC-Concurrent-To\":\"<urn:uuid:03dc2f87-d258-472c-9602-25e6f2109723>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/2b28f8\",\"WARC-Payload-Digest\":\"sha1:PWDUW7WJ6BUQ2JTTHLTPILVJO3XZ7ZJL\",\"WARC-Block-Digest\":\"sha1:C7IPJBGYDVM4ER4FPQCM2VIAX7BGHK3J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573065.17_warc_CC-MAIN-20190917081137-20190917103137-00066.warc.gz\"}"}
https://docs.w3cub.com/javascript/errors/invalid_array_length
[ "/JavaScript\n\n# RangeError: invalid array length\n\nThe JavaScript exception \"Invalid array length\" occurs when specifying an array length that is either negative, a floating number or exceeds the maximum supported by the platform (i.e. when creating an `Array` or `ArrayBuffer`, or when setting the `length` property).\n\nThe maximum allowed array length depends on the platform, browser and browser version. For `Array` the maximum length is 4GB-1 (2^32-1). For `ArrayBuffer` the maximum is 2GB-1 on 32-bit systems (2^31-1). From Firefox version 89 the maximum value of `ArrayBuffer` is 8GB on 64-bit systems (2^33).\n\nNote: `Array` and `ArrayBuffer` are independent data structures (the implementation of one does not affect the other).\n\n## Message\n\n```RangeError: invalid array length (V8-based & Firefox)\nRangeError: Array buffer allocation failed (V8-based)\nRangeError: Array size is not a small enough positive integer. (Safari)\n```\n\n## What went wrong?\n\nAn invalid array length might appear in these situations:\n\nIf you are creating an `Array`, using the constructor, you probably want to use the literal notation instead, as the first argument is interpreted as the length of the `Array`.\n\nOtherwise, you might want to clamp the length before setting the length property, or using it as argument of the constructor.\n\n## Examples\n\n### Invalid cases\n\n```new Array(Math.pow(2, 40))\nnew Array(-1)\nnew ArrayBuffer(Math.pow(2, 32)) // 32-bit system\nnew ArrayBuffer(-1)\n\nconst a = [];\na.length = a.length - 1; // set the length property to -1\n\nconst b = new Array(Math.pow(2, 32) - 1);\nb.length = b.length + 1; // set the length property to 2^32\nb.length = 2.5; // set the length property to a floating-point number\n\nconst c = new Array(2.5); // pass a floating-point number\n```\n\n### Valid cases\n\n```[ Math.pow(2, 40) ] // [ 1099511627776 ]\n[ -1 ] // [ -1 ]\nnew ArrayBuffer(Math.pow(2, 32) - 1)\nnew ArrayBuffer(Math.pow(2, 33)) // 64-bit systems after Firefox 89\nnew ArrayBuffer(0)\n\nconst a = [];\na.length = Math.max(0, a.length - 1);\n\nconst b = new Array(Math.pow(2, 32) - 1);\nb.length = Math.min(0xffffffff, b.length + 1);\n// 0xffffffff is the hexadecimal notation for 2^32 - 1\n// which can also be written as (-1 >>> 0)\n\nb.length = 3;\n\nconst c = new Array(3);\n```" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7573457,"math_prob":0.9747642,"size":666,"snap":"2023-14-2023-23","text_gpt3_token_len":158,"char_repetition_ratio":0.163142,"word_repetition_ratio":0.0,"special_character_ratio":0.23573573,"punctuation_ratio":0.096,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9947877,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-29T20:22:34Z\",\"WARC-Record-ID\":\"<urn:uuid:38a2015b-69a7-4215-90ad-166ddd2e38b8>\",\"Content-Length\":\"19290\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dac5a3a3-bd9b-4e71-83c7-e71660a11296>\",\"WARC-Concurrent-To\":\"<urn:uuid:a51d188d-a877-4f80-8c24-ec3125626ae0>\",\"WARC-IP-Address\":\"104.21.8.155\",\"WARC-Target-URI\":\"https://docs.w3cub.com/javascript/errors/invalid_array_length\",\"WARC-Payload-Digest\":\"sha1:6VQI5DLKBQPYTWSDM6J3GKLFMAUOA6CC\",\"WARC-Block-Digest\":\"sha1:5PGSE4JMQLW2JSE2TL5EXQKNXALJLTUB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949025.18_warc_CC-MAIN-20230329182643-20230329212643-00353.warc.gz\"}"}
https://www.ndt.net/article/v11n06/rosyidi/rosyidi.htm
[ "NDT.net • June 2006 • Vol. 11 No.6\n\n## Estimating G-Max & Field CBR of Soil Subgrade Using a Seismic Method\n\nS.A. Rosyidi1, K.A.M. Nayan2, M.R. Taha3 & A. ISMAIL4\n1Lecturer, Division of Transportation Eng., Department of Civil Engineering\nMuhammadiyah University of Yogyakarta, Lingkar Barat, 55183, Yogyakarta, Indonesia\nemail: atmaja_sri@umy.ac.id\n2Lecturer, 3Professor, 4Assoc.Prof., Department of Civil & Structural Engineering,\nUniversiti Kebangsaan Malaysia. 43600, Bangi, Malaysia\nemail: khairul@eng.ukm.my, drmrt@eng.ukm.my, abim@eng.ukm.my.\n\n### ABSTRACT\n\nThe knowledge of the in-situ strength and stiffness of the ground is normally required for the design monitoring and evaluation of highway pavement so as to ensure an adequate margin of safety. In order to estimate the stiffness of the pavement foundation a method called the spectral analysis of surface wave (SASW) has been developed. The method consists of generation, measurement and processing of the dispersive Rayleigh waves recorded from two vertical transducers. Subsequently, an inversion process is carried out to obtain the shear wave velocity versus depth profile of the site from the dispersive Rayleigh wave data. The results presented in this paper showed that the SASW method is able to determine reliably the shear modulus of the soil subgrade layer of the pavement profile. In situ subgrade bearing capacity test using the field CBR test was also carried out in the same location of SASW test. An empirical relationship between the CBR value and the dynamic soil stiffness from the SASW measurements was also established for practical applications for the purpose of pavement design and maintenance.\n\nKeywords: SASW, shear wave velocity, shear modulus, pavement subgrade layer\n\n### INTRODUCTION\n\nThe performance of pavement structures is strongly influenced by the stiffness of the soil subgrade layer. In order to establish the stiffness of subgrade structures of the existing roads, accurate information of the moduli of the various pavement layers is needed. The shear modulus parameter is used to calculate the bearing capacity and to characterize the mechanical behavior of the materials under different types of traffic loading in order to predict the performance, select and to design appropriate rehabilitation techniques. In order to effectively measure and evaluate the stiffness of soil subgrade layers, a non-destructive test (NDT) of the spectral analysis of surface wave (SASW) which is economic and fast is needed. The method is based on the dispersion of Rayleigh waves (R waves) to determine the shear wave velocity each layer of the pavement profile. The SASW method has been utilized in different applications over the past decade (Stokoe et al., 1994) after the advancement and improvement of the well-known steady-state (Jones, 1958) technique. These applications include detection of soil profile, evaluation of concrete structures, detection of anomalies, detection of the structural layer of cement mortar, assessing compaction of fills and the evaluation of railway ballast. The purpose of this paper is to estimate the dynamic shear modulus of the soil subgrade layer measured from the SASW test and to derive the empirical correlation between the dynamic shear modulus parameter and the CBR values from different sites.\n\n### LITERATURE REVIEW\n\nThe SASW method is based on the particles motion of R wave in heterogeneous media. The energy of R waves from the source propagates mechanically along the surface of media and their amplitude decrease rapidly with depth. Particle motions associated with R wave are composed of both vertical and horizontal components, which when combined, formed a retrogressive ellipse close to the surface. In homogenous, isotropic, elastic half-space, R wave velocity does not vary with frequency. However, R wave velocity varies with frequency in layered medium where there is a variation of stiffness with depth (Stokoe et al., 1994). This phenomenon is termed dispersion where the frequency is dependent on R wave velocity. The ability to detect and evaluate the depth of the medium is influenced by the wavelength and the frequency generated. The shorter wavelength of high frequency penetrates the shallower zone of the near surface and the longer wavelength of lower frequency penetrates deeper into the medium.\n\nThe range of wavelength to be used as a guide for the receiver spacing can be estimated from the shear wave velocities of the material anticipated at the site:", null, "where f is the frequency and VS is shear wave velocity. The higher and low frequency waves groups needed can be generated by various transient sources of different weights and shapes. Waves of low frequency for the base and subgrade layer could be generated from hammer weights of 3 to 5 kg (Rosyidi et al., 2005a, 2005b).\n\nThe experimental dispersion curve of phase velocity and wavelength may be developed from phase information of the transfer function at the frequency range satisfying the coherence criterion. In addition, most of researchers apply the filtering criteria (Heisey et al., 1982) with a wavelength greater than ½ and less than 3 receiver spacings. The time of travel between the receivers for each frequency can be calculated by:", null, "where f is the frequency, t(f) and ff are respectively the travel time and the phase difference in degrees at a given frequency. The distance of the receiver (d) is a known parameter. Therefore, R wave velocity, VR or the phase velocity at a given frequency is simply obtained by:", null, "and the corresponding wavelength of the R wave, LR may be written as:", null, "The actual shear wave velocity of the pavement profile is produced from the inversion of the composite experimental dispersion curve. In the inversion process, a profile of set of a homogeneous layer extending to infinity in the horizontal direction is assumed. The last layer is usually taken as a homogeneous half-space. Based on the initial profile, a theoretical dispersion curve is then calculated using an automated forward modeling analysis of the dynamic stiffness matrix method (Kausel & Röesset, 1981). The theoretical dispersion curve is ultimately matched to the experimental dispersion curve of the lowest RMS error with an optimization technique. Finally, the profile from the best-fitting (lowest RMS) of the theoretical dispersion curve to the experimental dispersion curve is used that represents the most likely pavement profile of the site. The dynamic shear moduli of the materials can be easily obtained using the shear wave velocity parameter of SASW from the following equation (Yoder & Witczak, 1975):", null, "where G is the dynamic shear modulus, VS the shear wave velocity, g the gravitational acceleration, ? the total unit weight of the material and µ the Poisson ratio. Nazarian & Stokoe (1986) explained that the shear modulus parameter of material obtained from the SASW test approaches to the maximum shear modulus at a strain below about 0.001 %. In this strain range, modulus of the subgrade materials is also taken as constant.\n\n### METHODOLOGY\n\nExperimental Set Up\n\nAn impact source on a pavement surface is used to generate R waves. These waves are detected using two accelerometers where the signals are recorded using an analog digital recorder and a notebook computer for post processing (Figure 1). Several configurations of the receiver and the source spacings are required in order to sample different depths. The best configuration in the SASW is the mid point receiver spacings (Heisey et al., 1982).\n\nIn this study, the short receiver spacings of 5 and 10 cm with a high frequency source (ball bearing) are used to sample the AC layers while the long receiver spacings of 20, 40 cm and 80, 160 cm with a set of low frequencies sources (a set of hammers) are used to sample the base and subgrade layers, respectively. The SASW tests were carried out at two sites which include 30 test locations on the main road in the campus of Universiti Kebangsaan Malaysia in Bangi, Selangor, Malaysia and 20 test locations on the State Road of Prambanan to Pakem and Piyungan to Gading, Yogyakarta Province, Indonesia. Data were collected together with the field CBR tests conducted on the same SASW measured centre points.", null, "Figure 1. (a) SASW equipments, (b) impact sources, (c) SASW experimental set up, and (d) SASW test conducted in field\n\nData Analysis\n\nAll the data collected from the recorder are transformed using the Fast Fourier Transform (FFT) to frequency domain by the dBFA32 software resident in the notebook computer. Two functions in the frequency domain between the two receivers are of great importance: (1) the coherence function and (2) the phase information of the transfer function. The coherence function is used to visually inspect the quality of signals being recorded in the field and have a real value between zero and one in the range of frequencies being measured. The value of one indicates a high signal-to-noise ratio (i.e., perfect correlation between the two signals) while values of zero represents no correlation between the two signals. The transfer function spectrum is used to obtain the relative phase shift between the two signals in the range of the frequencies being generated.\n\nFigure 2 shows a typical set of the coherence and the phase plot of the transfer function from the measurement of an 80 cm receiver spacing at the site of UKM's road. By unwrapping the data of the phase angle from the transfer function, a composite experimental dispersion curve of all the receiver spacings are generated. By repeating the procedure outlined above and using equation (2) through (4) for each frequency value, the R wave velocity corresponding to each wavelength is evaluated and the experimental dispersion curve is subsequently generated. Figure 3 shows the example of the composite experimental dispersion curve from measurements of all the receiver spacings.", null, "Figure 2. The coherence and the transfer function spectrum for an 80 cm receiver spacing on UKM's road.", null, "Figure 3. A typical dispersion curve from a set of SASW tests on the pavement showing the portion of the phase velocity for subgrade layer\n\n### RESULTS AND DISCUSSION\n\nBy unwrapping data of the phase angle from the transfer function (Fig.2 for site 1), the composite experimental dispersion curve obtained is as shown in Figure 3. The figure shows the horizontal dash lines for wavelengths ranging from 0.8 to 3 m, the subgrade layer with the minimum phase velocity of 180 m/s to the maximum phase velocity of 230 m/s are obtained.\n\nIn order to generate the actual shear wave velocity of the subgrade layer, an inversion process using 3 D forward modeling from the stiffness matrix method (Kausel & Röesset, 1981) and an optimization technique of the maximum likelihood method (Joh, 1996) were conducted. For developing the pavement profile from the inversion analysis, the starting model parameter is obtained from the cored road profile that was found to be consisting of an average asphalt concrete (AC) layer (70 mm thick), a base layer (400 mm thick) over a subgrade layer. Descriptions of model parameters and typical thickness of the pavement layers are shown in Figure 4.", null, "Figure 4. A typical pavement profile for starting model parameter\n\nThe pavement profile obtained from inversion process is shown in Figure 5. The profile is an example of the SASW result from the first location (UKM, Malaysia). Core drilling was also conducted in the same location after the SASW measurement. There is a reasonable agreement of the profile depth between the results from the SASW measurement and the core drilling. The average of inverted shear wave velocity for UKM's road measuring points is 178.419 m/s with a range of 116.44 to 263.226 m/s.\n\nThe dynamic shear modulus is then obtained from the shear wave velocity profile using the dynamic material equation (Equation 5). The average shear modulus of the subgrade material from the analysis is 69.779 MPa. Based on the shear modulus, the subgrade material maybe classified as a sandy soil material. The shear wave velocities and their corresponding shear modulus from this study were listed in Table 1 in comparison with the results of SASW testing obtained by other researchers such as Puri (1969) and Nazarian & Stokoe (1986). It is important to note that Puri (1969) obtained the dynamic properties of silty sand using the free vertical vibration stress waves measured at 1.0 x 10-4 % strain level.\n\nThe shear wave velocities from the SASW were then correlated to the CBR values for the evaluation of the bearing capacities of the subgrade materials. The relationship between the shear wave velocities and CBR values can also be derived as shown in Figure 6 for the subgrade layer.\n\n Table 1. Comparison of subgrade shear wave velocity and shear modulus. Compared parameter This study Puri (1969) Nazarian & Stokoe (1986) Shear wave velocity (m/s) 178.42 m/s --- 147.5 - 211.9 m/s Shear Modulus (MPa) 69.78 MPa Sandy soil with poorly graded 64.75 MPa Poorly graded fine silty sand 41.34 - 85.31 MPa Loose sand", null, "Figure 5. Comparison between actual pavement profile and the result from core drilling in the site\n\nFigure 6 also shows that the increased in the shear wave velocities correlates well with the increased in the CBR values. The coefficients of correlation obtained (Figure 6) indicate that the empirical equation derived between the shear wave velocities have significant correlations with the CBR value. The correlation coefficient, R2 of 0.938 was obtained for the subgrade layer. However, the empirical equations obtained only shows the best correlation of shear wave velocity to the CBR value that is not more than 400 m/s. Higher deviations obtained from Figure 6 for high values of CBR should be investigated. The derived equation of Vs and CBR can be written as:\n\nCBR = 0.0006 (VSS)1.99    (6)\n\nwhere, CBR is the field California Bearing Ratio in % and VS is the shear wave velocity in m/s. Figure 7 shows the empirical correlation between the CBR values to the dynamic shear modulus from SASW for the subgrade layer. The result shows a good agreement between the dynamic shear modulus from the SASW test and the CBR value with a deviation range of ± 20 %. The empirical equations obtained were summarized as below :\n\nCBR = 0.266 (G)1.0027, R2 = 0.947     (7)\n\nwhere G is an approach value of the maximum shear modulus in MPa obtained from the SASW analysis.", null, "Figure 6. Correlation between the shear wave velocity, DCP and CBR for the subgrade layer", null, "Figure 7. Empirical correlation between the CBR value and the dynamic elastic modulus from SASW for the subgrade layer\n\n### CONCLUSIONS\n\n1. Good agreements were obtained between the measured shear wave velocities and the corresponding dynamic shear modulus as compared to the work of Puri (1969) and Nazarian & Stokoe (1986). 2. This study has also managed to obtain good empirical correlations between the dynamic shear modulus and the field CBR values. 3. The SASW method is able to characterize the stiffness of the pavement subgrade layer in terms of shear wave velocity and its corresponding dynamic shear modulus satisfactorily for the propose of pavement design and evaluation.\n\n### ACKNOWLEDGEMENT\n\nThe authors would like to give our sincere appreciation to the Ministry of Science, Technology and Environmental of Malaysia for supporting this research through the IRPA Grant No.09-02-02-0055-EA151, and also to the Faculty of Engineering, Muhammadiyah University of Yogyakarta for supporting the study through Engineering Research Grant 2004. The authors also would like to thank Prof. Sung Ho Joh of the Chung Ang University, Korea for his assistance in using the WinSASW software in this study and Prof. Gucunski of Rutgers University, USA for his interested discussion.\n\n### REFERENCES\n\n1. Al-Hunaidi, M.O. 1998. Evaluation-Based Genetic Algorithms for Analysis of Non-Destructive Surface Waves Test on Pavements\". NDT&E international, Vol.31, No.4, 273-280.\n2. Heisey, J.S., Stokoe II, K.H. & Meyer, A.H. 1982. Moduli of Pavement Systems from Spectral Analysis of Surface Waves. Transportation Research Record (TRB) No.852, 22-31.\n3. Joh, S.H. 1996. Advance in Interpretation & Analysis Technique for Spectral Analysis of Surface Wave (SASW) Measurements. Ph.D Dissertation. The University of Texas at Austin.\n4. Jones, R.B. 1958. In-situ Measurement of the Dynamic Properties of Soil by Vibration Methods. Geotechnique, Vol.8, No.1, pp.1-21.\n5. Kausel, E. & Röesset, J.M. 1981. Stiffness Matrices for Layered Soils. Bulletin of the Seismological Society of America, Vol.71, No.6, pp.1743-1761.\n6. Nazarian, S. & Stokoe, K.H.II. 1986. In Situ Determination of Elastic Moduli of Pavement Systems by Spectral-Analysis-of-Surface-Wave Method (Theoretical Aspects). Research Report 437-2. Center of Transportation Research. Bureau of Engineering Research. The University of Texas at Austin.\n7. Stokoe, K.H.II, Wright, S.G., Bay, J.A. & Röesset, J.M. 1994. Characterization of Geotechnical Sites by SASW Method. GEOPHYSICAL CHARACTERIZATION OF SITES. XIII ICSMFE. 1994. Oxford & IBH Publishing Co.PVT.Ltd. New Delhi.\n8. Puri, V.K. 1969. Natural Frequency of Block Foundation under Free and Force Vibration. Master Thesis. University of Roorkee. India.\n9. Rosyidi, S.A., Taha, M.R., Nayan, K.A.M. & Ismail, A. 2005a. Predicting Soil Bearing Capacity of Pavement Subgrade System using SASW Method. Proceeding of the International Symposium of Geoline 2005, Lyon, France.\n10. Rosyidi, S.A., Taha, M.R. & Nayan, K.A.M. 2005b. Assessing In Situ Dynamic Stiffness of Pavement Layers with Simple Seismic Test. Proceeding of International Seminar and Exhibition on Road Constructions. Semarang, Indonesia. pp.15-24.\n11. Yoder, E.J. & Witczak, M.W. 1975. PRINCIPLES OF PAVEMENT DESIGN. New York: John Wiley & Son, Inc." ]
[ null, "https://www.ndt.net/article/v11n06/rosyidi/eq1.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/eq2.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/eq3.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/eq4.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/eq5.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig1.jpg", null, "https://www.ndt.net/article/v11n06/rosyidi/fig2.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig3.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig4.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig5.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig6.gif", null, "https://www.ndt.net/article/v11n06/rosyidi/fig7.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9086169,"math_prob":0.8821343,"size":14733,"snap":"2019-26-2019-30","text_gpt3_token_len":3070,"char_repetition_ratio":0.15629031,"word_repetition_ratio":0.02764781,"special_character_ratio":0.2009774,"punctuation_ratio":0.08880455,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95649916,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-18T15:10:45Z\",\"WARC-Record-ID\":\"<urn:uuid:0f7320e7-b1c7-460e-bd77-b6f133ae9930>\",\"Content-Length\":\"22835\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e66d86dd-7110-4a8b-9776-d84f54dd7b22>\",\"WARC-Concurrent-To\":\"<urn:uuid:2ef1f1d0-b92e-4e0c-905d-4b3acac36c3b>\",\"WARC-IP-Address\":\"89.107.190.37\",\"WARC-Target-URI\":\"https://www.ndt.net/article/v11n06/rosyidi/rosyidi.htm\",\"WARC-Payload-Digest\":\"sha1:HRXWVF25F4BMOLZDI67YZVGAIT3PYDEV\",\"WARC-Block-Digest\":\"sha1:BAZUO4EF2KYZLLGW5XKKRTT53CKYT4GV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525659.27_warc_CC-MAIN-20190718145614-20190718171614-00347.warc.gz\"}"}
https://physics.stackexchange.com/questions/263791/confusion-with-newtons-third-law
[ "# Confusion with Newton's third law\n\n“Every action has an equal and opposite reaction.”\n\nI have a query about the word every in that sentence.\n\nSuppose we have two objects A and B. A pushes B with a force of 5N and B will push A with a force of 5N. However, won’t the reaction that B has caused on A, serve as an action for A, causing A to again push B with its reaction and thus making a total of 10N? (And then, of course, B will also apply a force of 10N on A.)\n\n• You are counting the A on B force twice. There are not three (or more) forces, only two. – garyp Jun 21 '16 at 1:47\n• The reaction isn't really a separate thing from the action. They come as a pair. The 'action' is the reaction to the reaction (should that be rereaction?). – dmckee --- ex-moderator kitten Jun 21 '16 at 2:09\n• I think it means at every point of application, each force can be matched with a force of equal magnitude pointing in the opposite direction. – Emil Jun 21 '16 at 5:33\n• The law says every action HAS an equal and opposite reaction, not every action CREATES an equal and opposite reaction. If you start with A, then A's push on B will \"create\" the reaction, but B's push on A will already have its reaction, namely the original push. – João Mendes Jun 21 '16 at 10:52\n• Another analogy: \"every married person has a spouse\". I'm married, so I have a wife. But that means my wife is married, so she must have a husband, and that husband must have a wife, and ... – Harry Johnston Jun 21 '16 at 23:10\n\nThe way we are all taught Newton's Laws (by reciting them like mantras as children) is unfortunate because the traditional wording is misleading in many ways.\n\nA big problem (though not the only one) with the traditional wording of both Newton's second and third laws is that they incorrectly suggest cause and effect (and hence imply a chain of events, as you put it).\n\nNewton's second law, for example, suggests that a force 'causes' an acceleration, implying it happens first. It doesn't. The force and the acceleration occur jointly and concurrently, despite the persistent misconception and stubborn illusion of a temporal sequence.\n\nBut let's not get distracted with the second law right now, because you are understandably perplexed by the third ...\n\nAgain, the wording of the third law suggests that an 'action' happens first and then it 'causes' a 'reaction'. If this were literally true, you'd have every right to cry infinite regress!\n\nThe truth is, the forces occur jointly and simultaneously, and are not the causes of each other. If you want a better way to think about it, you can hardly do better than the way Newton himself came up with the third law. He argued for it as follows:\n\nSuppose you had a system of two objects interacting with each other, with no external forces acting on the system. Then you should be able to consider that system as a 'whole' if you want to, and from that perspective the system as a whole must not accelerate as it has no net force acting on it. But this can only be the case if the two objects making up the system have equal and opposite forces between them (i.e. all internal forces of the system must cancel out).\n\nDo you see how this argument does not involve any 'causal sequence' or 'chain' of forces? It is just an observation about what must be the case in order for Newton's force-based scheme to work consistently.\n\nNot convinced? Let me try an analogy. You and your friend each have a certain amount of money. You buy something from your friend. Your balance goes down and your friend's goes up. Was there a time-delayed causal sequence here? Nope. Your balance decreased concurrently (as you handed over the money) as your friend's balance increased. Looking at the system as a whole, we know that since no money flowed into or out of the system during the transaction, the net balance must be zero. Every payment entails a receipt and every receipt entails a payment, but, despite the illusion, there is no sequence (much less a perpetual one!).\n\nNote: You could also translate this argument into the language of momentum conservation, but I have tried to answer the question in the same language in which you phrased it.\n\nUPDATE: The 'infinite regress' problem highlighted here is not the only confusion that arises when we use the suggestive language of 'action' and 'reaction'. I've identified two other problems this language causes along with my proposed solution here.\n\n• Thanks for a great answer! But i did not get the crux! Whats the key point that you’re trying to highlight, that proves my statement wrong? – Aaryan Dewan Jun 21 '16 at 15:13\n• The gist is this: The popular idea of A pushing/pulling B and then B pushing/pulling A back in response is wrong. In the Newtonian model, at any given time each body in the system has a single force vector assigned to it (determined by whatever force-laws are in play). At any given time the sum of all those vectors is zero (assuming the system is isolated). If there are only two bodies in the system, this means their forces are equal and opposite. But this is not to be thought of as some sort of sequential tit-for-tat. There is just a background law assigning forces to bodies at each instant. – Physics Footnotes Jun 21 '16 at 15:25\n• Newton's language of Action/Reaction turns my clinical account into a compelling narrative that makes the story understandable. But if you take the narrative too seriously it achieves the exact opposite, leading as it has in your case, into the absurd idea that an object must remember that it has already pushed another object once so it had better not push again or else it will ruin all the equations. – Physics Footnotes Jun 21 '16 at 15:45\n• Please let me know if the above comments help, because if they do I'll transcribe them into my main answer for the benefit of others. – Physics Footnotes Jun 21 '16 at 16:10\n• Yeah I like the idea of \"the push\" being the causal agent of both the force and the acceleration. Both force and acceleration are technical parts of the abstraction, whereas \"the push\" is more colloquial, since we haven't decided what exactly this push is acting on. I think it's very dangerous to say both \"the force is not the cause of the acceleration\" and \"F=ma\" in the same sentence. The only correct form of N2 is $\\sum \\vec{F}=m\\vec{a}$, and then it's clear that \"THE force is the cause....\" is wrong. – levitopher Jun 24 '16 at 20:28\n\nIt does not matter which one you call action and which one reaction, what the law says is that two objects make the same force on each other. Thus if A pushed B with a force of 5 Newtons, B will also push A with the same force.\n\nYou need a better statement of Newton's Law. The one you are using is meaningless, because the word action is not defined. (In today's language of physics the word action is used in an entirely different context, sense, and meaning.) It's based on what Newton wrote, but is only half of what he wrote. Wikipedia gives us the whole thing\n\nTo every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.\n\nBut this statement still has the archaic language. We need to stop repeating Newton's use of the word action. It means nothing to us today.\n\nI intended to find a link to a good version of the law. I could not find one. I'm sure there are good ones out there, but a quick search came up with a bunch of bad ones, almost all of them using the words action and reaction. Here's a version based on the statement of the law in the book \"Integrated Science\" by Tillery.\n\nWhenever two objects interact, the force exerted on the first by the second is equal in strength and opposite in direction to the force exerted on the second by the first.\n\nBut no matter how it is phrased, it needs explanation and elaboration. The short statements of the law are not good ways to learn what the law is about. Hyperphysics (scroll to the bottom) does a pretty good job explaining it.\n\nYou're assuming \"action\" and \"reaction\" are the same things. Ok, there are lots of reasons why we might consider them to be either similar or exactly the same, but since the third law doesn't say \"for every action there is an equal and opposite action\", the third law is logically consistent.\n\nFor the purposes of the third law, reaction is NOT the same as action.\n\nThis might sound like a bit of a linguistic, rather then physical, argument, but the third law is motivated by the form of our analysis. We develop interactions as forces, and then we ask what happens under action of those forces. Well, for every force we 100% know exists (\"me pushing on the wall\"), the third law tells us that there is another, reactionary force (\"the wall pushing on me\"). \"reaction\" is a kind of force, not a name for all forces.\n\nHow about considering a specific force, such as the Newtonian gravitational force between two point masses $m_1$ and $m_2$. We could write the force that mass 1 exerts on mass 2 as follows:\n\n$$\\vec{F}_{12} =-G\\frac{m_1 m_2} {r_{12}^2} \\hat{r}_{12},$$\n\nwhere $r_{12}$ and $\\hat{r}_{12}$ are the distance 2 is from 1 and unit vector from 1 to 2, respectively. Does 2 exert a force on 1? According to Newton's Universal Law of Gravitation, it does (just as it's written above):\n\n$$\\vec{F}_{21} =-G\\frac{m_2 m_1} {r_{21}^2} \\hat{r}_{21}.$$\n\nHow are $\\vec{F}_{21}$ and $\\vec{F}_{21}$ similar? How are they different? Is there a difference in sign?\n\nIf you want to consider EVERY so-called action, then you need to consider different forces, keeping in mind the idea of \\it{force} being classical.\n\nRegarding (re)action, which force is exerted \"first\"? I don't think one can say. As mentioned in other answers, the wording is unfortunate and misleadingly.\n\nNote that Newton's Third Law is often (re)stated as follows:\n\nForces come in equal and opposite pairs.\n\nI might be a little late in answering this question, but I hope it'll help.\n\nPhysics Footnotes emphasised that action and reaction forces occur simultaneously at the same time. This is correct. The words action and reaction do create the misconception that one force is the reason for the other.\n\nLet me explain why these two forces happen simultaneously, with that knowledge you will understand why the reaction force(so called) does not act as yet another force. To understand this we must understand what causes a force.\n\nA force is always caused by the interaction of two bodies.(We are not considering fictitious forces here) These two objects can be touching each other or may be some distance apart(Eg - gravitational force)\n\nTaking your example, how would A have exerted the force of 5N, upon B? Possibly, A was in motion (relative to the earth) previously and would collide with B, thus exerting the force. (It is easy to visualise A as your hand and B as some object)\n\nBefore the collision, A would be in motion towards B,relative to the earth and thus, relative to B (B is in the same state of motion as the earth, which is the state of being still. So, as the earth and B share the same state of motion, a motion relative to the earth, is a motion relative to B as well) Also, relative to A, B would be in motion towards A.( If we regard A to be stationary, then B is the one that is moving)\n\n• So, relative to A, B is the moving object and A is the stationary object. So, when the two objects collide, relative to A, It is B that exerts the force. (Because relative to A, it is B that comes towards it and collides) Relative to A, A was just moving along happily until This B came along and bumped into him, exerting a force upon A\n• As in the traditional view, it is A that moves and collides with B. So, the collision would cause a force from A on B. Relative to B, B was sitting still, minding its own business until A came and bumped into him, thus exerting the force.\n\nIt is these two forces that are popularly regarded as action reaction force pairs.\n\nBoth forces exist simultaneously, relative to A, the acting force is a force of 5N, exerted upon it by B. Relative to B, the acting force is force of 5N exerted upon it by A.\n\nWith this understanding on how the forces concerned are created, it is easy understand that that the force exerted by B upon A (F1)does not lead to a whole new reaction force(so called) In fact, relative to A, the force exerted by it upon B can be regarded as the reaction force,to F1 (with the true sense of the third law, of course, which is to say that it is not a result of the first force)\n\nIf there is a certain force in some direction, the existence of another force is unavoidable( in the opposite direction, acting on the object which caused the force, to which we referred to first) Which is to say forces exist in pairs. Now, relative to A, it is B that exerts the force, So, relative to A, the action is the force exerted by B upon A.( Let's call it F1) Even as this action takes place relative to A, relative to B yet another action takes place. ( force exerted by A upon B, F2) For A, The action is F1. At the same time F2 is also exerted. For A, F2 is an indirect consequence of the collision. It can be considered to be the reaction force relative to A. ( The term \"reaction\" is not really suitable, but that is the commonly used term) Likewise For B, F1 is the indirect consequence; reaction. The creation of a whole new force as a reaction is not what Newton meant by the third law. So, every action has a reaction, as stated by the third law\n\n• Great answer! Thanks a lot. Can you please explain the last part, or the crux of your answer? – Aaryan Dewan Jul 5 '16 at 4:34\n• I edited my answer, see if it answers your problem – SNB Jul 5 '16 at 15:38", null, "It should be \"Every action has equal and opposite reaction of SAME TYPE\" , the best way to understand these contact force related questions is to draw a large clear free body diagram. Which will eventually lights up your problems.\n\nDraw all possible forces on both object(s) and or contact surface.\n\nPls see the image , the force you applied is not belong to the action, it is a separate force, action reaction forces are (Ra and Rb) their magnitude remains equal regardless of situation (acceleration, declaration, constant velocity etc) , and those are the action reaction pair, not the force you applied on the body.\n\nIf you are concerning about the reaction force due to 5N force applied on the object A , it will be acting on your hand which is still 5N acting opposite direction. Also to clarify your concern, newton pair of force always acts on different bodies not on the same body\n\n• please read my question again. – Aaryan Dewan Jun 21 '16 at 4:35\n• Pls see the image , the force you applied is not belong to the action, it is a separate force, action reaction forces are (Ra and Rb) their magnitude remains equal regardless of situation (acceleration, declaration, constant velocity etc) , and those are the action reaction pair, not the force you applied on the body. If you are concerning about the reaction force due to 5N force applied on the object A , it will be acting on your hand which is still 5N acting opposite direction. Also to clarify your concern, newton pair of force always acts on different bodies not on same body – Manoj Jun 21 '16 at 5:48" ]
[ null, "https://i.stack.imgur.com/cteHw.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9708956,"math_prob":0.8991062,"size":3597,"snap":"2020-24-2020-29","text_gpt3_token_len":838,"char_repetition_ratio":0.18229891,"word_repetition_ratio":0.020558003,"special_character_ratio":0.22685571,"punctuation_ratio":0.108949415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9771119,"pos_list":[0,1,2],"im_url_duplicate_count":[null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-15T02:56:14Z\",\"WARC-Record-ID\":\"<urn:uuid:14ac96a8-f750-472c-a926-377882c4a56f>\",\"Content-Length\":\"200341\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc0a942e-9a3a-4109-8f4a-cf98a5c9cc6d>\",\"WARC-Concurrent-To\":\"<urn:uuid:c86585ea-a9fe-4d8c-90e8-33fef0e4e1bf>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/263791/confusion-with-newtons-third-law\",\"WARC-Payload-Digest\":\"sha1:Y4TBO63MC2LLMEGFMMU5MRCIPHJSX3PO\",\"WARC-Block-Digest\":\"sha1:FTOMDMRPRPV6P4SUDHB5L5I2SSMQR2XT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657154789.95_warc_CC-MAIN-20200715003838-20200715033838-00404.warc.gz\"}"}
https://www.quantstart.com/articles/Cholesky-Decomposition-in-Python-and-NumPy/
[ "# Cholesky Decomposition in Python and NumPy\n\nCholesky Decomposition in Python and NumPy\n\nFollowing on from the article on LU Decomposition in Python, we will look at a Python implementation for the Cholesky Decomposition method, which is used in certain quantitative finance algorithms.\n\nIn particular, it makes an appearance in Monte Carlo Methods where it is used to simulating systems with correlated variables. Cholesky decomposition is applied to the correlation matrix, providing a lower triangular matrix L, which when applied to a vector of uncorrelated samples, u, produces the covariance vector of the system. Thus it is highly relevant for quantitative trading.\n\nCholesky decomposition assumes that the matrix being decomposed is Hermitian and positive-definite. Since we are only interested in real-valued matrices, we can replace the property of Hermitian with that of symmetric (i.e. the matrix equals its own transpose). Cholesky decomposition is approximately 2x faster than LU Decomposition, where it applies.\n\nIn order to solve for the lower triangular matrix, we will make use of the Cholesky-Banachiewicz Algorithm. First, we calculate the values for L on the main diagonal. Subsequently, we calculate the off-diagonals for the elements below the diagonal:\n\n\\begin{eqnarray*} l_{kk} &=& \\sqrt{ a_{kk} - \\sum^{k-1}_{j=1} l^2_{kj}}\\\\ l_{ik} &=& \\frac{1}{l_{kk}} \\left( a_{ik} - \\sum^{k-1}_{j=1} l_{ij} l_{kj} \\right), i > k \\end{eqnarray*}\n\nAs with LU Decomposition, the most efficient method in both development and execution time is to make use of the NumPy/SciPy linear algebra (linalg) library, which has a built in method cholesky to decompose a matrix. The optional lower parameter allows us to determine whether a lower or upper triangular matrix is produced:\n\nimport pprint\nimport scipy\nimport scipy.linalg # SciPy Linear Algebra Library\n\nA = scipy.array([[6, 3, 4, 8], [3, 6, 5, 1], [4, 5, 10, 7], [8, 1, 7, 25]])\nL = scipy.linalg.cholesky(A, lower=True)\nU = scipy.linalg.cholesky(A, lower=False)\n\nprint \"A:\"\npprint.pprint(A)\n\nprint \"L:\"\npprint.pprint(L)\n\nprint \"U:\"\npprint.pprint(U)\n\n\nThe output from the code is given below:\n\nA:\narray([[ 6, 3, 4, 8],\n[ 3, 6, 5, 1],\n[ 4, 5, 10, 7],\n[ 8, 1, 7, 25]])\nL:\narray([[ 2.44948974, 0. , 0. , 0. ],\n[ 1.22474487, 2.12132034, 0. , 0. ],\n[ 1.63299316, 1.41421356, 2.30940108, 0. ],\n[ 3.26598632, -1.41421356, 1.58771324, 3.13249102]])\nU:\narray([[ 2.44948974, 1.22474487, 1.63299316, 3.26598632],\n[ 0. , 2.12132034, 1.41421356, -1.41421356],\n[ 0. , 0. , 2.30940108, 1.58771324],\n[ 0. , 0. , 0. , 3.13249102]])\n\n\nAs with LU Decomposition, it is unlikely that you will ever need to code up a Cholesky Decomposition in pure Python (i.e. without NumPy/SciPy), since you can just include the libraries and use the far more efficient implements found within. However, for completeness I have included the pure Python implementation of the Cholesky Decomposition so that you can understand how the algorithm works:\n\nfrom math import sqrt\nfrom pprint import pprint\n\ndef cholesky(A):\n\"\"\"Performs a Cholesky decomposition of A, which must\nbe a symmetric and positive definite matrix. The function\nreturns the lower variant triangular matrix, L.\"\"\"\nn = len(A)\n\n# Create zero matrix for L\nL = [[0.0] * n for i in xrange(n)]\n\n# Perform the Cholesky decomposition\nfor i in xrange(n):\nfor k in xrange(i+1):\ntmp_sum = sum(L[i][j] * L[k][j] for j in xrange(k))\n\nif (i == k): # Diagonal elements\n# LaTeX: l_{kk} = \\sqrt{ a_{kk} - \\sum^{k-1}_{j=1} l^2_{kj}}\nL[i][k] = sqrt(A[i][i] - tmp_sum)\nelse:\n# LaTeX: l_{ik} = \\frac{1}{l_{kk}} \\left( a_{ik} - \\sum^{k-1}_{j=1} l_{ij} l_{kj} \\right)\nL[i][k] = (1.0 / L[k][k] * (A[i][k] - tmp_sum))\nreturn L\n\nA = [[6, 3, 4, 8], [3, 6, 5, 1], [4, 5, 10, 7], [8, 1, 7, 25]]\nL = cholesky(A)\n\nprint \"A:\"\npprint(A)\n\nprint \"L:\"\npprint(L)\n\n\nThe output from the pure Python implementation is given below:\n\nA:\n[[6, 3, 4, 8], [3, 6, 5, 1], [4, 5, 10, 7], [8, 1, 7, 25]]\nL:\n[[2.449489742783178, 0.0, 0.0, 0.0],\n[1.2247448713915892, 2.1213203435596424, 0.0, 0.0],\n[1.6329931618554523, 1.414213562373095, 2.309401076758503, 0.0],\n[3.2659863237109046,\n-1.4142135623730956,\n1.5877132402714704,\n3.1324910215354165]]\n\n\nThe SciPy implementation and the pure Python implementation both agree, although we haven't calculated the upper version for the pure Python implementation. In production code you should use SciPy as it will be significantly faster at decomposing larger matrices." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.71294,"math_prob":0.99515694,"size":4332,"snap":"2019-51-2020-05","text_gpt3_token_len":1444,"char_repetition_ratio":0.115295745,"word_repetition_ratio":0.06865671,"special_character_ratio":0.39358264,"punctuation_ratio":0.23217922,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9987934,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-20T15:17:54Z\",\"WARC-Record-ID\":\"<urn:uuid:913b25a1-fe43-4e09-bd51-e9b1fb149f7e>\",\"Content-Length\":\"17837\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3d210a4e-2da6-49e8-9b9f-168e4ee9a721>\",\"WARC-Concurrent-To\":\"<urn:uuid:3be7cdb2-f65b-4bc8-976c-4d221842d617>\",\"WARC-IP-Address\":\"23.23.50.20\",\"WARC-Target-URI\":\"https://www.quantstart.com/articles/Cholesky-Decomposition-in-Python-and-NumPy/\",\"WARC-Payload-Digest\":\"sha1:GZ44EOUEGL36CZXFXHVSBCADADFKKH7D\",\"WARC-Block-Digest\":\"sha1:FGROCOHZIDEXCTX24JJLLHDFLNBIUM5T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250598800.30_warc_CC-MAIN-20200120135447-20200120164447-00406.warc.gz\"}"}
https://www.elsevier.com/books/feedback-systems-input-output-properties/desoer/978-0-12-212050-3
[ "", null, "# Feedback Systems: Input-output Properties\n\n1st Edition - January 28, 1975\n\nWrite a review\n\n• Editor: C.A. Desoer\n• eBook ISBN: 9780323157797\n\n## Purchase options\n\nPurchase options\nDRM-free (PDF)\nSales tax will be calculated at check-out\n\n#### Institutional Subscription\n\nFree Global Shipping\nNo minimum order\n\n## Description\n\nFeedback Systems: Input-output Properties deals with the basic input-output properties of feedback systems. Emphasis is placed on multiinput-multioutput feedback systems made of distributed subsystems, particularly continuous-time systems. Topics range from memoryless nonlinearities to linear systems, the small gain theorem, and passivity. Norms and general theorems are also considered. This book is comprised of six chapters and begins with an overview of a few simple facts about feedback systems and simple examples of nonlinear systems that illustrate the important distinction between the questions of existence, uniqueness, continuous dependence, and boundedness with respect to bounded input and output. The next chapter describes a number of useful properties of norms and induced norms and of normed spaces. Several theorems are then presented, along with the main results concerning linear systems. These results are used to illustrate the applications of the small gain theorem to different classes of systems. The final chapter outlines the framework necessary to discuss passivity and demonstrate the applications of the passivity theorem. This monograph will be a useful resource for mathematically inclined engineers interested in feedback systems, as well as undergraduate engineering students.\n\n• Preface\n\nAcknowledgments\n\nList of Symbols\n\nI Memoryless Nonlinearities\n\n1 Sector Conditions\n\n2 Linear Feedback around a Nonlinearity (Memoryless Case)\n\n3 Multiple Nonlinearities\n\nNotes and References\n\nII Norms\n\n1 Norms: Definitions and Examples\n\n2 Equivalent Norms\n\n3 Relations between Normed Spaces\n\n4 Geometric Interpretation of Norms\n\n5 Induced Norms of Linear Maps\n\n6 Two Examples\n\n8 The Measure of a Matrix\n\nNotes and References\n\nIII General Theorems\n\n1 Setting of the Problem\n\n2 Small Gain Theorem\n\n3 Small Gain Theorem: Incremental Form\n\n4 A Boundedness Result\n\n5 An Existence and Uniqueness Theorem\n\n6 Loop Transformation Theorem\n\n7 L Stability\n\n8 General Feedback Formula\n\nNotes and References\n\nIV Linear Systems\n\n0 Introduction\n\n1 Linear Feedback Systems with Rational Transfer Functions\n\n2 Necessary and Sufficient Conditions: Factorization Method\n\n3 Linear Feedback Systems with Dynamics in the Feedback Path (Rational Transfer Functions Case)\n\n4 Convolution Feedback Systems\n\n5 Graphical Test\n\n6 Discrete-Time Systems\n\n7 Linear Time-Varying Systems\n\n8 Slowly Varying Systems\n\n9 Linearization\n\nNotes and References\n\nV Applications of the Small Gain Theorem\n\n1 Continuous-Time Systems—LP Stability\n\n2 L2 Stability—Circle Criterion\n\n3 Exponential Weighting—L∞ Stability\n\n4 Discrete-Time Systems—LP Stability\n\n5 Slowly-Varying Linear Systems\n\n6 Nonlinear Circuit Example\n\n7 Existence of Periodic Solutions\n\n8 Popov Criterion\n\n9 Instability\n\nNotes and References\n\nVI Passivity\n\n0 Introduction\n\n1 Motivation from Circuit Theory\n\n2 Scalar Products\n\n3 Formal Framework\n\n4 Passive Systems: Definition and Examples\n\n5 Passivity Theorem\n\n6 The Popov Criterion\n\n7 Discrete-Time Case\n\n8 Average Logarithmic Variation Criterion\n\n9 Multiplier Theory\n\n10 Relation between the Passivity Theorem and the Small Gain Theorem\n\n11 Invertibility of I + H\n\n12 Instability Theorems\n\nNotes and References\n\nAppendixes\n\nA Integrals and Series\n\nA.1 Regulated Functions\n\nA.2 Integrals\n\nA.3 Series\n\nB Fourier Transforms\n\nB.1 L1 Theory\n\nB.2 L2 Theory\n\nB.3 Laplace Transform\n\nC Convolution\n\nC.1 Introduction\n\nC.2 Convolution of Functions\n\nC.3 Convolution of a Measure and a Function\n\nC.4 Convolution of Sequences\n\nD Algebras\n\nD.1 Algebras\n\nD.2 Ideals\n\nD.3 Inverses in A\n\nE Bellman-Gronwall Lemma\n\nReferences\n\nIndex\n\n## Product details\n\n• No. of pages: 2\n• Language: English" ]
[ null, "https://secure-ecsd.elsevier.com/covers/80/Tango2/large/9780122120503.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7829713,"math_prob":0.6830013,"size":4259,"snap":"2022-05-2022-21","text_gpt3_token_len":979,"char_repetition_ratio":0.12949471,"word_repetition_ratio":0.0,"special_character_ratio":0.19464663,"punctuation_ratio":0.07834758,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9741592,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-20T11:56:29Z\",\"WARC-Record-ID\":\"<urn:uuid:4f66e1f2-dcb1-42e9-ba6d-6abf63cad86f>\",\"Content-Length\":\"192782\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:133d73c6-5183-4350-aaa3-58fa0455b5d2>\",\"WARC-Concurrent-To\":\"<urn:uuid:c72e9900-f9fd-4d15-b69d-34e2bb6d0455>\",\"WARC-IP-Address\":\"203.82.26.7\",\"WARC-Target-URI\":\"https://www.elsevier.com/books/feedback-systems-input-output-properties/desoer/978-0-12-212050-3\",\"WARC-Payload-Digest\":\"sha1:SSR4EVZOPTWQ5CLPCMQH4Y5KFOZATC4U\",\"WARC-Block-Digest\":\"sha1:LHGISTOMVJANAE3EQ7M4NCX6ZFMVITZH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662531779.10_warc_CC-MAIN-20220520093441-20220520123441-00120.warc.gz\"}"}
https://www.actucation.com/grade-6-maths/word-problems-
[ "Informative line\n\n# Word Problems on Fractions\n\n• To solve the word problems, we need to follow the given steps:\n\nStep 1: Read and understand the given situations.\n\n• In this step, we need to identify the keyword that will help us to determine which operation symbol to be used.\n\nStep 2: Choose the correct operation and solve the problem.\n\nTo understand the above steps in a better way, we should understand how problems involve the basic four operations:\n\n1. Addition:  A problem in which two or more quantities are being combined.\n\nKeywords: Sum, in all, combined, altogether, added etc.\n\nFor example: Emma bought 2 cupcakes and Carl bought 5. How many cupcakes did they buy in all?\n\nKeyword = 'in all'\n\n2. Subtraction:  A problem in which two quantities are given and one is being removed from another.\n\nKeywords: Left, left over, decreased by, take away, less, less than etc.\n\nFor example: Jose takes $$\\dfrac{1}{4}$$ minutes less than Marc to reach the staff-room from the corridor. If Marc takes $$\\dfrac{3}{4}$$ minutes to reach the staff-room, how many minutes does Jose take?\n\nIn this example, 'less than' is the keyword that helps to identify that subtraction is to be done.\n\n3. Multiplication: A problem in which repeated addition needs to be done.\n\nKeywords: Each, every, how much, of etc.\n\nFor example: What is $$\\dfrac{1}{2}$$ of $$4$$?\n\nIn this example, 'of'  is the keyword that helps us to identify that we should use multiplication to solve this problem.\n\n4. Division: A problem in which a single quantity is divided into many equal parts.\n\nKeywords: Split, divide, shared, per etc.\n\nFor example: Kelvin teaches 8 students. He divides them equally into two groups. How many students are in each group?\n\nHere, the keyword is 'divided ', which means we need to divide.\n\n#### Lara runs a mile in an average of $$9 \\dfrac{3}{6}$$ minutes. She does a cool down jog in an average of $$3 \\dfrac{2}{3}$$ minutes. If her daily workout is running a mile and then doing the cool down jog, how long does it take her to do this workout?\n\nA $$\\dfrac{54}{5}$$ minutes\n\nB $$13\\dfrac{5}{6}$$ minutes\n\nC $$\\dfrac{58}{3}$$ minutes\n\nD $$13\\dfrac{1}{6}$$ minutes\n\n×\n\nAverage time taken by Lara to run a mile  $$=9\\dfrac{3}{6}$$ minutes\n\n$$=\\dfrac{57}{6}$$ minutes\n\nAverage time taken by her for cool down jog $$=3\\dfrac{2}{3}$$ minutes\n\n$$=\\dfrac{11}{3}$$ minutes\n\nTotal time taken for workout\n\n$$=\\dfrac{57}{6}+\\dfrac{11}{3}$$\n\n$$=\\dfrac{57+22}{6} = \\dfrac{79}{6}$$\n\n$$=\\dfrac{79}{6}$$ minutes\n\n$$=13\\dfrac{1}{6}$$ minutes\n\nThus, the total time taken for workout is $$13\\dfrac{1}{6}$$ minutes.\n\nHence, option (D) is correct.\n\n### Lara runs a mile in an average of $$9 \\dfrac{3}{6}$$ minutes. She does a cool down jog in an average of $$3 \\dfrac{2}{3}$$ minutes. If her daily workout is running a mile and then doing the cool down jog, how long does it take her to do this workout?\n\nA\n\n$$\\dfrac{54}{5}$$ minutes\n\n.\n\nB\n\n$$13\\dfrac{5}{6}$$ minutes\n\nC\n\n$$\\dfrac{58}{3}$$ minutes\n\nD\n\n$$13\\dfrac{1}{6}$$ minutes\n\nOption D is Correct\n\n# Mathematical Modeling on Addition and Subtraction\n\nMany times in real life problems, we need to deal with more than one operations. Only addition or only subtraction would not help. We need to make use of the combination of operations in order to solve the problem.\n\nFor example:\n\nA town has a total population of $$20,000$$. There are $$2,000$$ children, $$1,250$$ youths, $$750$$ infants and rest are aged people. What fraction of the total population represents the aged people?\n\nTotal population of town $$=20,000$$\n\nNumber of children $$=2,000$$\n\nFraction of children to total population $$=\\dfrac {2,000}{20,000}$$\n\nNumber of youths $$=1,250$$\n\nFraction of youths to total population $$=\\dfrac {1,250}{20,000}$$\n\nNumber of infants $$=750$$\n\nFraction of infants to total population $$=\\dfrac {750}{20,000}$$\n\nTotal fraction of children, youths and infants\n\n$$=\\dfrac {2,000}{20,000}+\\dfrac {1,250}{20,000}+\\dfrac {750}{20,000}$$\n\n$$=\\dfrac {4,000}{20,000}=\\dfrac {1}{5}$$\n\n$$\\therefore\\;$$ Fraction of aged people  $$=1-\\dfrac {1}{5}=\\dfrac {4}{5}$$\n\nThus, $$\\dfrac {4}{5}$$ of the total population represents the aged people.\n\n#### In a chutes and ladders game board, there are $$100$$ square blocks, $$9$$ chutes and $$10$$ ladders. What fraction of the total square blocks have the chutes and the ladders? Also find the fraction of the rest of the blocks.(chutes and ladders belong to the blocks where they begin)\n\nA $$\\dfrac {19}{100},\\dfrac {81}{100}$$\n\nB $$\\dfrac {18}{100},\\dfrac {82}{100}$$\n\nC $$\\dfrac {17}{100},\\dfrac {83}{100}$$\n\nD $$\\dfrac {16}{100},\\dfrac {84}{100}$$\n\n×\n\nTotal number of square blocks $$=100$$\n\nNumber of chutes $$=9$$\n\nNumber of ladders $$=10$$\n\nFraction of $$9$$ chutes to total square blocks $$=\\dfrac {9}{100}$$\n\nFraction of $$10$$ ladders to total square blocks $$=\\dfrac {10}{100}$$\n\nTotal fraction $$=\\dfrac {9}{100}+\\dfrac {10}{100}$$\n\n$$=\\dfrac {19}{100}$$\n\nFraction for remaining blocks $$=1-\\dfrac {19}{100}$$\n\n$$=\\dfrac {81}{100}$$\n\nThus, $$\\dfrac {19}{100}$$ part of the total square blocks have chutes and ladders while remaining blocks constitute $$\\dfrac {81}{100}$$ part of the total square blocks.\n\nHence, option (A) is correct.\n\n### In a chutes and ladders game board, there are $$100$$ square blocks, $$9$$ chutes and $$10$$ ladders. What fraction of the total square blocks have the chutes and the ladders? Also find the fraction of the rest of the blocks.(chutes and ladders belong to the blocks where they begin)\n\nA\n\n$$\\dfrac {19}{100},\\dfrac {81}{100}$$\n\n.\n\nB\n\n$$\\dfrac {18}{100},\\dfrac {82}{100}$$\n\nC\n\n$$\\dfrac {17}{100},\\dfrac {83}{100}$$\n\nD\n\n$$\\dfrac {16}{100},\\dfrac {84}{100}$$\n\nOption A is Correct\n\n# Mathematical Modeling on Addition and Division\n\nHere, we will use the combination of addition and division to solve the problem.\n\nFor example:\n\nCarl puts $$\\dfrac{4}{5}$$ kilogram of fruits in a basket. After a while he adds $$\\dfrac{1}{4}$$ kilogram of fruits more to it. He then distributes the total fruits equally among $$3$$ children. What quantity of fruits does each child get?\n\nQuantity of fruits added to the basket by Carl at first $$=\\dfrac{4}{5}$$ kg\n\nQuantity of fruits added later $$=\\dfrac{1}{4}$$ kg\n\nTotal quantity of fruits in the basket $$=\\dfrac{4}{5}+\\dfrac{1}{4}$$\n\n$$=\\dfrac{16+5}{20}$$\n\n$$=\\dfrac{21}{20}$$ kg\n\nCarl distributes the total fruits equally among $$3$$ children.\n\nSo, the quantity of fruits each child got $$=\\dfrac{21}{20}\\div3$$\n\n$$=\\dfrac{21}{20}\\times \\dfrac{1}{3}$$\n\n$$=\\dfrac{7}{20}$$ kg\n\nThus, each child got $$\\dfrac{7}{20}$$ kilogram of fruits.\n\n#### Sam has $$\\dfrac{5}{3}$$ pounds of tomatoes in a basket. He adds $$\\dfrac{3}{2}$$ pounds of tomatoes more to it and distributes them equally among $$4$$ kids. What quantity of tomatoes does each child get?\n\nA $$\\dfrac{19}{15}$$ pounds\n\nB $$\\dfrac{90}{19}$$ pounds\n\nC $$\\dfrac{20}{15}$$ pounds\n\nD $$\\dfrac{19}{24}$$ pounds\n\n×\n\nQuantity of tomatoes Sam already had in the basket $$=\\dfrac{5}{3}$$ pounds\n\nQuantity of tomatoes he added $$=\\dfrac{3}{2}$$ pounds\n\n$$\\therefore$$ Total quantity of tomatoes in the basket$$=\\dfrac{5}{3}+\\dfrac{3}{2}$$\n\n$$=\\dfrac{10+9}{6}$$\n\n$$=\\dfrac{19}{6}$$ pounds\n\nSam distributed the total quantity of tomatoes equally among $$4$$ kids.\n\nSo, the quantity of tomatoes that each kid got $$=\\dfrac{19}{6}\\div4$$\n\n$$=\\dfrac{19}{6}\\times\\dfrac{1}{4}$$\n\n$$=\\dfrac{19}{24}$$ pounds\n\nThus, each kid got $$\\dfrac{19}{24}$$ pounds of tomatoes.\n\nHence, option (D) is correct.\n\n### Sam has $$\\dfrac{5}{3}$$ pounds of tomatoes in a basket. He adds $$\\dfrac{3}{2}$$ pounds of tomatoes more to it and distributes them equally among $$4$$ kids. What quantity of tomatoes does each child get?\n\nA\n\n$$\\dfrac{19}{15}$$ pounds\n\n.\n\nB\n\n$$\\dfrac{90}{19}$$ pounds\n\nC\n\n$$\\dfrac{20}{15}$$ pounds\n\nD\n\n$$\\dfrac{19}{24}$$ pounds\n\nOption D is Correct\n\n# Mathematical Modeling on Division and Subtraction\n\nHere, we will use the combination of division and subtraction to solve the problem.\n\nFor example:\n\nChris and Sarah together had 4 apples. They divided all the apples equally among themselves. If Chris ate $$\\dfrac{1}{2}$$ of the apples he got, how many apples were left with him?\n\nTotal number of apples $$=4$$\n\nNumber of apples each got $$=4\\div 2$$\n\n$$=4\\times\\dfrac{1}{2}$$\n\n$$=2$$\n\nNumber of apples Chris ate $$=\\dfrac{1}{2}$$ of the apples he got $$=2\\times \\dfrac{1}{2}=1$$\n\nNumber of apples left with Chris $$=2-1$$\n\n$$=1$$\n\nThus, 1 apple was left with Chris.\n\n#### Keith and Kara have a $$5$$ liter juice can. They pour $$\\dfrac{2}{3}$$ fraction of juice in a bottle and divide it equally among themselves. If Keith drinks $$\\dfrac{1}{2}$$ of the juice he gets, how much quantity of juice is left with him?\n\nA $$\\dfrac{42}{5}$$ liters\n\nB $$\\dfrac{5}{6}$$ liters\n\nC $$\\dfrac{31}{2}$$ liters\n\nD $$\\dfrac{10}{3}$$ liters\n\n×\n\nTotal quantity of juice $$=5$$ liters\n\nQuantity of juice Kara and Keith poured $$=\\dfrac{2}{3}$$ of juice\n\n$$=5\\times \\dfrac{2}{3}$$\n\n$$=\\dfrac{10}{3}$$ liters\n\nQuantity of juice each got $$=\\dfrac{10}{3}\\div2$$\n\n$$=\\dfrac{10}{3}\\times\\dfrac{1}{2}$$\n\n$$=\\dfrac{5}{3}$$ liters\n\nQuantity of juice Keith drinks $$=\\dfrac{1}{2}$$ of juice he got\n\n$$=\\dfrac{1}{2}\\times\\dfrac{5}{3}=\\dfrac{5}{6}$$ liters\n\n$$\\therefore$$ Quantity of juice left with him\n\n$$=\\dfrac{5}{3}-\\dfrac{5}{6}$$\n\n$$=\\dfrac{30-15}{18}$$\n\n$$=\\dfrac{15}{18} =\\dfrac{5}{6}$$ liters\n\nThus, $$\\dfrac{5}{6}$$ liters of juice is left with Keith.\n\nHence, option (B) is correct.\n\n### Keith and Kara have a $$5$$ liter juice can. They pour $$\\dfrac{2}{3}$$ fraction of juice in a bottle and divide it equally among themselves. If Keith drinks $$\\dfrac{1}{2}$$ of the juice he gets, how much quantity of juice is left with him?\n\nA\n\n$$\\dfrac{42}{5}$$ liters\n\n.\n\nB\n\n$$\\dfrac{5}{6}$$ liters\n\nC\n\n$$\\dfrac{31}{2}$$ liters\n\nD\n\n$$\\dfrac{10}{3}$$ liters\n\nOption B is Correct\n\n#### Which one of the following options represents the mixed number which has the value between $$\\dfrac{7}{5} \\;and\\; \\dfrac{8}{5}$$?\n\nA $$2 \\dfrac{1}{5}$$\n\nB $$7 \\dfrac{1}{3}$$\n\nC $$1 \\dfrac{1}{2}$$\n\nD $$1 \\dfrac{1}{5}$$\n\n×\n\nGiven: $$\\dfrac{7}{5}$$ and $$\\dfrac{8}{5}$$\n\nFinding the equivalent fractions by multiplying numerator and denominator with the same non-zero number.\n\n$$\\dfrac{7}{5} = \\dfrac{7 \\times2}{5 \\times2} = \\dfrac{14}{10}$$\n\n$$\\dfrac{8}{5} = \\dfrac{8 \\times2}{5 \\times2} = \\dfrac{16}{10}$$\n\nThe two new fractions are:\n\n$$\\dfrac{14}{10}$$ and $$\\dfrac{16}{10}$$\n\nThus, we can say that the fraction between the above two fractions is:\n\n$$\\dfrac{15}{10}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\Bigg(\\because\\dfrac{14}{10},\\dfrac{15}{10},\\dfrac{16}{10}\\Bigg)$$\n\nThe greatest common factor of $$15$$ and $$10$$ is $$5$$. So, on simplifying the fraction $$\\dfrac{15}{10}$$, we get\n\n$$\\dfrac{15 \\div 5}{10 \\div 5}=\\dfrac{3}{2}$$\n\n$$3$$ and $$2$$ do not have any common factor other than 1. So, the fraction $$\\dfrac{3}{2}$$ is in its simplest form.\n\nOn dividing, we get the mixed fraction $$=1\\dfrac{1}{2}$$", null, "So, the mixed fraction between  $$\\dfrac{7}{5}$$ and $$\\dfrac{8}{5}$$  is  $$1\\dfrac{1}{2}$$.\n\nHence, option (C) is correct.\n\n### Which one of the following options represents the mixed number which has the value between $$\\dfrac{7}{5} \\;and\\; \\dfrac{8}{5}$$?\n\nA\n\n$$2 \\dfrac{1}{5}$$\n\n.\n\nB\n\n$$7 \\dfrac{1}{3}$$\n\nC\n\n$$1 \\dfrac{1}{2}$$\n\nD\n\n$$1 \\dfrac{1}{5}$$\n\nOption C is Correct\n\n# Mathematical Modeling on Addition and Multiplication\n\nMany times in real life problems, we need to deal with more than one operations. Only addition or only multiplication would not help. We need to make use of the combination of operations in order to solve the problem.\n\nFor example:\n\nCarl bought $$14$$ cookies at $$\\dfrac{2}{7}$$ each and $$20$$ candies at $$\\dfrac{4}{9}$$ each. What is the total amount he spent?\n\nNumber of cookies Carl bought $$=14$$\n\nPrice of $$1$$ cookie $$=\\dfrac{2}{7}$$\n\nPrice of $$14$$ cookies $$= 14 \\times \\dfrac{2}{7}$$ $$=4$$\n\nNumber of candies he bought $$=20$$\n\nPrice of $$1$$ candy $$=\\dfrac{4}{9}$$\n\nPrice of 20 candies $$=20 \\times \\dfrac{4}{9}$$ $$=\\dfrac{80}{9}$$\n\n$$\\therefore$$ Total money he spent $$=4+ \\dfrac{80}{9}$$\n\n$$=(\\dfrac{36+80}{9})$$\n\n$$=\\dfrac{116}{9}$$\n\n#### Sam bought $$13$$ chocolates and ate $$\\dfrac{1}{2}$$ of them. Casey bought $$10$$ chocolates and ate $$\\dfrac{3}{4}$$ of them. Find the total number of chocolates they both ate in all.\n\nA $$10$$\n\nB $$14$$\n\nC $$13$$\n\nD $$15$$\n\n×\n\nChocolates bought by Sam $$=13$$\n\nHe ate $$\\dfrac{1}{2}$$ of the chocolates $$=13\\times\\dfrac{1}{2}=\\dfrac{13}{2}$$\n\nChocolates bought by Casey $$=10$$\n\nShe ate $$\\dfrac{3}{4}$$ of the chocolates $$=\\dfrac{3}{4}\\times10 = \\dfrac{15}{2}$$\n\n$$\\therefore$$ Total number of chocolates they both ate $$=\\dfrac{13}{2}+\\dfrac{15}{2}$$\n\n$$=\\dfrac{13+15}{2}$$\n\n$$=\\dfrac{28}{2}$$\n\n$$=14$$\n\nThus , the total number of chocolates they both ate equals $$14$$.\n\nHence, option (B) is correct.\n\n### Sam bought $$13$$ chocolates and ate $$\\dfrac{1}{2}$$ of them. Casey bought $$10$$ chocolates and ate $$\\dfrac{3}{4}$$ of them. Find the total number of chocolates they both ate in all.\n\nA\n\n$$10$$\n\n.\n\nB\n\n$$14$$\n\nC\n\n$$13$$\n\nD\n\n$$15$$\n\nOption B is Correct\n\n# Mathematical Modeling on Subtraction and Multiplication\n\nHere, we will use the combination of subtraction and multiplication to solve the problem.\n\nFor example:\n\nMaria buys $$\\dfrac{1}{2}$$ kilogram(kg) of strawberries at the rate of $$10$$ per kg and Jacob buys the same amount of strawberries at the rate of $$12$$ per kg. Find who spends more and by how much.\n\nRate at which Maria buys strawberries $$=10$$ per kg\n\nQuantity of strawberries she buys $$=\\dfrac{1}{2}$$ kg\n\nTotal price of $$\\dfrac{1}{2}$$ kilogram of strawberries $$=\\dfrac{1}{2}\\times10$$ $$=5$$\n\nRate at which Jacob buys strawberries $$=12$$ per kg\n\nQuantity of strawberries he buys $$=\\dfrac{1}{2}$$ kg\n\nTotal price of $$\\dfrac{1}{2}$$ kilogram of strawberries $$=\\dfrac{1}{2}\\times12$$ $$=6$$\n\nThus, Jacob spends more.\n\nThe amount Jacob spends more  $$= 6-5$$ $$=1$$\n\nHence, Jacob spends  $$1$$ more than Maria.\n\n#### Kyle had $$3$$ bottles of milk. Each bottle contained $$\\dfrac{3}{5}$$ liters of milk. She emptied the milk of each bottle into a big jar, out of which she used  $$\\dfrac{2}{5}$$ liters of milk for making coffee. How much quantity of milk was left in the jar?\n\nA $$\\dfrac{3}{4}\\;liters$$\n\nB $$\\dfrac{7}{5}\\;liters$$\n\nC $$\\dfrac{2}{3}\\;liters$$\n\nD $$\\dfrac{2}{5}\\;liters$$\n\n×\n\nTotal number of bottles of milk $$=3$$\n\nQuantity of milk in each bottle $$=\\dfrac{3}{5}$$ liters\n\nTotal quantity of milk in $$3$$ bottles $$=3\\times \\dfrac{3}{5}$$\n\n$$=\\dfrac{9}{5}$$  [Total quantity of milk in the jar before making coffee]\n\nQuantity of milk she used for coffee $$=\\dfrac{2}{5}$$ liters\n\n$$\\therefore$$ Quantity of milk left in the jar $$=\\dfrac{9}{5}-\\dfrac{2}{5}$$\n\n$$=\\dfrac{9-2}{5}$$\n\n$$=\\dfrac{7}{5}$$ liters\n\nThus, $$\\dfrac{7}{5}$$ liters of milk was left in the jar.\n\nHence, option (B) is correct.\n\n### Kyle had $$3$$ bottles of milk. Each bottle contained $$\\dfrac{3}{5}$$ liters of milk. She emptied the milk of each bottle into a big jar, out of which she used  $$\\dfrac{2}{5}$$ liters of milk for making coffee. How much quantity of milk was left in the jar?\n\nA\n\n$$\\dfrac{3}{4}\\;liters$$\n\n.\n\nB\n\n$$\\dfrac{7}{5}\\;liters$$\n\nC\n\n$$\\dfrac{2}{3}\\;liters$$\n\nD\n\n$$\\dfrac{2}{5}\\;liters$$\n\nOption B is Correct\n\n# Mathematical Modeling on Multiplication and Division\n\nHere, we will use the combination of multiplication and division to solve the problem.\n\nFor example:\n\nFor a project, Isaac buys $$6$$ packets of pens for $$\\dfrac{20}{3}$$ each and decides to share the price among the $$5$$ project team members including him. How much does each member have to pay?\n\nPackets of pens Isaac buys $$=6$$\n\nPrice of $$1$$ packet $$=\\dfrac{20}{3}$$\n\nPrice of $$6$$ packets of pens $$=6\\times \\dfrac{20}{3}$$\n\n$$=40$$\n\nIsaac shares the price with his $$5$$ project team members $$=40\\div 5$$\n\n$$=40\\times \\dfrac{1}{5}$$\n\n$$=8$$\n\nThus, each member pays $$8$$.\n\n#### Julie has to clean her house, so she decides to do $$200\\,\\text{m}^2$$ area of her house today. If she cleans only $$\\dfrac{1}{5}$$ area of what she decided and asks her $$4$$ sisters to clean the rest of the area, find the area that each sister has to clean. Assume each sister has to clean equal amount of area.\n\nA $$25\\;\\text{m}^2$$\n\nB $$40\\;\\text{m}^2$$\n\nC $$30\\;\\text{m}^2$$\n\nD $$35\\;\\text{m}^2$$\n\n×\n\nTotal area to be cleaned $$=200\\;\\text{m}^2$$\n\nJulie cleans only $$\\dfrac{1}{5}$$ area of what she decided  $$=200\\times\\dfrac{1}{5}$$\n\n$$=40\\;\\text{m}^2$$\n\nArea remained uncleaned by Julie  $$=200\\;\\text{m}^2$$ $$-40\\;\\text{m}^2$$\n\n$$=160\\;\\text{m}^2$$\n\nShe divides the rest of her work equally among her $$4$$ sisters\n\n$$=160\\div 4=\\dfrac{160}{4}$$\n\n$$=40\\;\\text{m}^2$$\n\nThus, each sister has to clean  $$40\\;\\text{m}^2$$ area.\n\nHence, option (B) is correct.\n\n### Julie has to clean her house, so she decides to do $$200\\,\\text{m}^2$$ area of her house today. If she cleans only $$\\dfrac{1}{5}$$ area of what she decided and asks her $$4$$ sisters to clean the rest of the area, find the area that each sister has to clean. Assume each sister has to clean equal amount of area.\n\nA\n\n$$25\\;\\text{m}^2$$\n\n.\n\nB\n\n$$40\\;\\text{m}^2$$\n\nC\n\n$$30\\;\\text{m}^2$$\n\nD\n\n$$35\\;\\text{m}^2$$\n\nOption B is Correct" ]
[ null, "https://www.actucation.com/img/uploads/images/IllusSolG2L56M491.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.879529,"math_prob":0.9999914,"size":7012,"snap":"2021-31-2021-39","text_gpt3_token_len":2197,"char_repetition_ratio":0.14840183,"word_repetition_ratio":0.12268744,"special_character_ratio":0.37407303,"punctuation_ratio":0.109104045,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999595,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-27T19:21:24Z\",\"WARC-Record-ID\":\"<urn:uuid:433b082f-5429-4625-9d97-74606cc8f48f>\",\"Content-Length\":\"290962\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8bd39ba9-ab33-427e-80e5-5125778adb8d>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a05cfb8-3bac-490a-af12-940be774e6e2>\",\"WARC-IP-Address\":\"166.62.28.118\",\"WARC-Target-URI\":\"https://www.actucation.com/grade-6-maths/word-problems-\",\"WARC-Payload-Digest\":\"sha1:YDWJMQAF5ZWT4UAF3AVI5SNQN5MUEWQM\",\"WARC-Block-Digest\":\"sha1:OZYQ5GA62CLAPO6NX7D6QM624QXGNV3D\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153474.19_warc_CC-MAIN-20210727170836-20210727200836-00375.warc.gz\"}"}
https://www.homeschoolingbooks.com/product-page/working-with-numbers-level-e-student-workbook
[ "`This arithmetic series is a survey program that offers solid practice in basic math skills at each grade level. The workbook is in two-color, with guided practice, regular exercises, and mixed review pages. Both computational and problem-solving skills are covered.The answers are in the corresponding teacher's guide, sold separately.  Level E covers: place value through millions, review of arithmetic operations, multiplying and dividing multi-digit numbers, estimating, fraction, equivalent fractions, comparing and ordering fractions, higher terms and simplest terms, mixed numbers, arithmetic operations on fractions (like and unlike denominators), decimals, decimal place value, reading and writing decimals, comparing and ordering decimals, estimation and rounding, customary and metric measurement, comparing measurements, angles, perimeter and area, formulas, and problem-solving.  160 pp.`\n\n# Working with Numbers - Level E - Student Workbook\n\nSKU: 010489-1703E\n\\$24.13 Regular Price\n\\$11.49Sale Price\n• ISBN-10: 073989160X\nISBN-13: 9780739891605\nPublisher: Harcourt Achieve\nFormat: Paperback\nAge: 10, 11" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8427479,"math_prob":0.8977636,"size":1081,"snap":"2019-43-2019-47","text_gpt3_token_len":218,"char_repetition_ratio":0.11420613,"word_repetition_ratio":0.0,"special_character_ratio":0.21091582,"punctuation_ratio":0.21164021,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.981806,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-21T18:43:11Z\",\"WARC-Record-ID\":\"<urn:uuid:57cf57cd-3dbd-484b-ac5a-f6424a42ea98>\",\"Content-Length\":\"411405\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f07b8997-8b50-4684-ab3f-eb2580fe9969>\",\"WARC-Concurrent-To\":\"<urn:uuid:dc6cf564-7025-4d13-abfe-b3bcdc182050>\",\"WARC-IP-Address\":\"185.230.60.211\",\"WARC-Target-URI\":\"https://www.homeschoolingbooks.com/product-page/working-with-numbers-level-e-student-workbook\",\"WARC-Payload-Digest\":\"sha1:C7INXXLLVCOFUXT73ZL2Z3HY5RZSP2XR\",\"WARC-Block-Digest\":\"sha1:E64MEWZHSHE2XNLVQRYTYZ2S3E5NJEQ2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670948.64_warc_CC-MAIN-20191121180800-20191121204800-00435.warc.gz\"}"}
https://www.vernier.com/experiment/chem-i-17_acid-base-titrations/
[ "### Introduction\n\nA titration is a process used to determine the volume of a solution needed to react with a given amount of another substance. When titrating a solution of the strong acid hydrochloric acid, HCl, with a solution of the strong base sodium hydroxide, NaOH, the hydrogen ions from the HCl react with hydroxide ions from the NaOH in a one-to-one ratio to produce water in the overall reaction:", null, "${{\\text{H}}^{\\text{ + }}}{\\text{(aq) + C}}{{\\text{l}}^ - }{\\text{(aq) + N}}{{\\text{a}}^{\\text{ + }}}{\\text{(aq) + O}}{{\\text{H}}^ - }{\\text{(aq)}} \\to {{\\text{H}}_{\\text{2}}}{\\text{O(l) + N}}{{\\text{a}}^{\\text{ + }}}{\\text{(aq) + C}}{{\\text{l}}^ - }{\\text{(aq)}}$\n\nWhen an HCl solution is titrated with an NaOH solution, the pH of the acidic solution is initially low. As base is added, the change in pH is quite gradual until close to the equivalence point, when equimolar amounts of acid and base have been mixed. Near the equivalence point, the pH increases very rapidly. The change in pH then becomes more gradual again, before leveling off with the addition of excess base.\n\n### Objectives\n\nIn the Preliminary Activity, you will titrate a solution of the strong acid hydrochloric acid, HCl, with a solution of the strong base sodium hydroxide, NaOH. The concentration of the NaOH solution is given and you will determine the unknown concentration of the HCl.\n\nAfter completing the Preliminary Activity, you will first use reference sources to find out more about acids, bases, and acid-base titrations before you choose and investigate a researchable question utilizing acid-base titrations." ]
[ null, "https://s0.wp.com/latex.php", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.90631187,"math_prob":0.9837545,"size":1326,"snap":"2021-31-2021-39","text_gpt3_token_len":284,"char_repetition_ratio":0.1633888,"word_repetition_ratio":0.13953489,"special_character_ratio":0.18627451,"punctuation_ratio":0.10080645,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9913221,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-25T17:48:08Z\",\"WARC-Record-ID\":\"<urn:uuid:a6dabf84-7678-45eb-8364-bd42ac583021>\",\"Content-Length\":\"313064\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:94f0264e-2c0c-4e9f-abbf-cbefd9d9e520>\",\"WARC-Concurrent-To\":\"<urn:uuid:4e9ab3b6-8269-4757-92a7-38a2564b18ad>\",\"WARC-IP-Address\":\"172.67.69.150\",\"WARC-Target-URI\":\"https://www.vernier.com/experiment/chem-i-17_acid-base-titrations/\",\"WARC-Payload-Digest\":\"sha1:KLEJYLLLYVUQO6O46EUXZGXQUTLUMJ2M\",\"WARC-Block-Digest\":\"sha1:LJBOQSXYCGHUKDIEYEMIWCLTVWTC6NK7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057733.53_warc_CC-MAIN-20210925172649-20210925202649-00595.warc.gz\"}"}
https://emeritus.org/blog/data-analytics-what-is-logistic-regression/
[ "# What is Logistic Regression? A Guide to Get Your Basics Right\n\nIf you’re trying to enter the field of data analytics, you must be looking for ways to grasp the various tools and techniques of the trade. One such particular type of analysis technique that data analysts commonly use is logistic regression. So, what is logistic regression? How does it work? What are its uses and advantages?\n\nThis guide will help you understand everything- from its importance to its uses and benefits. By the end of this post, you will know the difference between logistic and linear regression and become familiar with its different types.\n\n## What is Logistic Regression?\n\nAccording to Tech Target, it is a statistical analysis method to predict a binary outcome, such as yes or no, based on prior observations of a data set.\n\nIn other words, logistic regression models predict a dependent variable by analyzing the relationship between one or more independent variables. For instance, it predicts whether a student will get or not get admission into a particular university. These binary outcomes enable a straightforward decision between two alternative variables.\n\n## How Does Logistic Regression Work?\n\nThe analysis model considers multiple input criteria into the picture. In the above case of university acceptance, the logistic function can consider factors like grade point average, admission test score, and extracurricular activities. Based on the historical data about earlier outcomes with the same input criteria, the model scores the new cases on their chance of falling into one of the binary outcome categories.\n\n## Where is Logistic Regression Used?\n\nLet us now explore some real-world scenarios where this is relevant.\n\nCalculating the probability of a binary event occurring can help us classify whether an email is spam or not or whether a credit card transaction is a fraud or not. In the medical context, it can be used to predict a health outcome, such as whether a tumor is malignant or not.\n\nSo you can see logistic regression predicts the likelihood of all kinds of yes/no outcomes. By making predictions, the model helps data scientists make informed business decisions to minimize risks, optimize spending and maximize profits. And, isn’t that what all businesses are looking for?\n\nFor example, a credit card company cannot possibly issue a card to every person who applies. They need to analyze the two possible binary outcomes, the person “will default” or “not default” using a model to categorize customers who might be a good fit for the credit card.\n\n## What is Logistic Regression in Machine Learning?\n\nLogistic regression is a crucial technique in artificial intelligence and machine learning (AI/ML). Machine Learning (ML) models are software programs you can tune and train to perform complex data processing tasks without manual intervention. ML models built using logistic regression can provide actionable insights from business data and conduct predictive analysis to reduce operational expenses and increase productivity.\n\n## What are the Advantages of Logistic Regression?\n\nHere are some of the advantages of such analysis that bring value for data analysts:\n\n1. Simplicity: Models are mathematically less complex than other ML models and hence very useful in the machine learning context. Thus, you can build, train and deploy efficient ML models using logistic regression, even if you lack in-depth ML expertise.\n2. Speed: It processes large data sets at high speed because they require less computational capacities in terms of memory and processing power. This makes them ideal for programmers working on complex ML projects while aspiring for quick wins.\n3. Visibility: Analysis gives programmers greater visibility into the internal software processes than other data analysis techniques. Troubleshooting becomes easier as calculations using the equation are less complex.\n\n##", null, "What are the Different Types of Logistic Regression?\n\nIn this post, we’ve explained just one type so far- binary regression, where you have only two possible outcomes. However, there are three types:\n\n1. Binary: This statistical model predicts the relationship between the dependent variable (Y) and the independent variable X), where the dependent variable is binary. So the outcome is in terms of success/failure, 0/1, yes/no, or true/false.\n2. Multinomial: In this statistical analysis, you have one dependent variable with two or more discrete outcomes. For example, let’s say you want to predict the most popular transport type in 2040. Here the transport type will be a dependent variable with several possible outcomes like a train, bus, car, or bike.\n3. Ordinal: In this technique, the dependent variable (Y) has a meaningful order with two or more categorical variables. For example, let’s consider shirt size (S/M/L/XL) or an audience poll with (Agree/Disagree/Neutral) options.\n\n## Linear Regression vs Logistic Regression: What’s the Difference\n\nLinear regression equation uses continuous variables as targets, while in the logistic regression model, the target is a discrete variable or a binary value. The predicted value for linear regression is the mean of the target variables. Whereas, the predicted value is the probability of the target variables.\n\n## How to Learn About Logistic Regression\n\nEmeritus in association with the world’s best universities offers top data science and analytics courses. These completely online courses are designed to help you dive deep into the concepts and techniques used in data analysis, machine learning, and deep learning. You will also get to apply all the knowledge and skills to develop an ML model, build a job-ready portfolio, capture your prospective employer’s attention, and help land your dream job!\n\nBy Swet Kamal\n\nWrite to us content@emeritus.org", null, "" ]
[ null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.89294195,"math_prob":0.85513484,"size":5875,"snap":"2023-14-2023-23","text_gpt3_token_len":1111,"char_repetition_ratio":0.13251576,"word_repetition_ratio":0.0,"special_character_ratio":0.1853617,"punctuation_ratio":0.10400763,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9870725,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-08T18:29:10Z\",\"WARC-Record-ID\":\"<urn:uuid:045098d9-ec37-4749-9e0e-81e5004f0429>\",\"Content-Length\":\"196193\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1efe3984-a838-4a74-9b39-6a2dcdae6797>\",\"WARC-Concurrent-To\":\"<urn:uuid:01a97724-f238-4401-a209-e053e6807695>\",\"WARC-IP-Address\":\"104.18.16.18\",\"WARC-Target-URI\":\"https://emeritus.org/blog/data-analytics-what-is-logistic-regression/\",\"WARC-Payload-Digest\":\"sha1:YRUW5ZAIN53DJBDTPJXJQW2QM3W5TM2N\",\"WARC-Block-Digest\":\"sha1:TB5K5J2XKCRVUGWMOE7PQJKJCTJ4AB26\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224655092.36_warc_CC-MAIN-20230608172023-20230608202023-00483.warc.gz\"}"}
https://research.chalmers.se/publication/81492
[ "Branching of some holomorphic representations of SO(2,n) Artikel i vetenskaplig tidskrift, 2007\n\nIn this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball D = SO(2,n)/S(O(2) x O(n)) and the corresponding holomorphic unitary (projective) representations of SO(2, n) on these spaces. These representations are known to be irreducible. Our aim is to decompose them under the subgroup SO(1, n) which acts as the isometry group of a totally real submanifold H of D. We give a proof of a general decomposition theorem for certain unitary representations of semisimple Lie groups. In the particular case we are concerned with, we find an explicit formula for the Plancherel measure of the decomposition as the orthogonalising measure for certain hypergeometric polynomials. Moreover, we construct an explicit generalised Fourier transform that plays the role of the intertwining operator for the decomposition. We prove an inversion formula and a Plancherel formula for this transform. Finally we construct explicit realisations of the discrete part appearing in the decomposition and also for the minimal representation in this family.\n\nbounded symmetric domain\n\nintertwining operator\n\nspherical function\n\nKERNELS\n\nBEREZIN TRANSFORM\n\nLie group\n\nLie algebra\n\nrepresentation\n\nhypergeometric function\n\nBOUNDED SYMMETRIC DOMAINS\n\nunitary\n\nPOLYNOMIALS\n\nFörfattare\n\nHenrik Seppänen\n\nChalmers, Matematiska vetenskaper, Matematik\n\nGöteborgs universitet\n\nJournal of Lie Theory\n\n0949-5932 (ISSN)\n\nVol. 17 1 191-227\n\nMatematik\n\n2017-10-06" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.84729975,"math_prob":0.9342882,"size":1368,"snap":"2019-43-2019-47","text_gpt3_token_len":304,"char_repetition_ratio":0.12536657,"word_repetition_ratio":0.0,"special_character_ratio":0.1754386,"punctuation_ratio":0.06726457,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97520256,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-18T07:12:31Z\",\"WARC-Record-ID\":\"<urn:uuid:14f260d1-72c8-4684-b0ae-5fc33d977a10>\",\"Content-Length\":\"30960\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88647283-dbdf-4720-9a8b-d855d75a3a11>\",\"WARC-Concurrent-To\":\"<urn:uuid:fd271d59-a8cc-45e1-9380-f3fdab3c67fc>\",\"WARC-IP-Address\":\"40.113.65.9\",\"WARC-Target-URI\":\"https://research.chalmers.se/publication/81492\",\"WARC-Payload-Digest\":\"sha1:UI2ILN7B23YAZQIC4ZAYTKGB4IPWJJ2H\",\"WARC-Block-Digest\":\"sha1:RHM4RMKXCV7VJ2X7XZICA63NYPQPXFD4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986677964.40_warc_CC-MAIN-20191018055014-20191018082514-00374.warc.gz\"}"}
https://www.jiskha.com/questions/1424067/7-0-kilograms-of-ice-at-0-0c-and-are-melted-to-water-at-0-0c-find-the-increase-in
[ "# Physics\n\n7.0 kilograms of ice at 0 0C and are melted to water at 0 0C. Find the increase in internal energy of the ice as it is melted to water at 0 0C. Use 3.33x 105 J for Lf of ice. Express your answers in calories.\n\n1. 👍\n2. 👎\n3. 👁\n1. What is 7*Lf ?\n\nNow for calories, multiply Joules by .239\n\n1. 👍\n2. 👎\n👤\nbobpursley\n\n## Similar Questions\n\n1. ### Chemistry\n\ncalculate the final temperature (once the ice has melted) of a mixture made up of initially of 75.0mL liquid water at 29 degrees Celsius and 7.0 g of ice at 0.0 degrees Celsius\n\n2. ### physics\n\nFive kilograms of water at 40◦C is poured on a large block of ice at 0◦C. How much(in Kg) ice melts ? Hf = 335 kJ/kg cw = 4.184 kJ/(kg·◦C\n\n3. ### Chemistry\n\nAn ice cube at 0.00 degree celsius with a mass of 23.5 g is placed into 550.0 g of water, initially at 28.0 degree celsius, in an insulated container. Assuming that no heat is lost to the surroundings, what is the temperature of\n\n4. ### Chemistry - Heat of Fusion of Ice\n\nConclusion question(s) from a lab we did to find the heat of fusion of ice: Does the value obtained for the molar heat of fusion depend on the volume of water used? Does it depend on the mass of ice melted? Does it depend on the\n\n1. ### Chemistry - Energy: Phase Changes\n\nIf 13.4 kJ of energy are added to 1.00 kg of ice at 0 degrees Celsius, how much water at 0 degrees Celsius is produced? How much ice is left? The molar heat of melting is 6.01 kJ/mol. So... 6.01 kJ -> 1 mol (6.01 kJ of energy can\n\n2. ### chemistry\n\nDetermine the specific heat of a metal from the following data. A 75 g piece of the metal at 100.0 C was placed into an ice water bath. The heat loss from the metal melted 255g of ice. Some unmelted ice remained in the ice water\n\n3. ### Chemistry\n\nCalculate the final temperature (once the ice has melted) of a mixture made up initially of 75.0 mL liquid water at 29.0 Celsius and 7.0 g ice at 0.0 Celsius?\n\n4. ### physics\n\nYears ago, a block of ice with a mass of about 22kg was used daily in a home icebox. The temperature of the ice was 0.0 degrees Celsius when delivered. As it melted, how much heat did a block of ice that size absorb? The latent\n\n1. ### science\n\nan ice cube, a glass of cold water, and a swimming pool are each exposed to the same amount of sunlight on a hot day. after five minutes, the ice cube is melted and the cold drink is two degrees warmer, but the temperature of the\n\n2. ### physics\n\nAn insulated Thermos contains 140 cm3 of hot coffee at 89.0°C. You put in a 11.0 g ice cube at its melting point to cool the coffee. By how many degrees (in Celsius) has your coffee cooled once the ice has melted and equilibrium\n\n3. ### Chemistry\n\nHey, for chemistry class we are given days in the lab to conduct an experiment, then answer a number of questions that correlate with that experiment and how we can make use of it. This week we looked at the Molar Fusion of Ice\n\n4. ### Chemistry\n\nTo treat a burn on your hand, you decide to place an ice cube on the burned skin. The mass of the ice cube is 16.0 g, and its initial temperature is -11.4 °C. The water resulting from the melted ice reaches the temperature of" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9283764,"math_prob":0.91752344,"size":2859,"snap":"2021-43-2021-49","text_gpt3_token_len":787,"char_repetition_ratio":0.13169877,"word_repetition_ratio":0.035587188,"special_character_ratio":0.2672263,"punctuation_ratio":0.10110585,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98953944,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-07T06:08:36Z\",\"WARC-Record-ID\":\"<urn:uuid:13fd5bd3-ce65-4c3b-acb8-b44440d371d3>\",\"Content-Length\":\"17135\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0bfaedb3-9859-486a-8a9b-d066328dffce>\",\"WARC-Concurrent-To\":\"<urn:uuid:234f2f00-caae-472e-8af4-50dca0c0d0f3>\",\"WARC-IP-Address\":\"66.228.55.50\",\"WARC-Target-URI\":\"https://www.jiskha.com/questions/1424067/7-0-kilograms-of-ice-at-0-0c-and-are-melted-to-water-at-0-0c-find-the-increase-in\",\"WARC-Payload-Digest\":\"sha1:3CSCM2XSWKCZHDCZTIT5NWSHVVLUFNON\",\"WARC-Block-Digest\":\"sha1:Z5TUECHJMQNA72XHBOGXAAF4MRXOKZ6M\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363336.93_warc_CC-MAIN-20211207045002-20211207075002-00216.warc.gz\"}"}
https://www.thefreelibrary.com/Non-Darcy+mixed+convective+heat+and+mass+transfer+flow+of+a+viscous+...-a0323408511
[ "Non-Darcy mixed convective heat and mass transfer flow of a viscous electrically conducting fluid through a porous medium in a circular annulus in the presence of temperature gradient heat sources with Soret and Dufour effects--a finite element study.\n\nIntroduction\n\nConvection flows driven by temperature and concentration differences have been studied extensively in the past and various extensions of the problems have been reported in the literature with both temperature and concentration interacting simultaneously, the convection have become quite complex. Bejan and Khair have investigated the vertical free convection flow embedded in a porous medium resulting from the combined heat and mass transfer. Jang and Chang have used an implicit finite difference method to study the buoyancy induced inclined boundary layer in a porous medium resulting from the combined heat and mass buoyancy effects.\n\nHeat transfers in thermal insulation within vertical cylindrical annuli provide us insight into the mechanism of energy transport and enable engineers to use insulation more efficiently. In particular design engineers require relationship between heat transfer, geometry and boundary conditions which can be utilized cost-benefit analysis to determine the amount of insulation that will yield the maximum investment. An understanding of convective heat transfer in porous annuli is essential for its applications in packed-bed catalytic reactors, Geophysics, thermal insulation, design of regenerative heat exchangers, Geological disposal of high-level nuclear waste, petroleum resources and many other uses. Free convection in a vertical porous annulus has been extensively studied by Prasad , Prasad and Kulacki and Prasad et al., both theoretically and experimentally. Convection through annular regions under steady conditions has also been discussed with the two cylindrical surfaces kept at different temperatures . This work has been extended in temperature dependent convection flow as well as convection flow through horizontal porous channel whose inner surface is maintained at constant temperature, while the other surface is maintained at circumferentially varying sinusoidal temperature .\n\nThe applications of electromagnetic fields in controlling the heat transfer as in aerodynamic heating leads to the study of Magneto hydrodynamic heat transfer. This MHD heat transfer has gained significance owing to recent advancement of space technology. The MHD heat transfer can be divided into two sections. One contains problems in which the heating is an incidental by product of the electromagnetic fields as in MHD generators and pumps etc. and the second consist of problems in which the primary use of electromagnetic fields is to control the heat transfer(5). With fuel crisis deepening all over the world, there is a great concern to utilize the enormous power beneath the earth's crust in the geothermal region (10). Liquid in the geothermal region is an electrically conducting liquid because of high temperature and that they undergo the influence of magnetic field.\n\nIn many industrial applications of transient free convection flow problems, there occurs a heat source or a sink which is either a constant or temperature gradient or temperature dependent heat source. This heat source occurs in the form of a coil or a battery. Gokhale and Behnaz-Farman analyzed Transient free convection flow of a n incompressible fluid past an isothermal plate with temperature gradient dependent heat sources. Implicit finite difference scheme which is unconditionally stable has been used to solve the governing partial differential equations of the flow. Transient temperature and velocity profiles are plotted to show the effect of heat source. Muthukumara swamy et al has analyzed the radiation effect on moving vertical plate with variable temperature and mass diffusion. Sreevani has analyzed the Soret effect on convective heat and mass transfer flow of a viscous fluid in a cylindrical annulus with heat generating sources. Sivaiah has discussed the convective heat and mass transfer flow in a circular duct with Soret effect.\n\nLiterature suggests that the effect of viscous dissipation on heat transfer has been studied for different geometries. Brinkman have studied the viscous dissipation effect on natural convection in horizontal cylinder embedded in porous medium. Their study showed that the viscous dissipation effect might not be neglected. Saffman have studied the viscous dissipation effect on natural convection in a porous cavity and found that the heat transfer rate at hot surface decreases with increase of viscous dissipation parameter. Thermal radiation plays a significant role in the overall surface hear transfer where convective heat transfer is small. Verschoor et al have studied the effect of viscous dissipation and radiation on unsteady magneto hydro dynamic free convection flow fast vertical plate in porous medium. They found that the temperature profile increases when viscous dissipation increases. A good amount of work has been done to understand natural convection in porous cavity. In spite of endeavor efforts to study heat transfer in porous cavity, the combined effect of viscous dissipation and radiation on porous medium filled inside a square cavity has not received attention.\n\nThe Soret and Dufour effects have garnered considerable interest in both Newtonian and non-Newtonian convective heat and mass transfer. Such effects are significant when density differences exist in the flow regime. Soret and Dufour effects are important for intermediate molecular weight gases in coupled heat and mass transfer in binary systems, often encountered in chemical process engineering and also in high-speed aerodynamics. Soret and Dufour effects are also critical in various porous flow regimes occurring in chemical and geophysical systems. There are few studies about the Soret and Dufour effects in a Darcy or non-Darcy porous medium. Anghel et al has examined the composite Soret and Dufour effects on free convective heat and mass transfer in a Darcian porous medium with Soret and Dufour effects. Very recently, Barletta. A, Lazzari.S, and others have studied on Mixed convection with heating effects in a vertical porous annulus with a radially varying magnetic field. Emmunuel Osalusi, Jonathan Side, Robert Harris have discussed Thermal-diffusion and diffusion thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and ohmic heating.\n\nThe Weighted residual method is of the generalization of the Ritz-variational method where in we seek an approximate solution in the form of linear combination of suitable approximation functions. The parameters in the linear combination as determined by setting integral of a weighted residual of the approximation over the domain zero. A comprehensive description of a weighted residual method. In many situations the Galerkin method which is one of the important weighted residual methods is equivalent to the Ritz method for solving variational problems. The finite element method is piece--wise applications of weighted residual method in which the Ritz-Galerkin type methods are employed over each element of the domain. The finite element method was initially developed as an adhoc engineering procedure for constructing matrix solutions to stress and displacement calculations in structural analysis. Very few fluid dynamic problems can be expressed in a variational form. Consequently most of the finite element applications in fluid dynamics have used in Galerkin finite element formulation. The Galerkin finite element method has two important futures. Firstly the approximate solution is written directly as a linear combination of approximating functions in terms of the nodal unknowns. Secondly the approximating functions or the shape functions are chosen exclusively from low order piecewise polynomials restricted to contiguous elements.\n\nIn this paper we discuss the mixed convective viscous dissipative flow through a porous medium in a circular cylindrical annulus with Thermal-Diffusion and Diffusion-Thermo effects in the presence of temperature gradient heat source, where the inner wall is maintained constant temperature while the outer wall is maintained constant heat flux and the concentration is constant on the both walls. The coupled momentum, energy and diffusion equations are solved by using finite element analysis with quadratic interpolation polynomials. The effect of temperature gradient heat sources on the flow and heat transfer characteristics are analyzed. The stress, rate of heat transfer and the rate of mass transfer are discussed numerically for different variations of the governing parameters.\n\nFormulation of the Problem\n\nWe consider free and force convective flow of a viscous, electrically conducting fluid through a porous medium in a circular cylindrical annulus with Thermal-Diffusion and Diffusion-Thermo effects in the presence of temperature gradient heat source, whose inner wall is maintained at a constant temperature and the outer wall is maintained constant heat flux. Also the concentration is constant on the both walls. A uniform radial magnetic field is applied on the flow. The flow, temperature and concentration in the fluid are assumed to be fully developed. Both the fluid and porous region have constant physical properties and the flow is a mixed convection flow taking place under thermal and molecular buoyancies and uniform axial pressure gradient. The boussenissque approximation is invoked so that the density variation is confined to the thermal and molecular buoyancy forces. The Brinkman-Forchhimer-Extended Darcy model which accounts for the inertia and boundary effects has been used for the momentum equation in the porous region. In the momentum, energy and diffusion are coupled and non-linear. Also the flow in is unidirectional along the axial cylindrical annulus. Making use of the above assumptions the governing equations are Equation of linear momentum\n\n[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)\n\nEquation of Energy\n\n[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)\n\nEquation of diffusion\n\n[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)\n\nEquation of state\n\n[rho] - [[rho].sub.0] = -[beta][[rho].sub.0](T - [T.sub.0]) - [[beta].sup.*][[rho].sub.0](C - [C.sub.0]) (4)\n\nWhere u is the axial velocity in the porous region, T & C are the temperature and concentrations of the fluid, k is the permeability of porous medium, F is a function that depends on Reynolds number and the microstructure of the porous medium and [D.sub.1] is the Molecular diffusivity, [D.sub.m] is the coefficient of mass diffusitivity, [T.sub.m] is the mean fluid temperature, [K.sub.t] is the thermal diffusion, [C.sub.s] is the concentration susceptibility, [C.sub.p] is the specific heat, [rho] is density, g is gravity, [beta] is the coefficient of thermal expansion, [[beta].sup.*] is the coefficient of volume expansion. [sigma] is the electrical conductivity, [[mu].sub.e] is the magnetic permeability.\n\nu = 0, T = [T.sub.i], C = [C.sub.i] at r = a (6)\n\nu = 0, [partial derivative]T/[partial derivative]r = [Q.sub.1], C = Co at r = a + s (7)\n\nThe axial temperature gradient [partial derivative]T/[partial derivative]r and concentration gradient [partial derivative]C/[partial derivative]z are assumed to be constant say A and B respectively.\n\nUsing equations (2.5) and (2.6) equation (2.2) reduces to\n\n[[rho].sub.0][C.sub.p]uA = [lambda]([T.sub.rr] + [1/r] [T.sub.r]) + [[D.sub.m][K.sub.t]/[C.sub.s][C.sub.P]] ([C.sub.rr] + [1/r] [C.sub.r]) (8)\n\n[[rho].sub.0][C.sub.P]uB = [lambda]([C.sub.rr] + [1/r] [C.sub.r]) + [[D.sub.m][K.sub.t]/[C.sub.s][C.sub.P]] ([T.sub.rr] + [1/r] [T.sub.r]) (9)\n\nWe now define the following non-dimensional variables\n\n[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)\n\nIntroducing these non-dimensional variables, the governing equations in the non-dimensional form are (on removing the stars)\n\n[[d.sup.2]u/d[r.sup.2] + [1/r][du/dr]] = P + [delta]([D.sup.-1] + [[M.sup.2]/[r.sup.2]])u + [[delta].sup.2][LAMBDA] [u.sup.2] - [delta]G[theta] (11)\n\n[[d.sup.2][theta]/d[r.sup.2] + [1/r][d[theta]/dr] + [[alpha]/r] [d[theta]/dr]] = [P.sub.r][N.sub.T]u + Du[N.sub.t] ([d.sup.2]C/d[r.sup.2] + [1/r][d[theta]/dr]) + [P.sub.r][E.sub.c] [(du/dr).sup.2] (12)\n\n[d[r.sup.2]C/d[r.sup.2] + [1/r][dC/dr]] = Sc[N.sub.c]u + ScSr ([d.sup.2][theta]/d[r.sup.2] + [1/r][d[theta]/dr]) (13)\n\nwhere\n\n[LAMBDA] = F[D.sup.-1] (Forchheimer number)\n\n[P.sub.r] = [mu]/[C.sub.p]/[lambda] (Prandtl number)\n\nG = g[beta]([T.sub.1] - [T.sub.0])[a.sup.3]/[v.sup.2] (Grashof number)\n\n[D.sup.-1] = [a.sup.2]/k (Inverse Darcy parameter)\n\n[N.sub.t] = Aa/[T.sub.1] - [T.sub.0] (Temperature gradient)\n\n[N.sub.c] = Ba/[C.sub.1] - [C.sub.0] (Non-dimensional concentration gradient)\n\nDu = ([D.sub.m][K.sub.t][DELTA][ca.sup.2]/[C.sub.s][C.sub.p][DELTA]T][lambda]) (Dufour Number)\n\nSc = v/[D.sub.1] (Schmidt number)\n\nSr = ([D.sub.m][K.sub.t][DLETA]T/v[T.sub.m][DELTA]C) (Soret number)\n\n[alpha] = Q[L.sup.2]/[lambda][C.sub.p] (Heat source parameter)\n\n[M.sup.2] = [sigma][[mu].sup.2.sub.e][H.sup.2.sub.0][a.sup.2]/[[gamma].sup.2] (Hartman number)\n\n[E.sub.c] = [v.sup.2]/[a.sup.2](Aa)[c.sub.p] (Eckert number)\n\nWith the corresponding boundary conditions as:\n\nu = 0, [theta] = 0, C = 1 at r = 1 (14)\n\nu = 0, [partial derivative][theta]/[partial derivative]r = [Q.sub.1], C = 0 at r = 1 + s (15)\n\nNumerical Analysis\n\nThe finite element method has been implemented to obtain numerical solutions of equations (11) to (13) under boundary conditions (14) and (15). This technique is extremely efficient and allows robust solutions of complex coupled, nonlinear multiple degree differential equation systems. The fundamental steps comprising the method are now summarized:\n\nPhase 1] Discretization of the domain into elements\n\nPhase 2] Derivation of element equations\n\nPhase 3] Assembly of Element Equations\n\nPhase 4] Imposition of boundary conditions\n\nPhase 5] Solution of assembled equations\n\nThe shear stress are evaluated on the cylinder using the formula\n\n[tau] = [(du/dr).sub.r=1,1+s]\n\nThe rate of heat transfer (Nusselt number) are evaluated on the cylinder using the formula\n\nNu = [(d[theta]/dr).sub.r=1]\n\nThe rate of mass transfer (Sherwood Number) is evaluated using the formula\n\nSh = -[(dC/dr).sub.r=1,1+s]\n\nDiscussion of the Numerical Results\n\nIn this analysis we investigate thermo-Diffusion and Diffusion-Thermo effects on convective heat and mass transfer flow of a viscous conducting fluid through a porous medium in circular annulus in the presence of temperature gradient dependent heat source with viscous dissipation. The inner cylinder is maintained at constant temperature and the outer wall is maintained constant heat flux while the concentration is maintained constant on both the cylinders. The axial flow is in vertically downword direction, u > 0 indicates a reversal flow. The velocity, temperature and concentration distributions are shown in figures 1-27 for different values of the parameters G, [D.sup.-1], M, Sc, Sr, Du, N, [alpha] and Ec.\n\nThe variation of u with Grashof number G shows that the axial flow enhances with increase in G and the region of reversal flow enhances with increase in G (fig.1). With respect to the variation of u with [D.sup.-1] we find that lesser the permeability of porous medium smaller the magnitude of u and for further lowering of the permeability larger th-1e magnitude of u in the entire flow region, the region of reversal flow shrinks with [D.sup.-1] [less than or equal to] 2 X [10.sup.3] and enhances with higher [D.sup.-1] [greater than or equal to] 3 X [10.sup.3] (fig.2). From fig.3 we find that higher the Lorentz force larger the velocity in the flow region. Also the region of reversal flow enhances with increase in M. Fig.4 represents the variation of u with Sc. We notice that lesser the molecular diffusitivity smaller [absolute value of u] and for further lowering of molecular diffusitivity it experiences a depreciation in the entire flow region and it attains maximum at r = 1.5.\n\n[FIGURE 1 OMITTED]\n\n[FIGURE 2 OMITTED]\n\n[FIGURE 3 OMITTED]\n\n[FIGURE 4 OMITTED]\n\nThe variation of u with Soret parameter Sr shows that the velocity experiences an enhancement with increase in Sr [less than or equal to] 0.8 and for further increase in Sr [greater than or equal to] 1 it depreciates in its magnitude (fig.5). From fig.6 we observe that the region of reversal velocity enlarges with increase in Du and [absolute value of u] enhances with Du. The variation of u with N shows that when the molecular buoyancy force dominates over the thermal buoyancy force the actual axial velocity experiences a depreciation when the buoyancy forces act in the same direction while for the forces acting in the opposite directions it experiences an enhancement in the flow region (fig.7). The influence of heat source parameter [alpha] on u is shown in fig.8.\n\n[FIGURE 5 OMITTED]\n\n[FIGURE 6 OMITTED]\n\n[FIGURE 7 OMITTED]\n\n[FIGURE 8 OMITTED]\n\nAn increase in [alpha] < 0 enhances the actual axial velocity u while it depreciates with [alpha] > 0. This shows that in the presence of the temperature heat source depreciates the velocity in the flow region with maximum in the mid region. The influence of dissipative effect on u is shown in fig.9. We conclude that the axial velocity u experiences an enhancement with Ec.\n\n[FIGURE 9 OMITTED]\n\nThe non-dimensional temperature ([theta]) is shown in fig 10-18 for different values of the parameters. It is found that the non-dimensional temperature gradually increases from its prescribed value 0 on r = 1 to attain its prescribed value 1 at r = 2. An increase in G enhances the temperature (fig.10). The variation of [theta] with [D.sup.-1] shows that lesser the permeability of porous medium larger the actual temperature in the flow region (fig.11). From fig.12 we find that lesser the Lorentz force larger the temperature. With respect to Sc, we notice that lesser the molecular diffusitivity smaller the temperature in the flow region (fig.13).\n\n[FIGURE 10 OMITTED]\n\n[FIGURE 11 OMITTED]\n\n[FIGURE 12 OMITTED]\n\n[FIGURE 13 OMITTED]\n\nAn increase in Soret parameter Sr results in a depreciation in the actual temperature in the region (fig.14). The variation of [theta] with Dufour parameter Du shows that the actual temperature enhances gradually with increase in Du (fig.15). When the molecular buoyancy force dominates over the thermal buoyancy force the actual temperature decreases irrespective of the directions of the buoyancy forces (fig.16). The influence of temperature gradient heat source parameter [alpha] on [theta] is shown in fig.17. It found that the temperature is negative for [alpha] = 0, [alpha] < 0 and positive for [alpha] > 0. The actual temperature experiences a depreciation with increase in the strength of the heat sources. The variation of [theta] with Eckert number Ec is shown in fig.18. We find that the actual temperature enhances with increase in Ec.\n\n[FIGURE 14 OMITTED]\n\n[FIGURE 15 OMITTED]\n\n[FIGURE 16 OMITTED]\n\n[FIGURE 17 OMITTED]\n\n[FIGURE 18 OMITTED]\n\nThe non-dimensional concentration ([phi]) is shown in fig 19-27 for different values of the parameters G, [D.sup.-1], M, Sc, Sr, Du, N, [alpha] and Ec. It is found that the non-dimensional concentration gradually increases from its prescribed value 0 on r = 1 and attain its prescribed value 1 at r = 2. Fig.19. shows the variation of [phi] with G. It is noticed that the concentration depreciates with increase in the Grashof number G. The variation of [phi] with [D.sup.-1] shows that lesser the permeability of porous medium higher the actual concentration in the flow region and for further lowering of the permeability smaller the actual concentration in the flow region (fig.20). From fig.21 we find that higher the Lorentz force larger the concentration in the flow region. Lesser the molecular diffusitivity smaller the concentration in the flow field (fig.22). An increase in the Soret parameter Sr enhances the concentration everywhere in the flow region (fig.23). The variation of [phi] with Dufour parameter Du shows that the concentration experiences a marginal depreciation in the flow region (fig.24). The variation of [phi] with N shows that when the molecular buoyancy force dominates over the thermal buoyancy force the actual concentration experiences an enhancement when the buoyancy forces act in the same direction while for the forces acting in the opposite directions it experiences a depreciation in the flow region (fig.25). From fig.26, we observe that [phi] experiences a marginal enhancement with [alpha] > 0 and a depreciation with [alpha] < 0. The inclusion of the dissipation in the flow enhances the concentration in the flow region (fig.27).\n\n[FIGURE 19 OMITTED]\n\n[FIGURE 20 OMITTED]\n\n[FIGURE 21 OMITTED]\n\n[FIGURE 22 OMITTED]\n\n[FIGURE 23 OMITTED]\n\n[FIGURE 24 OMITTED]\n\n[FIGURE 25 OMITTED]\n\n[FIGURE 26 OMITTED]\n\n[FIGURE 27 OMITTED]\n\nReferences\n\n Angel M, Takhar HS, and Pop I (2000): Dofour and Soret effects on free convection boundary layer over a vertical surface embedded in a porous medium. Studia universities-Bolyai, Mathematica XLV, pp. 11-21.\n\n Barletta.A, Lazzari.S,(2008): Mixed convection with heating effects in a vertical porous annulus with a radially varying magnetic field.\n\n Bejan, A and Khair, K.R: Heat and mass transfer by natural convection in a pourous medium., Int.J. Heat and mass transfer, V.28.PP.908-818(1985).\n\n Brinkman H.C (1948): A Calculation of the viscous force eternal by a flowing fluid on a dense swarm of particles. Appl.Science Research, Ala, p81.\n\n Chandra sekhar. S: Hydrodynamic and Hydro magnetic stability, Clarandon press, oxford (1961).\n\n Emmunuel Osalusi, Jonathan Side, Robert Harris:\"Thermal-diffusion and diffusion thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and ohmic heating: Int.Communications in heat and mass transfer,Vol.35,PP.908-915(2008).\n\n Gokhale, M.Y, Behnaz-Farnam: \"Transient free convection flow on an isothermal plate with temperature dependent heat sources\", International review of Pure and Applied Mathematics, Vol.3, No.1, pp.129-136(2007).\n\n Jang J.Y and Chang W.J: The flow and vertex instability of horizontal natural convection in a porous medium resulting from combined heat and mass buoyancy effects. Int. Heat and Mass Transfer, V. 31, p.769-777 (1987).\n\n Muthukumara Swamy, Maheswari, J, Pandurangan, J: \"Study of MHD and Radiation effects on moving vertical plate with variable temperature and mass diffusion\", International Review of Pure and Applied Mathematics, Vol.3, No.1, pp.95-103(2007).\n\n Nanda, R.S and Mohan, M: Proc. Ind Acad.Sci., V.876 A,No.5,P.147(1978).\n\n Prasad, V: Natural convection in a vertical porous annulus, Int. J. Heat and Mass Transfer, V. 27, p 207-219 (1984).\n\n Prasad, V and Kulacki, F. A: Natural convection in porous media bounded by short concentric vertical cylinders, ASME J. Heat Transfer, V. 107, p 147-154 (1985).\n\n Prasad, V, Kulacki, F.A and Keyhani, M: Natural convection in porous media, J. fluid mech., V. 150, p 89-119 (1985).\n\n Saffman .P.G (1971): on the boundary conditions at the free surface of a porous medium. Stud.Appl.Maths, V.2, p 93.\n\n Sivaiah (2004): Thermo-diffusion effect on convective heat and mass transfer flow through a porous medium in ducts. Ph.D thesis, S.K. University. Anantapur.\n\n Sreevani, M: Mixed convection heat and mass transfer through a porous medium in channels with dissipative effects, Ph.D thesis, S, K.University, Anantpur, India(2003).\n\n Vasseur, P, Nguyen, T.H., Robillard and Thi. V.K.T: Int. Heat Mass Transfer, V. 27, p 337 (1984).\n\n Verschoor et al: Int. Heat and Mass Transfer, V. 31(1992).\n\nP. Sudarsan Reddy (1), G. Srinivas (2), P. Sreenivasa Rao (3), DRV. Prasada Rao (4)\n\n(1) Asst. Professor, Dept of Mathematics, RGM Engg. College, Nandyal, JNTU Anantapur, India Email: suda1983@gmail.com\n\n(2) Assoc. Professor, Dept of Mathematics, Vignan Engg. College, JNTU Hyderabad, India\n\n(3) Assoc. professor, Dept. of Physics, Jyothismathi Engg.College, Karimnagar, JNTU Kakinada, India.\n\n(4) Professor, Dept of Mathematics, SK University, Anantapur. India" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.85529876,"math_prob":0.9535485,"size":24420,"snap":"2019-26-2019-30","text_gpt3_token_len":5897,"char_repetition_ratio":0.14863205,"word_repetition_ratio":0.13884297,"special_character_ratio":0.23423423,"punctuation_ratio":0.13962908,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98045397,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-25T05:53:39Z\",\"WARC-Record-ID\":\"<urn:uuid:515eb736-77db-48a4-ad6d-55e7e3aa0858>\",\"Content-Length\":\"62840\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e8981844-d630-4262-a86e-89b948125f15>\",\"WARC-Concurrent-To\":\"<urn:uuid:d126b845-569a-4f5e-883c-3ab217bb9534>\",\"WARC-IP-Address\":\"45.35.33.117\",\"WARC-Target-URI\":\"https://www.thefreelibrary.com/Non-Darcy+mixed+convective+heat+and+mass+transfer+flow+of+a+viscous+...-a0323408511\",\"WARC-Payload-Digest\":\"sha1:32GTHLAWJGWXKVXVTHPT47JE4W6HQQYC\",\"WARC-Block-Digest\":\"sha1:K5MEZLZ62ISLGFO5W4EWMLQZJCUYEGZG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627999800.5_warc_CC-MAIN-20190625051950-20190625073950-00499.warc.gz\"}"}
https://www.sciences360.com/index.php/can-you-divide-by-0-yes-11886/
[ "", null, "Mathematics\n\n# Can you Divide by 0 – Yes", null, "Hunter J.'s image for:\n\"Can you Divide by 0 - Yes\"\nCaption:\nLocation:\nImage by:", null, "Ah zero, such an interesting number. A number even today we do not know much about. One of the most popular questions asked today of course is: Is it really impossible for something to be divided by zero? My answer is, yes it is.\n\nTo understand zero we must understand the definition of a number. A number is simply something that can list a quantity of something and that we can do something to change its value. But then is zero even a number? After all, it doesn't list the quantity of anything because zero well, is simply nothing. However, we must note that nothing is still a quantity because it shows the value of something. Therefore it is first concluded that zero is infact a number.\n\nNext we must study zero in many ways. We know of course that any number multiplied by zero will equal zero. We also note that an number added or subtracted to zero will equal itself. We also know that anything to the zeroth power will always equal one. Now for each number property there is always a pattern.  For example, we know that if we multiply a number by anything >1 then the number will go up. We also know that if we subtract a positive number from a number and add a negative number to a number the ending quantity will go down. Concurringly, if we add a positive number or subtract a negative number from any number, the number quantity will go up.\n\nNow let's look at the pattern of division. It seems that each time we divide a number closer to zero from another number, the larger the quantity becomes. For example 1/.25.1/.5. It seems however that no matter how close the number line is to 0, the matching result will always be another number. Because of this, it is safe to assume that any number divided by zero is infinity. This is because it seems that no matter how close you get to the number 0, there is never a matching result, so if you get a number infinitely close to zero that the number is zero, the matching result will of course have to be infinity.\n\nSo now we have figured that anything divided by 0 is infinity, we must understand what infinity is. Infinity, does not follow any mathematical pattern. If added, subtracted, multiplied it will equal itself. If divided it will equal a number infinitely close to 0. Therefore, it is safe to conclude that infinity is in fact not a number. Some argue that infinity does in fact represent a quantity, a quantity that is infinitely large. However, my argument is that although it is a quantity, we can do nothing to change its quantity. If we subtract, add, or multiply, the number with another number we get the same number. If you divide that number with something such as infinity/8, we reach inifinity still. If you divide infinity by a number, as previously stated, the number is still 1/infinity or 0. We can reach infinity, but we can never change infinity.\n\nTherefore, just like how infinity does not follow the rules of algebra, any number divided by 0 also does not follow the rules of algebra. In this way, we are unable to use anything divided by 0. This is exactly why we can conclude that anything divided by 0 is absolutely impossible.\n\nTweet" ]
[ null, "https://www.sciences360.com/wp-content/themes/helium/img/microsite-logos/360-degrees.png", null, "https://app.heliumnetwork.com/heliumnetwork", null, "https://www.sciences360.com/wp-content/themes/helium/img/loginBoxClose_buttonClose.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9551353,"math_prob":0.9877707,"size":3115,"snap":"2022-27-2022-33","text_gpt3_token_len":671,"char_repetition_ratio":0.17454195,"word_repetition_ratio":0.021238938,"special_character_ratio":0.21348314,"punctuation_ratio":0.11419753,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994491,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-25T14:06:42Z\",\"WARC-Record-ID\":\"<urn:uuid:8baa0261-e1cb-44ad-b1a4-43aed472e53d>\",\"Content-Length\":\"21604\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9df38e6f-d07f-4df2-94d7-c69bc4a201ba>\",\"WARC-Concurrent-To\":\"<urn:uuid:df35363e-2c08-4b98-999d-42353b57b2cf>\",\"WARC-IP-Address\":\"104.21.14.125\",\"WARC-Target-URI\":\"https://www.sciences360.com/index.php/can-you-divide-by-0-yes-11886/\",\"WARC-Payload-Digest\":\"sha1:CRDRGC2KZAYSLXA4TUZ6NZYWLQA2KJ6I\",\"WARC-Block-Digest\":\"sha1:IYUQLY3J3BJ7EI7HKOFRG47XZ557FIS3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103035636.10_warc_CC-MAIN-20220625125944-20220625155944-00193.warc.gz\"}"}
https://ixtrieve.fh-koeln.de/birds/litie/document/6257
[ "# Document (#6257)\n\nAuthor\nTitle\n¬The digitisation of library material\nSource\nInformation management and technology. 26(1993) no.3, S.128-132\nYear\n1993\nAbstract\nConsiders conversion of materials currently held on paper or microfilm to electronic media using imaging technology. Briefly describes current research projects in the UK and USA. Explains the digitization process and describes document and microfilm scanners. Details scanning of print and microfilm, explaining the different problems and special needs each medium, outlines image enhancement and optical character recognition\n\n## Similar documents (content)\n\n1. Initiatives for access (1993) 0.38\n```0.3848097 = sum of:\n0.3848097 = product of:\n1.2025304 = sum of:\n0.04521752 = weight(abstract_txt:image in 2657) [ClassicSimilarity], result of:\n0.04521752 = score(doc=2657,freq=1.0), product of:\n0.08974971 = queryWeight, product of:\n1.0503087 = boost\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.015900604 = queryNorm\n0.50381804 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.046611827 = weight(abstract_txt:currently in 2657) [ClassicSimilarity], result of:\n0.046611827 = score(doc=2657,freq=1.0), product of:\n0.09158534 = queryWeight, product of:\n1.0609952 = boost\n5.428738 = idf(docFreq=515, maxDocs=43254)\n0.015900604 = queryNorm\n0.5089442 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.428738 = idf(docFreq=515, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.06748595 = weight(abstract_txt:recognition in 2657) [ClassicSimilarity], result of:\n0.06748595 = score(doc=2657,freq=1.0), product of:\n0.117211655 = queryWeight, product of:\n1.200289 = boost\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.015900604 = queryNorm\n0.57576144 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.08059361 = weight(abstract_txt:character in 2657) [ClassicSimilarity], result of:\n0.08059361 = score(doc=2657,freq=1.0), product of:\n0.13193569 = queryWeight, product of:\n1.2734491 = boost\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.015900604 = queryNorm\n0.6108553 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.19777049 = weight(abstract_txt:digitization in 2657) [ClassicSimilarity], result of:\n0.19777049 = score(doc=2657,freq=3.0), product of:\n0.16642904 = queryWeight, product of:\n1.4302601 = boost\n7.318136 = idf(docFreq=77, maxDocs=43254)\n0.015900604 = queryNorm\n1.1883172 = fieldWeight in 2657, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n7.318136 = idf(docFreq=77, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.11602856 = weight(abstract_txt:optical in 2657) [ClassicSimilarity], result of:\n0.11602856 = score(doc=2657,freq=1.0), product of:\n0.16821775 = queryWeight, product of:\n1.4379253 = boost\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.015900604 = queryNorm\n0.6897522 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.032197684 = weight(abstract_txt:describes in 2657) [ClassicSimilarity], result of:\n0.032197684 = score(doc=2657,freq=1.0), product of:\n0.09016852 = queryWeight, product of:\n1.4888225 = boost\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.015900604 = queryNorm\n0.3570834 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.6166247 = weight(abstract_txt:microfilm in 2657) [ClassicSimilarity], result of:\n0.6166247 = score(doc=2657,freq=1.0), product of:\n0.73883855 = queryWeight, product of:\n5.2195835 = boost\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.015900604 = queryNorm\n0.8345865 = fieldWeight in 2657, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.09375 = fieldNorm(doc=2657)\n0.32 = coord(8/25)\n```\n2. Initiatives for access (1994) 0.36\n```0.35989177 = sum of:\n0.35989177 = product of:\n1.1246618 = sum of:\n0.03768127 = weight(abstract_txt:image in 4906) [ClassicSimilarity], result of:\n0.03768127 = score(doc=4906,freq=1.0), product of:\n0.08974971 = queryWeight, product of:\n1.0503087 = boost\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.015900604 = queryNorm\n0.41984838 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.056238297 = weight(abstract_txt:recognition in 4906) [ClassicSimilarity], result of:\n0.056238297 = score(doc=4906,freq=1.0), product of:\n0.117211655 = queryWeight, product of:\n1.200289 = boost\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.015900604 = queryNorm\n0.47980124 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.059145216 = weight(abstract_txt:conversion in 4906) [ClassicSimilarity], result of:\n0.059145216 = score(doc=4906,freq=1.0), product of:\n0.1212167 = queryWeight, product of:\n1.2206234 = boost\n6.245499 = idf(docFreq=227, maxDocs=43254)\n0.015900604 = queryNorm\n0.4879296 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.245499 = idf(docFreq=227, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.067161344 = weight(abstract_txt:character in 4906) [ClassicSimilarity], result of:\n0.067161344 = score(doc=4906,freq=1.0), product of:\n0.13193569 = queryWeight, product of:\n1.2734491 = boost\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.015900604 = queryNorm\n0.5090461 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.08926522 = weight(abstract_txt:scanning in 4906) [ClassicSimilarity], result of:\n0.08926522 = score(doc=4906,freq=1.0), product of:\n0.15949151 = queryWeight, product of:\n1.4001328 = boost\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.015900604 = queryNorm\n0.55968636 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.13674097 = weight(abstract_txt:optical in 4906) [ClassicSimilarity], result of:\n0.13674097 = score(doc=4906,freq=2.0), product of:\n0.16821775 = queryWeight, product of:\n1.4379253 = boost\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.015900604 = queryNorm\n0.81288075 = fieldWeight in 4906, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.16457558 = weight(abstract_txt:digitisation in 4906) [ClassicSimilarity], result of:\n0.16457558 = score(doc=4906,freq=1.0), product of:\n0.23980577 = queryWeight, product of:\n1.7168417 = boost\n8.784473 = idf(docFreq=17, maxDocs=43254)\n0.015900604 = queryNorm\n0.686287 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.784473 = idf(docFreq=17, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.5138539 = weight(abstract_txt:microfilm in 4906) [ClassicSimilarity], result of:\n0.5138539 = score(doc=4906,freq=1.0), product of:\n0.73883855 = queryWeight, product of:\n5.2195835 = boost\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.015900604 = queryNorm\n0.69548875 = fieldWeight in 4906, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.078125 = fieldNorm(doc=4906)\n0.32 = coord(8/25)\n```\n3. Alexander, M.: Digitising books, manuscripts and scholarly materials : preparation, handling, scanning, recognition, compression, storage formats (1998) 0.30\n```0.29804727 = sum of:\n0.29804727 = product of:\n1.2418637 = sum of:\n0.05079366 = weight(abstract_txt:projects in 5687) [ClassicSimilarity], result of:\n0.05079366 = score(doc=5687,freq=1.0), product of:\n0.087512545 = queryWeight, product of:\n1.0371357 = boost\n5.306658 = idf(docFreq=582, maxDocs=43254)\n0.015900604 = queryNorm\n0.5804157 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.306658 = idf(docFreq=582, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.07873361 = weight(abstract_txt:recognition in 5687) [ClassicSimilarity], result of:\n0.07873361 = score(doc=5687,freq=1.0), product of:\n0.117211655 = queryWeight, product of:\n1.200289 = boost\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.015900604 = queryNorm\n0.6717217 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.12497131 = weight(abstract_txt:scanning in 5687) [ClassicSimilarity], result of:\n0.12497131 = score(doc=5687,freq=1.0), product of:\n0.15949151 = queryWeight, product of:\n1.4001328 = boost\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.015900604 = queryNorm\n0.7835609 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.037563965 = weight(abstract_txt:describes in 5687) [ClassicSimilarity], result of:\n0.037563965 = score(doc=5687,freq=1.0), product of:\n0.09016852 = queryWeight, product of:\n1.4888225 = boost\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.015900604 = queryNorm\n0.4165973 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.23040581 = weight(abstract_txt:digitisation in 5687) [ClassicSimilarity], result of:\n0.23040581 = score(doc=5687,freq=1.0), product of:\n0.23980577 = queryWeight, product of:\n1.7168417 = boost\n8.784473 = idf(docFreq=17, maxDocs=43254)\n0.015900604 = queryNorm\n0.9608018 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.784473 = idf(docFreq=17, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.71939546 = weight(abstract_txt:microfilm in 5687) [ClassicSimilarity], result of:\n0.71939546 = score(doc=5687,freq=1.0), product of:\n0.73883855 = queryWeight, product of:\n5.2195835 = boost\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.015900604 = queryNorm\n0.97368425 = fieldWeight in 5687, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.109375 = fieldNorm(doc=5687)\n0.24 = coord(6/25)\n```\n4. Goldberg, E.: ¬The retrieval problem in photography (1932) (1992) 0.15\n```0.14751257 = sum of:\n0.14751257 = product of:\n1.2292714 = sum of:\n0.04521752 = weight(abstract_txt:image in 1323) [ClassicSimilarity], result of:\n0.04521752 = score(doc=1323,freq=1.0), product of:\n0.08974971 = queryWeight, product of:\n1.0503087 = boost\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.015900604 = queryNorm\n0.50381804 = fieldWeight in 1323, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.374059 = idf(docFreq=544, maxDocs=43254)\n0.09375 = fieldNorm(doc=1323)\n0.11602856 = weight(abstract_txt:optical in 1323) [ClassicSimilarity], result of:\n0.11602856 = score(doc=1323,freq=1.0), product of:\n0.16821775 = queryWeight, product of:\n1.4379253 = boost\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.015900604 = queryNorm\n0.6897522 = fieldWeight in 1323, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.09375 = fieldNorm(doc=1323)\n1.0680254 = weight(abstract_txt:microfilm in 1323) [ClassicSimilarity], result of:\n1.0680254 = score(doc=1323,freq=3.0), product of:\n0.73883855 = queryWeight, product of:\n5.2195835 = boost\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.015900604 = queryNorm\n1.4455463 = fieldWeight in 1323, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n8.902256 = idf(docFreq=15, maxDocs=43254)\n0.09375 = fieldNorm(doc=1323)\n0.12 = coord(3/25)\n```\n5. Ramsden, A.: ELINOR electronic library system (1998) 0.15\n```0.14741832 = sum of:\n0.14741832 = product of:\n0.61424303 = sum of:\n0.07634427 = weight(abstract_txt:details in 3404) [ClassicSimilarity], result of:\n0.07634427 = score(doc=3404,freq=1.0), product of:\n0.10504781 = queryWeight, product of:\n1.1363025 = boost\n5.814059 = idf(docFreq=350, maxDocs=43254)\n0.015900604 = queryNorm\n0.72675735 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.814059 = idf(docFreq=350, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.08998127 = weight(abstract_txt:recognition in 3404) [ClassicSimilarity], result of:\n0.08998127 = score(doc=3404,freq=1.0), product of:\n0.117211655 = queryWeight, product of:\n1.200289 = boost\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.015900604 = queryNorm\n0.76768196 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.1414557 = idf(docFreq=252, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.107458144 = weight(abstract_txt:character in 3404) [ClassicSimilarity], result of:\n0.107458144 = score(doc=3404,freq=1.0), product of:\n0.13193569 = queryWeight, product of:\n1.2734491 = boost\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.015900604 = queryNorm\n0.8144737 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.5157895 = idf(docFreq=173, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.14282435 = weight(abstract_txt:scanning in 3404) [ClassicSimilarity], result of:\n0.14282435 = score(doc=3404,freq=1.0), product of:\n0.15949151 = queryWeight, product of:\n1.4001328 = boost\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.015900604 = queryNorm\n0.89549816 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.1639853 = idf(docFreq=90, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.15470475 = weight(abstract_txt:optical in 3404) [ClassicSimilarity], result of:\n0.15470475 = score(doc=3404,freq=1.0), product of:\n0.16821775 = queryWeight, product of:\n1.4379253 = boost\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.015900604 = queryNorm\n0.9196696 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.357357 = idf(docFreq=74, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.04293024 = weight(abstract_txt:describes in 3404) [ClassicSimilarity], result of:\n0.04293024 = score(doc=3404,freq=1.0), product of:\n0.09016852 = queryWeight, product of:\n1.4888225 = boost\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.015900604 = queryNorm\n0.4761112 = fieldWeight in 3404, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.8088896 = idf(docFreq=2606, maxDocs=43254)\n0.125 = fieldNorm(doc=3404)\n0.24 = coord(6/25)\n```" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6739163,"math_prob":0.99854183,"size":14124,"snap":"2021-31-2021-39","text_gpt3_token_len":5452,"char_repetition_ratio":0.24199717,"word_repetition_ratio":0.48796242,"special_character_ratio":0.53617954,"punctuation_ratio":0.28343558,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998729,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-17T06:52:17Z\",\"WARC-Record-ID\":\"<urn:uuid:04362925-6039-4bba-b33b-ff96634c3788>\",\"Content-Length\":\"24149\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b1155a5c-9e4a-489f-a12b-ad3b9166e4e6>\",\"WARC-Concurrent-To\":\"<urn:uuid:d56afbac-bcf5-4e14-addd-36b28e68d5b9>\",\"WARC-IP-Address\":\"139.6.160.6\",\"WARC-Target-URI\":\"https://ixtrieve.fh-koeln.de/birds/litie/document/6257\",\"WARC-Payload-Digest\":\"sha1:YCXIZUA35L7KKVRQIVAUCYY6I4XQHJOK\",\"WARC-Block-Digest\":\"sha1:3H2TDBPO3WA3VJW77NBAU2OBFNCVKE4U\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780055601.25_warc_CC-MAIN-20210917055515-20210917085515-00499.warc.gz\"}"}
https://www.easycalculation.com/square-roots-325.html
[ "# What is Square Root of 325 ?\n\nThe square root is a number which results in a specific quantity when it is multiplied by itself. The square root of 325 is 18.02776\n\nSquare Root of 325\n √325 = √(18.028 x 18.028) 18.02776\n\nThe square root is a number which results in a specific quantity when it is multiplied by itself. The square root of 325 is 18.02776\n\nThe nearest previous perfect square is 324 and the nearest next perfect square is 361 ." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.94035953,"math_prob":0.9996704,"size":353,"snap":"2020-24-2020-29","text_gpt3_token_len":82,"char_repetition_ratio":0.17191978,"word_repetition_ratio":0.7096774,"special_character_ratio":0.2719547,"punctuation_ratio":0.06944445,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99519116,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T22:57:27Z\",\"WARC-Record-ID\":\"<urn:uuid:00d04b98-b8b8-4d61-a6ea-dbb8ba6a0350>\",\"Content-Length\":\"26969\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3e9bfa76-a716-4d1a-befd-e1fb10adbb53>\",\"WARC-Concurrent-To\":\"<urn:uuid:f1e0835c-3bed-4b81-a940-d8018819ed60>\",\"WARC-IP-Address\":\"173.255.199.118\",\"WARC-Target-URI\":\"https://www.easycalculation.com/square-roots-325.html\",\"WARC-Payload-Digest\":\"sha1:SW4HEX6KGNCHQFXK6QUUI3EZ57XXZUEJ\",\"WARC-Block-Digest\":\"sha1:B2SW25GY6274OMXGVWMKP2PML255IREH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655880243.25_warc_CC-MAIN-20200702205206-20200702235206-00155.warc.gz\"}"}
https://www.colorhexa.com/1a7905
[ "# #1a7905 Color Information\n\nIn a RGB color space, hex #1a7905 is composed of 10.2% red, 47.5% green and 2% blue. Whereas in a CMYK color space, it is composed of 78.5% cyan, 0% magenta, 95.9% yellow and 52.5% black. It has a hue angle of 109.1 degrees, a saturation of 92.1% and a lightness of 24.7%. #1a7905 color hex could be obtained by blending #34f20a with #000000. Closest websafe color is: #336600.\n\n• R 10\n• G 47\n• B 2\nRGB color chart\n• C 79\n• M 0\n• Y 96\n• K 53\nCMYK color chart\n\n#1a7905 color description : Dark lime green.\n\n# #1a7905 Color Conversion\n\nThe hexadecimal color #1a7905 has RGB values of R:26, G:121, B:5 and CMYK values of C:0.79, M:0, Y:0.96, K:0.53. Its decimal value is 1734917.\n\nHex triplet RGB Decimal 1a7905 `#1a7905` 26, 121, 5 `rgb(26,121,5)` 10.2, 47.5, 2 `rgb(10.2%,47.5%,2%)` 79, 0, 96, 53 109.1°, 92.1, 24.7 `hsl(109.1,92.1%,24.7%)` 109.1°, 95.9, 47.5 336600 `#336600`\nCIE-LAB 44.096, -46.591, 47.202 7.29, 13.905, 2.443 0.308, 0.588, 13.905 44.096, 66.324, 134.627 44.096, -38.511, 52.945 37.289, -30.357, 22.217 00011010, 01111001, 00000101\n\n# Color Schemes with #1a7905\n\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #640579\n``#640579` `rgb(100,5,121)``\nComplementary Color\n• #547905\n``#547905` `rgb(84,121,5)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #05792a\n``#05792a` `rgb(5,121,42)``\nAnalogous Color\n• #790554\n``#790554` `rgb(121,5,84)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #2a0579\n``#2a0579` `rgb(42,5,121)``\nSplit Complementary Color\n• #79051a\n``#79051a` `rgb(121,5,26)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #051a79\n``#051a79` `rgb(5,26,121)``\n• #796405\n``#796405` `rgb(121,100,5)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #051a79\n``#051a79` `rgb(5,26,121)``\n• #640579\n``#640579` `rgb(100,5,121)``\n• #0a3002\n``#0a3002` `rgb(10,48,2)``\n• #0f4803\n``#0f4803` `rgb(15,72,3)``\n• #156104\n``#156104` `rgb(21,97,4)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #1f9106\n``#1f9106` `rgb(31,145,6)``\n• #25aa07\n``#25aa07` `rgb(37,170,7)``\n• #2ac208\n``#2ac208` `rgb(42,194,8)``\nMonochromatic Color\n\n# Alternatives to #1a7905\n\nBelow, you can see some colors close to #1a7905. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #377905\n``#377905` `rgb(55,121,5)``\n• #2d7905\n``#2d7905` `rgb(45,121,5)``\n• #247905\n``#247905` `rgb(36,121,5)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #107905\n``#107905` `rgb(16,121,5)``\n• #077905\n``#077905` `rgb(7,121,5)``\n• #05790d\n``#05790d` `rgb(5,121,13)``\nSimilar Colors\n\n# #1a7905 Preview\n\nThis text has a font color of #1a7905.\n\n``<span style=\"color:#1a7905;\">Text here</span>``\n#1a7905 background color\n\nThis paragraph has a background color of #1a7905.\n\n``<p style=\"background-color:#1a7905;\">Content here</p>``\n#1a7905 border color\n\nThis element has a border color of #1a7905.\n\n``<div style=\"border:1px solid #1a7905;\">Content here</div>``\nCSS codes\n``.text {color:#1a7905;}``\n``.background {background-color:#1a7905;}``\n``.border {border:1px solid #1a7905;}``\n\n# Shades and Tints of #1a7905\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #020800 is the darkest color, while #f6fff4 is the lightest one.\n\n• #020800\n``#020800` `rgb(2,8,0)``\n• #061b01\n``#061b01` `rgb(6,27,1)``\n• #0a2e02\n``#0a2e02` `rgb(10,46,2)``\n• #0e4003\n``#0e4003` `rgb(14,64,3)``\n• #125303\n``#125303` `rgb(18,83,3)``\n• #166604\n``#166604` `rgb(22,102,4)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #1e8c06\n``#1e8c06` `rgb(30,140,6)``\n• #229f07\n``#229f07` `rgb(34,159,7)``\n• #26b207\n``#26b207` `rgb(38,178,7)``\n• #2ac408\n``#2ac408` `rgb(42,196,8)``\n• #2ed709\n``#2ed709` `rgb(46,215,9)``\n• #32ea0a\n``#32ea0a` `rgb(50,234,10)``\n• #3bf512\n``#3bf512` `rgb(59,245,18)``\n• #4bf625\n``#4bf625` `rgb(75,246,37)``\n• #5af738\n``#5af738` `rgb(90,247,56)``\n• #6af84b\n``#6af84b` `rgb(106,248,75)``\n• #79f85d\n``#79f85d` `rgb(121,248,93)``\n• #89f970\n``#89f970` `rgb(137,249,112)``\n• #99fa83\n``#99fa83` `rgb(153,250,131)``\n• #a8fb96\n``#a8fb96` `rgb(168,251,150)``\n• #b8fba9\n``#b8fba9` `rgb(184,251,169)``\n• #c7fcbc\n``#c7fcbc` `rgb(199,252,188)``\n• #d7fdce\n``#d7fdce` `rgb(215,253,206)``\n• #e6fee1\n``#e6fee1` `rgb(230,254,225)``\n• #f6fff4\n``#f6fff4` `rgb(246,255,244)``\nTint Color Variation\n\n# Tones of #1a7905\n\nA tone is produced by adding gray to any pure hue. In this case, #3c443a is the less saturated color, while #177e00 is the most saturated one.\n\n• #3c443a\n``#3c443a` `rgb(60,68,58)``\n• #394935\n``#394935` `rgb(57,73,53)``\n• #364d31\n``#364d31` `rgb(54,77,49)``\n• #33522c\n``#33522c` `rgb(51,82,44)``\n• #305727\n``#305727` `rgb(48,87,39)``\n• #2d5c22\n``#2d5c22` `rgb(45,92,34)``\n• #29611d\n``#29611d` `rgb(41,97,29)``\n• #266618\n``#266618` `rgb(38,102,24)``\n• #236a14\n``#236a14` `rgb(35,106,20)``\n• #206f0f\n``#206f0f` `rgb(32,111,15)``\n• #1d740a\n``#1d740a` `rgb(29,116,10)``\n• #1a7905\n``#1a7905` `rgb(26,121,5)``\n• #177e00\n``#177e00` `rgb(23,126,0)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #1a7905 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.5756027,"math_prob":0.66656506,"size":3658,"snap":"2021-31-2021-39","text_gpt3_token_len":1641,"char_repetition_ratio":0.12370005,"word_repetition_ratio":0.011090573,"special_character_ratio":0.5697102,"punctuation_ratio":0.23608018,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99208474,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-24T15:17:58Z\",\"WARC-Record-ID\":\"<urn:uuid:869a0235-993c-4196-a762-0234fb98e1e6>\",\"Content-Length\":\"36204\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3a68ac50-6cda-45f1-8728-3d455f0c543e>\",\"WARC-Concurrent-To\":\"<urn:uuid:c2ad9408-33a7-4be9-9266-26c9805e7011>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/1a7905\",\"WARC-Payload-Digest\":\"sha1:PCRIHPHS2CF33CPHWYXEHMFAAFXDKPLX\",\"WARC-Block-Digest\":\"sha1:M5ZZC3I54GO3XXSJQZT7FE6D2WIUYB2Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046150266.65_warc_CC-MAIN-20210724125655-20210724155655-00593.warc.gz\"}"}
https://warrenadams.me/music-audio/how-to-make-a-double-box-plot.php
[ "Double box-and-whisker plots give you a quick visual comparison of 2 sets of data, as was also found with other double graph forms covered in. Read and learn for free about the following article: Box plot review. Let's make a box plot for the same dataset from above. Step 1: Scale and label an axis that. The box in the box-and-whisker plot contains, and thereby highlights, the middle portion of these data points. To create a box-and-whisker plot, we start by .\n\n## box and whisker plot problems\n\nQuickly make parallel box plots for your maths assignment. Then find out how to describe their spread and central tendency and compare them. A box and whisker plot is a diagram that shows the statistical distribution of a set of data. This makes it easy to see how data is distributed along. Note: After clicking Draw here, you can click the Copy to Clipboard button (in Internet Explorer), or right-click on the graph and choose Copy. In your Word.\n\nCreating box and whisker plots has never been so easy with Displayr's free online box and whisker plot maker. Generate professional area charts, customize . Box plots, or box-and-whisker plots, are fantastic little graphs that give you a lot of statistical information in a cute little square. Let's take a look. How to read a box plot/Introduction to box plots. Box plots are drawn for groups of [email protected] scale scores. They enable us to study the distributional characteristics of.\n\nMake box plots online with Excel, CSV, or SQL data. Make bar charts, histograms , box plots, scatter plots, line graphs, dot plots, and more. Free to get started!. Create a standard box plot to show the distribution of a set of data. Make a box-and-whisker plot for the ages of the members of the. U.S. Which statement is true about the double box-and-whisker plot?\n\n## box and whisker plot explained\n\nA box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum. The term box plot comes from the . In this article, you will learn to create whisker and box plot in R programming. You will also learn to draw multiple box plots in a single plot. However, there is no need to bother the double box plot for such as the following meteorological and astronomical phenomena is not easy. If you've never made one before, we'll show you how to create a box and whisker plot in Excel, then double-check the calculations, and. In this activity, you will create three parallel boxplots and compare them. Materials To change to the dot plot to a boxplot, select MENU > Plot Type >. Boxplot. An example of a formula is y~group where a separate boxplot for numeric variable y is generated for each value of group. Add varwidth=TRUE to make boxplot. This is actually more efficient because boxplot converts # a 2-D array into a list of the original sample, and a boxplot is one visual tool to make this assessment. A box and whisker plot (sometimes called a boxplot) is a graph that presents A breakdown of the various components that make up a box and whisker. The key information you want to get when reading box plots is: are these groups If two boxes do not overlap with one another, say, box A is. Box plot generator. Create AccountorSign In. enter your data into list A. enter your data into list A. 1. A = 5,27,7,2,8, \\$\\$ A. \\$\\$= 6 element list. 2. box plot." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8874269,"math_prob":0.93586016,"size":3692,"snap":"2020-10-2020-16","text_gpt3_token_len":846,"char_repetition_ratio":0.14560738,"word_repetition_ratio":0.015197569,"special_character_ratio":0.219935,"punctuation_ratio":0.12021136,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.987914,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-01T20:29:47Z\",\"WARC-Record-ID\":\"<urn:uuid:1062c267-829e-4e9e-9694-9482a6cd48d1>\",\"Content-Length\":\"13388\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:98c4c273-3042-4b02-80d7-4063962c10a6>\",\"WARC-Concurrent-To\":\"<urn:uuid:bbc65faa-bb30-4233-ac58-19394eca6dde>\",\"WARC-IP-Address\":\"104.31.78.58\",\"WARC-Target-URI\":\"https://warrenadams.me/music-audio/how-to-make-a-double-box-plot.php\",\"WARC-Payload-Digest\":\"sha1:FKKPY32EKRWOOKCHGVPE5JPQWUTZECEU\",\"WARC-Block-Digest\":\"sha1:YIQUVJJ3LHIFEQKKS64ICPUETFQMDCUG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370506121.24_warc_CC-MAIN-20200401192839-20200401222839-00456.warc.gz\"}"}
https://physics.stackexchange.com/questions/207115/harmonic-oscillator-relation-with-this-hamiltonian/207417
[ "# harmonic oscillator relation with this hamiltonian\n\nI have studied the annihilation and creation operators and number operator $N$ in relation with the simple harmonic oscillator that is governed by: $\\ H = \\hbar\\omega(N+ \\frac{1}{2})$.\nI don't understand the relation between the harmonic oscillator and, for example, this Hamiltonian $\\ H = \\hbar\\omega_0a^{\\dagger}a+\\hbar\\omega_1a^{\\dagger}a^{\\dagger}aa$ that I have found in an example in a lecture notes. They calculate the energies of this system.\n\nThey use the annihilation operator that is defined from the simple harmonic oscillator to solve that system. what is physically this system? why I can use the SHO to calculate the energies? I feel that I am confused with the a operator. I thought that it was defined from the Hamiltonian of the simple harmonic oscillator ,,,, isn't it ?\n\n• First, do you understand the meaning of the Hamiltonian of a system? $H=\\hbar\\omega(N+\\frac{1}{2})$ is the reduced form of the Hamiltonian of a harmonic oscillator or electromagnetic field. – TBBT Sep 15 '15 at 6:07\n• Thanks for your response. Yes i understand , N here is the number operator equal to N=aa+ , but here they use the simple harmonic oscillator to solve this problem? why the a, a+ and N are the same ? i thought that those operators are ONLY for the simple harmonic oscillator. – Mati Sep 15 '15 at 6:13\n• That is not what I meant. – TBBT Sep 15 '15 at 6:14\n• TBBT please can you explain? thanks in advance – Mati Sep 15 '15 at 6:17\n• I am writing an answer as we speak. – TBBT Sep 15 '15 at 6:18\n\nLet's quickly review the quantum harmonic oscillator. We have a single particle moving in one dimension, so the Hilbert space is $L^2(\\mathbb{R})$: the set of square-integrable complex functions on $\\mathbb{R}$. The harmonic oscillator Hamiltonian is given by\n\n$$H= \\frac{P^2}{2m} + \\frac{m\\omega^2}{2}X^2$$\n\nwhere $X$ and $P$ are the usual position and momentum operators: acting on a wavefunction $\\psi(x)$ they are $X \\psi(x) = x\\psi(x)$ and $P \\psi(x) = -i\\hbar\\ \\partial \\psi / \\partial x$. Of course, we can also think of them as acting on an abstract vector $|\\psi\\rangle$.\n\nBy letting $P \\to -i\\hbar\\ \\partial/\\partial x$ we could solve the time independent Schrödinger equation $H \\psi = E \\psi$, but this is a bit of a drag. So instead we define operators $a$ and $a^\\dagger$ as in your post. Notice that the definition of $a$ and $a^\\dagger$ has nothing whatsoever to do with our Hamiltonian. It just so happen that these definitions are convenient because the Hamiltonian turns out to be $\\hbar \\omega (a^\\dagger a + 1/2)$.\n\nFor convenience we define the number operator $N = a^\\dagger a$; at this stage number is just a name with no physical interpretation. Using the commutation relation $[a,a^\\dagger] = 1$ and some algebra we notice that $N$ has a nondegenerate spectrum given by the natural numbers. In other words, the eigenvalues of $N$ are $\\{0,1,2,\\dots\\}$, and to each eigenvalue $n$ there corresponds a single state $|n\\rangle$ with $N|n\\rangle = n |n\\rangle$. Notice that, again, $N$ is independent of our Hamiltonian. However, because the Hamiltonian turns out to be $\\hbar \\omega (N+1/2)$ we immediately know that the states $|n\\rangle$ are its eigenvectors, with energies $\\hbar \\omega (n + 1/2)$.\n\nNow you are given a different Hamiltonian. The Hilbert space is still exactly the same, and so are $a$, $a^\\dagger$ and $N$, because their definition had nothing to do with the original Hamiltonian. You can still use their properties to find energies, eigenvectors, and so on. The states $|n\\rangle$ are still the eigenstates of $N$, though a priori they might not be eigenstates of the new $H$ (exercise 31 asks you to prove that they in fact are eigenstates of the new $H$). The important point here is that operators are (usually) defined independently of the Hamiltonian. They characterize the physical system. After all, you know that there are operators $X$ and $P$, and you have no qualms about using them with different Hamiltonians. The Hamiltonian gives the energy and the time evolution, but the observables and related operators are independent of your choice of Hamiltonian.\n\nAbout the physical interpretation... exercise 31 asks you to prove that $H=\\hbar\\omega_0 N + \\hbar \\omega_1 (N^2-N)$; notice that we have gotten rid of $\\hbar\\omega_0 /2$ since it is just a constant. I would usually expect $\\omega_1$ to be smaller than $\\omega_0$ so this is a small perturbation (for small $n$ at least), but we don't really care about that right now. You can see that $|n\\rangle$ are still the eigenstates of the Hamiltonian; all we did is shift the energies by an amount $\\hbar \\omega_1 (N^2-N)$.\n\n• Just a comment, i was born in BSAS :) – Mati Sep 19 '15 at 6:13\n\nThe Annihilation and Creation Operators are NOT specific to any particular Hamiltonian. They are defined through X and P which are position and momentum operators for ANY system that you are studying. It just so turned out that these operators facilitate the calculations in SHO specifically. (In fact, I believe these operators originated from Dirac's study of SHO)\n\nYour new Hamiltonian is different from SHO formally, but really the OPERATORs have NOT Changed! N is still the same N! Since arguments of H ONLY involve one operator N and arbitrary scalars, H and N commute and thus eigenstates of N are also eigenstates of H. So if H acts on an eigenstate of N, the output is just the energy. Here notice that although n no longer COUNTS the excitation level of a single oscillator, it is still a sufficiently good label for the energy levels of your new system.\n\nTo summarize, N is just a tool. You could have expressed your Hamiltonian in terms of other \"ingenious\" (or stupid) operators and solve the problem in terms of eigenstates of those operators! N is by NO MEANS unique. It can exist on its own without reference to SHO. I guess that is the biggest point to make.\n\n• Yes, this $a^\\dagger$ is related with the harmonic oscillator! The relation is very close as it creates eigenstates of this Hamiltonian. (Of course you can write other Hamiltonians in terms of these operators, but those Hamiltonians are in general not diagonalized by them). As you are generally interested in diagonalizing the Hamiltonian (as you can then read off the spectrum, ...) this counts for a lot. For another example, the operators creating Cooper pairs are related to the BCS Hamiltonian, they create the fundamental excitations of the system (as they diagonalize the Hamiltonian). – Sebastian Riese Sep 16 '15 at 18:36\n• Hi Sebastian Riese, I guess my answer was somewhat misleading. I am not saying that N is not associated with SHO. All I am saying is that it CAN exist on its own! And Mati's original confusion was \"why can we apply results of SHO to another Hamiltonian that seems unrelated.\" My answer is, we are not applying results of SHO, but rather just results derived from the operator N, which is universally applicable. – Zhengyan Shi Sep 17 '15 at 3:35\n• Your edit fixes the issues with the answer, so +1. – Sebastian Riese Sep 17 '15 at 10:58\n• @SebastianRiese , Zhengyan Shi thank you very much! – Mati Sep 19 '15 at 6:14\n\nHamiltonian of different systems is different. Hamiltonian of different systems do not have to be related. You are taught to study the dynamics of the harmonic oscillator in Quantum Mechanics is because it related to the electromagnetic field quantisation, which you will learn later on. Basically said, the Hamiltonian of the harmonic oscillator is the same with light field.\n\nAnyway, the exercise, which you are presented us, is asking you to study a quantum system with a total Hamiltonian of $H=\\hbar\\omega_{0}a^{\\dagger}a+\\hbar\\omega_{1}a^{\\dagger}a^{\\dagger}aa$. Therefore, you should be using this one to solve the exercise.\n\nThe annihilation operator is also given in the exercise. In case you wonder, that is the same as the relation you find in the harmonic oscillator system. I'll show you, $$a=\\sqrt{\\frac{m\\omega}{2\\hbar}}x+i\\sqrt{\\frac{1}{2m\\omega\\hbar}}p$$ and its Hermitian conjugate, $$a^{\\dagger}=\\sqrt{\\frac{m\\omega}{2\\hbar}}x-i\\sqrt{\\frac{1}{2m\\omega\\hbar}}p$$ From these to relations, you can be able to find $x$ and $p$.\n\nI can tell you are confusing with the fundamental concept of Quantum Mechanics. I suggest you to go back and read more materials. If you are not clear on the operators, as you said, you should learn more about Mathematics for Quantum Mechanics.\n\nI think this exercise is not very hard. Since you only asked us to clarify the confusion you have with the Hamiltonian, I won't go any further that this. If you find the exercise challenging, please ask us for specific assistant. Please note that this site is not for homework-solving but homework-helping. If you find my answer not helpful, please comment below.\n\n• Thanks. I understand that i need to use this Hamiltonian to solve the problem. I went back and read a lot before i wrote this question. Specifically i learned that a and a+ operators derive from the hamiltonian of the simple harmonic oscillator: H = p^2/2m + mw^2x^2/2 so why i can use them without adapting them to this problem ? – Mati Sep 15 '15 at 6:49" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9029816,"math_prob":0.98606694,"size":3124,"snap":"2021-31-2021-39","text_gpt3_token_len":853,"char_repetition_ratio":0.12371795,"word_repetition_ratio":0.035785288,"special_character_ratio":0.2647247,"punctuation_ratio":0.091362126,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9975716,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-29T17:57:42Z\",\"WARC-Record-ID\":\"<urn:uuid:0b874eb4-e932-4b09-a284-d0cffdf27c3c>\",\"Content-Length\":\"205943\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:931c65da-49b9-4e83-ac92-3e6840ad0041>\",\"WARC-Concurrent-To\":\"<urn:uuid:349b6e4d-55d1-4628-94f4-944cb74a2914>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/207115/harmonic-oscillator-relation-with-this-hamiltonian/207417\",\"WARC-Payload-Digest\":\"sha1:HIZM5DVCOVTAB5IVQ4G7SPKWCOTYGA67\",\"WARC-Block-Digest\":\"sha1:4TG5BV6WOSQM7J4JSYOLUY2DK3BDL6KP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153892.74_warc_CC-MAIN-20210729172022-20210729202022-00137.warc.gz\"}"}
https://www.blackstonetutors.com/free-pre-registration-pharmacist-recruitment-numeracy-exam-practice-questions/
[ "", null, "# Free Pre-Registration Pharmacist Recruitment Numeracy Exam Practice Questions\n\nAdvice & Insight From Pre-Registration Recruitment Exam Specialists\n\n## ​Practice Question 1\n\nA 54 year old female patient has been admitted onto the ward after receiving a kidney transplant and the consultant would like to estimate creatinine clearance prior to administration of treatment. The patient’s weight is 64kg and he has a serum creatinine of 126 micromol/litre.\n\nYou may use the following equation to support you answering this question:\n\nEstimated CrCl (ml/min) = (140 – Age) x Weight x Constant\nSerum creatinine\n\nWhere:\n\nAge = years\nWeight = kg\nSerum creatinine = micromole/litre\nConstant = 1.23 for men or 1.04 for women\n\nEstimated CrCl (ml/min) = (140 – Age) x Weight x Constant\nSerum creatinine\n\n= (140 – 54) x 64 x 1.04\n126\n\n= 45.43ml/min\n\n## Practice Question 2\n\nA drug has an elimination half-life of 14 hours, assuming it is completely absorbed and 1200mg of the drug is administered as the dose, how many mg would you expect to remain in the body after 48 hours? Assume the drug in question has first order pharmacokinetics.\n\n1200mg starting off and after 14 hours it is halved to 600mg then after another 14 hours halved again to 300mg and after another 14 hours halved again to 150mg but this equals to 42 hours and we need to work out for 48 hours.\n\nTherefore, in the next halve of between 150mg to 75mg in 14 hours the drug is reduced by 75mg so in one hour the drug reduces by 5.36mg and you can then multiply by 6 to work out total drug depletion in 6 hours = 32.14mg.\n\n75mg – 32.14mg = 42.86mg is depleted in 8 hours so you would add this to 75mg to arrive at 117.86mg after 48 hours\n\n## ​Practice Question 3\n\nHow many litres of a 0.91% stock solution are required to make 2L of a 0.8% solution, using water as the solvent?\n\nNeed to apply formula: C1V1 = C2V2\n\nWe know C1 (0.91%) but not V1 and we know C2 (0.8%) and V2 (2L = 2000mls) so simply plug in the known values:\n0.91% x V1 = 0.8% x 2000mls\n\nV1 = 0.8% x 2000mls/0.91\nV1 = 1758mls/1000 = 1.76 Litres\n\n## ​Practice Question 4\n\nYou have been asked to calculate how many milligrams of sodium ions are found in a 200mg tablet of sodium chloride which is required to be used to treat a salt deficiency in a patient.\n\nYou would need to know the molecular weight of the two components before starting; Sodium (Na) = 23 and Chloride (Cl) = 35.5\nThese added together: 23 + 35.5  = 58.5\n\nAs you are required to calculate milligrams of sodium:\n23/58.5 x 200mg tablet = 78.63mg\n\n##### Optimise Your Pre-Reg Oriel Performance\n\nLearn the best Pre-Reg Oriel strategies and practice with reflective questions & worked solutions.\n\n## ​Practice Question 5\n\n​You have been asked to calculate the dose for an antibiotic for a 7 year old child of a drug that is being used unlicensed according to the adult dose. The adult dose is 650mg OD.\n\nYou may find the following equation useful:\n\nDose for child = age (years) x adult dose\nAge + 12\n\nDose for child = age (years) x adult dose\nAge + 12\n\nDose for child = 7 x 650mg\n7 + 12\n\n= 239.47 mg rounded to 240mg\n\n## ​Practice Question 6\n\nYou receive a prescription for Levetiracetam 100mg/1ml oral syrup for a 5 month old baby weighing 7.2kg. The dose is 7mg/kg once daily, then increased in steps of up to 7mg/kg twice daily (max. per dose 21mg/kg twice daily), dose to be increased every two weeks. Calculate the total quantity you would dispense in mls for a 4 week supply.\n\n7mg per 1kg\n50.4mg =x per 7.2kg\n\n100mg in 1ml\n50.4mg in x mls = 0.5mls per day\n\nFirst two weeks: 0.5mls x 14 days = 7mls\nLast two weeks: 0.5mls BD x 14 days = 14mls\n\n7ml + 14mls = 21mls\n\nShopping Cart\nScroll to Top" ]
[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20300%2078'%3E%3C/svg%3E", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8751413,"math_prob":0.93601733,"size":4182,"snap":"2022-27-2022-33","text_gpt3_token_len":1184,"char_repetition_ratio":0.113212064,"word_repetition_ratio":0.07493188,"special_character_ratio":0.28168342,"punctuation_ratio":0.0882353,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9599303,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-11T02:25:08Z\",\"WARC-Record-ID\":\"<urn:uuid:bcab44d8-2342-4295-a3d1-b4356c15c09a>\",\"Content-Length\":\"536755\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c9b9fcba-1ae6-4ffa-a7a3-e9941d94ac21>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc7e5900-ca16-440f-bcbc-ccfd10cbd949>\",\"WARC-IP-Address\":\"35.214.24.216\",\"WARC-Target-URI\":\"https://www.blackstonetutors.com/free-pre-registration-pharmacist-recruitment-numeracy-exam-practice-questions/\",\"WARC-Payload-Digest\":\"sha1:2BGLT4LBFLNCYH7GX54SWQ4GL6W5FCKV\",\"WARC-Block-Digest\":\"sha1:PVCE4SKDJ3CC2PMGXGTG53GNJU4Y4RAD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571232.43_warc_CC-MAIN-20220811012302-20220811042302-00400.warc.gz\"}"}
https://elo.mastermath.nl/course/info.php?id=171
[ "### M1: Operator Algebras - 8EC\n\nPrerequisites\n\nStandard Bachelor courses on Analysis, plus some knowledge in Functional Analysis, as provided by the Mastermath course Functional Analysis (vGaans) or at least an introductory course like the \"Introduction to functional analysis\" as taught in Nijmegen. As an indication, you should be familiar with a reasonable part of the material in the first three chapters of Gert Pedersen's book \"Analysis NOW\", Springer-Verlag, 1989.\n\nAim of the course\n\nThe students are familiar with the basics of C*-algebras and von Neumann algebras, allowing them to specialize further or to apply operator algebras in the context of non-commutative geometry or the theory of infinite quantum systems. In 1929, J. von Neumann began studying what came to be called von Neumann algebras. C*-algebras were introduced by Gelfand and Nalmark in 1943. These two subjects together form the discipline of Operator Algebras, an important part of Functional Analysis with many applications in harmonic analysis and representation theory, quantum group theory, Connes' non-commutative geometry, and mathematical physics (quantum mechanics and field theory, statistical physics). The aim of this course is to lay the foundations for further studies of the subject and its applications.\n\nWe will cover at least the following subjects:\n\nBanach algebras, in particular spectral theory commutative C*-algebras ideals, quotients, homomorphisms states and representations weak topologies, density theorems von Neumann algebras Possible further subjects, time permitting:\n\ntensor products of C*-algebras some interesting examples of C*-algebras projections in von Neumann algebras and the type classification\n\nLecture Notes / Literature\n\nNecessary\n\nWe will mainly use the following book: Gerard J. Murphy: C*-algebras and operator theory, Academic Press, 1990. You need to find yourself a copy of this book to follow the course.\n\nOther literature\n\nFor some more advanced topics, we may also refer to the following book: Masamichi Takesaki: Theory of operator algebras I. Springer, 1979, 2001.\n\nA useful book giving many non-trivial examples of C*-algebras is: Kenneth R. Davidson: C*-Algebras by example. American Mathematical Society, 1996.\n\nLecturer\n\nM. Caspers (TUD)" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8670505,"math_prob":0.6326118,"size":2508,"snap":"2019-51-2020-05","text_gpt3_token_len":575,"char_repetition_ratio":0.12579872,"word_repetition_ratio":0.0,"special_character_ratio":0.203748,"punctuation_ratio":0.12072893,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98233366,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T17:24:40Z\",\"WARC-Record-ID\":\"<urn:uuid:74d73261-769e-46cb-9666-30d481537fb3>\",\"Content-Length\":\"39815\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:986c6a44-22e6-41a8-b4ce-fdecb515f0ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:b6d13851-a682-4381-a2ad-68f0f512ba41>\",\"WARC-IP-Address\":\"87.233.189.172\",\"WARC-Target-URI\":\"https://elo.mastermath.nl/course/info.php?id=171\",\"WARC-Payload-Digest\":\"sha1:3MGT76NAW64BZFM26UWU572NJBESGNOE\",\"WARC-Block-Digest\":\"sha1:MV57HNXO3AIXJUJJA52OKZ7BRMLXBPKB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251779833.86_warc_CC-MAIN-20200128153713-20200128183713-00479.warc.gz\"}"}
https://kannte-koffer-glaube.com/pin/465489311459067364w4-63z250100jk
[ "Home\n\n# Graph function\n\n## Graph of a function - Wikipedi\n\nThere is a slider with \"a =\" on it. You can use \"a\" in your formula and then use the slider to change the value of \"a\" to see how it affects the graph. Practice: Graphs of logarithmic functions. Vertical asymptote of natural log. In exponential functions, what is the dependent variable and in logarithmic functions\n\nWe need to model the height at time t based on what we know about cones. We also need to assume several things. (We make life easy for ourselves as we go along. We are allowed to do this since we just need to come up with a basic graph for the height of the water at time t). In this HowTech written tutorial, we're going to show you how to graph functions in Excel 2016. Don't forget to check out our main channel.. When plotting inequalities, the \"monochrome shading\" checkbox can be used. If this is checked, the shaded areas for all three functions are all the same light gray. This allows you to more easily see where complex functions overlap, since the more overlap there is, the darker the shading. If left unchecked, each function is shaded in a different color.\n\n### GraphSketch Permanent link to this graph page\n\n• Function Grapher is a full featured Graphing Utility that supports graphing two functions together.\n• Example 2. Sketch graph of the function `f(x)=(x+2)^2(x-1)^3`. There is no simpler function that initial function is obtained from. Function is neither even nor odd and not periodic\n• Online Graph draw: plot function, plot parametric curves,plot polar curves. The online curve plotting software, also known as a graph plotter, is an online curve plotter that allows you to plot functions..\n• Since there is no limit to the possible number of points for the graph of the function, we will follow this procedure at first:\n• To graph a function, start by plugging in 0 for x and then solving the equation to find y. Then, mark that spot on the y-axis with a dot. Next, find the slope of the line, which is the number that's right before the variable. Once you know your slope, write it as a fraction over 1 and then use the rise over run to plot the rest of the points from the spot you marked on the y-axis. Finally, use a ruler to draw a line connecting all of the points on your graph. To learn how to graph complicated functions by hand, scroll down! Did this summary help you?YesNo\n• Teaching Resources & Lesson Plans | Teachers Pay Teachers. Quadratic Function Graph Transformations - Notes, Charts, and Quiz I have found that practice makes perfect when teaching..\n\n## Video: Draw Function Graphs - Plotte\n\nAdd edges to a graph. add.vertex.shape. Various vertex shapes when plotting igraph graphs. How igraph functions handle attributes when the graph changes We choose values `0.5` seconds apart (if we were to use `t = 1\\ \"s\"` intervals, we would not see enough detail on the graph). The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also Characteristics of Graphs. Consider the function f(x) = 2 x + 1. We recognize the equation y = 2 x + 1.. We can only take the square root of a positive number so `x ≥ 0`. The square root of a number can only be positive, so `y ≥ 0`. function User_name(user) { return user.getName(); } Once a GraphQL service is running (typically at a URL on a web service), it can receive GraphQL queries to validate and execute. A received query is..\n\n### Function Grapher and Calculato\n\n• imum over the same interval. In mathematics, the graph of a function f is, formally, the set..\n• The graph of a function is the set of all points whose co-ordinates (x, y) satisfy the function `y = f(x)`. This means that for each x-value there is a corresponding y-value which is obtained when we substitute into the expression for `f(x)`.\n• Note: Some programs cannot handle URLs beyond a certain length. (E.G. Microsoft Word has a 256 byte limit). Certain very complex charts may produce URLs that are longer than this.", null, "Note: This feature can mislead you. For example if you enter 1/2sin(x) GFE inserts a multiply between the 2 and the sin. Since there are no parentheses, it is executed from left to right so it sees it as one half of sin(x). You may have meant it as one over 2sin(x). In mathematics, the graph of a function f is the set of ordered pairs , where f = y. In the common case where x For faster navigation, this Iframe is preloading the Wikiwand page for Graph of a function Everything you're expected to graph on your own is based on a more basic graph (parent function) that you NEED to memorize. Look at the image above and check with your teacher to see which you..\n\nLearn about exponential functions graphing with free interactive flashcards. Choose from 500 different sets of flashcards about exponential functions graphing on Quizlet Graphical Function Explorer (GFE). Operating instructions. GFE is a free online function graphing tool that allows you to plot up to three functions on the same set of axes", null, "### Graphing Linear Functions\n\n1. Function graph drawing/rendering application for use with audio applications. Exports .wav files. Crispy Plotter is a function graph plotter for mathematical functions, featuring high drawing speed..\n2. (2) We could have written the function in this example with h(t) rather than just h. The following 2 equations mean the same thing.\n3. The tangent function has a parent graph just like any other function. Therefore, the graph of tangent has asymptotes, which is where the function is undefined, at each of these places\n\n### 3 Ways to Graph a Function - wikiHo\n\n1. Graph a linear function: a step by step tutorial with examples and detailed solutions. Free graph paper is available.\n2. The ball hits the ground at approx `t = 2.04\\ \"s\"` (we can see this from Example 1). The velocity when the ball hits the ground from the graph we just drew is about `-11\\ \"m/s\"`. The graph stops at this point.\n3. 12345-1-2-3-4-512345-1-2-3-4xyOpen image in a new pageGraph of `y=1+1/x`, a hyperbola. It's a discontinuous function.\n4. Function Grapher and Calculator. Description :: All Functions. Description. Function Grapher is a full featured Graphing Utility that supports graphing two functions together\n5. Since we've recognized it is a straight line, we only need to plot 2 points and join them. But we find 3 points, just to make sure we have the correct line.\n6. The features of a function graph can show us many aspects of the relationship represented by the function. Let's take a look at the more popular graphical features. Be sure to pay attention to the..\n7. Graph piecewise-defined functions. Sometimes, we come across a function that requires more Because this requires two different processes or pieces, the absolute value function is an example of..\n\nLearn more about frequency response, graphic System Identification Toolbox. I want to know if exist some MATLAB function that can give me a transfer function by analysis from points of a frequency.. (c) We know something strange will happen near `x = 0` (since the graph is not defined there). So we check what happens at some typical points between `x = -1` and `x = 1`: Safari users: Safari defaults to suppress popups. In theory, this should not prevent this feature working, but it does. If you do not see the dialog to get the link, adjust the browser preferences to allow popups.\n\nGraph can plot standard functions, parametric functions and polar functions. Given an x-coordinate Graph will calculate the function value and the first two derivatives for any given function require 'graph/function' Graph::Function.as_x11. If you don't want to output to x11, just set config.terminal to a different option. Two convenience methods exist for gif and canva (a) There are no restrictions on the values that x can take in this example, since it is a general question with no practical significance.", null, "### Graphical Function Explorer grapher (GFE) - Math Open Referenc\n\n• e if a graph shows a function, we see if there's any value of x for which a vertical line through that value will hit..\n• Different Functions and their graphs. Modulus Function. Last updated at July 12, 2018 by Teachoo\n• Here is a set of practice problems to accompany the Graphing Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University\n\n### Functions and Their Graphs\n\n1. Safari users: This will be ignored if the browser is set to block pop ups - the default in Safari. (This blocking should not strictly happen, since the pages come from the same domain).\n2. If a function (such as sin() ) is preceded by a number, GFE assumes you want to multiply them. For example 3cos(2.1) will be automatically treated as if you entered 3*cos(2.1): three times the cosine of 2.1. It will not work if the function is preceded by a variable name.\n3. For example, in the chart above, press 'reset'. Note that the first function is sin(a*x). This means that each time a point is plotted, it is the sine of the current value of x multiplied by the variable a. This variable is controlled by the a slider on the right, so as you move the slider you can see the effect of varying its value. *\n4. Electrical / Rotating Equipment & Mechanical Functions\n5. Plotting and graphing are methods of visualizing the behavior of mathematical functions. Use Wolfram|Alpha to generate plots of functions, equations and inequalities in one..\n6. Graphing Logarithmic Functions: Intro (page 1 of 3). By nature of the logarithm, most log graphs tend to have the same The graph of the square root starts at the point (0, 0) and then goes off to the right\n\n## An online tool to draw, display and investigate graphs of many different\n\nClick on \"full size\" under the chart window. A new window will open with a new instance of GFE in it that is as large as your monitor will allow. This can be useful in a classroom with a projector. Function Grapher is graph maker to create 2D, 2.5D, 3D and 4D function graphs, animations and table graphs. 2D functions can be in the form of explicit, parametric, piecewise, implicit and inequality (1) This graph is height against time. The ball went straight up, not forward. (Our graph may give the impression the ball moved in the x- direction as well as up, but this was not the case.) Online graph sketching app that can graph functions and numerically solve differential equations. Requires Javascript HTML 5 Rewrite the function as an equation. Graph the line using the slope and the y-intercept, or the points\n\nWhen you enter your equations, you can refer to up to four variables that are controlled by sliders. These are named a, b, c and d, and you can adjust the value of each variable by moving the slider up or down. You can also enter an exact value into the box at the top of the slider, followed by the GRAPH button or the Enter key. . The graphs of the original and inverse functions are symmetric about the line y=x. . Composite function Suppose that a function y=f(u). depends on an intermediate variable u Close Necessary Always Enabled Once you have the charts exactly as you want them, you can click on 'Make Link' below the applet. This will build a link to the chart that you can paste into a web page or Word document. When you later click on that link, the chart will come up exactly as you want it immediately. Also, by pasting the address back into the browser address bar and pressing Enter, you can then save the chart as a browser bookmark or favorite. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more\n\n### 4. The Graph of a Function\n\n• However, you are encouraged to learn the general shapes of certain common curves (like straight line, parabola, trigonometric and exponential curves, which you'll come across in later chapters). It's much easier than plotting points and more useful for later!\n• The most sophisticated and comprehensive graphing calculator online. Includes all the functions and options you might need. Easy to use and 100% Free\n• GraphSketch.com. Click here to download this graph. Beyond simple math and grouping (like (x+2)(x-4)), there are some functions you can use as well\n• Graphing Exponential Functions. What is an Exponential Function? To begin graphing exponential functions we will start with two examples. We will graph the two exponential functions by making a..\n• function-graph. 0.1.2 • Public • Published 6 years ago. \\$ cd node_modules/function-graph. \\$ npm test\n\n### To plot a function just type it into the function box.\n\nGraphing Linear Functions. Graph a linear function: a step by step tutorial with examples and detailed solutions. Free graph paper is available Graphing Standard Function & Transformations. A few standard graphs. Graphing Standard Function & Transformations. The rules below take these standard plots and shift them horizontally.. Graph Individual (x,y) Points. The most basic plotting skill it to be able to plot x,y points. This page will help you to do that\n\n## Graph functions and relations (Algebra 2, How to graph functions\n\nEnter a formula into one of the three input boxes ( f(x), g(x), or h(x) ), then press GRAPH or the keyboard Enter key. For example: Press Clear, then in the top function box (f(x)) enter \"cos(x)\" then press GRAPH or the Enter key on the keyboard. The function will be plotted in the window above. The syntax rules are the same as for the typed-in expressions for the Math/Scientific Calculator. To zoom, use the zoom slider. To the left zooms in, to the right zooms out. When you let go of the slider it goes back to the middle so you can zoom more. (To convince yourself of this, plot points where `x = 0.4`, `x = 0.3`, `x = 0.2`, `x = 0.1` and even `x = 0.01`.) Graph functions and relations. In order to graph a linear equation we work in 3 steps: First we solve the equation for y. Second we make a table for our x- and y-values For the first `0.918\\ \"s\"`, the ball is going up (positive velocity - that is, the blue line is above the t-axis), but slowing down.\n\n### Graphs of Functions\n\n1. Function graph with dplyr. Ask Question. Asked 2 years ago. This is my function, it's walk when I try my code without function but it's not ok with function\n2. If the water drains out in `10` seconds, it means `100π/3\\ \"units\"^3` will drain out each second (This is just `1/10` of the volume). Thus the amount of water left after t seconds is given by\n3. Computations for graphing functions. Wanted: graphing procedure. Two young mathematicians discuss how to sketch the graphs of functions\n4. Syntax for Writing Functions in R. func_name <- function (argument) { statement }. Here, we can see that the reserved word function is used to declare a function in R. The statements within the curly..\n5. A graph of a function is a visual representation of a function's behavior on an x-y plane. Graphs help us understand different aspects of the function, which would be difficult to understand by just..\n\n### Zooming and Re-centering\n\nFunctions and Their Graphs. What you should learn. GOAL 2 Graph and evaluate linear functions, as applied in Exs. 55 and 56. Why you should learn it In these functions, a graph is represented either by a list of rules of the form {v_i _ 1->v_j _ 1 Graph Drawing Algorithms. The Wolfram Language provides functions for the aesthetic drawing of graphs © 2020 GeoGebra. Function Graph. Parent topic: Functions. Graphing The Derivative of a Function This lesson covers graphing functions by plotting points as well as finding the domain and range of a function after it has been graphed. Graphs are important in giving a visual representation of the.. Graphs of Functions. The coordinate plane can be used for graphing functions. To graph a function in the xy -plane, we represent each input x and its corresponding output f ( x ) as a point ( x..\n\nThe plot( ) function opens a graph window and plots weight vs. miles per gallon. click to view. Saving Graphs. You can save the graph in a variety of formats from the menu File -> Save As In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x) = y. In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in the Euclidean plane and thus form a subset of this plane A man who is `2\\ \"m\"` tall throws a ball straight up and its height at time t (in s) is given by h = 2 + 9t − 4.9t2 m.\n\n## Algebra - Graphing Functions (Practice Problems\n\nProvided is a method for creating a cardiac function graph of an atrial fibrillation or sinus arrhythmia patient and an analysis evaluation method for a pathophysiologic mechanism from thoracic.. Note the curve continues beyond what is shown in the graph. This is just a general question and there are no practical limits for either the x- or y-values. Mobile Version | Imprint & Privacy Instructions ← →   | | | | | | | | | | | | | | | | | | | | | | | | |\n\n## Example 2: Graph the function using the given values of x\n\nTake your graph with you Share. Export as... Scalable Vector Graphics (.svg) Encapsulated PostScript (.eps) Portable Document Format (.pdf) Portable Function Polar Parametric Points. Add The graph of the function \\$f(x,y)=x^2+y^2\\$ is called an elliptic paraboloid. More information about applet. One can, of course, plot the graphs of all sorts of functions. Some of the most interesting..\n\n### Using \"a\" Values\n\nGraphs and coordinates. Functions and Limits. Coordinate Planes and Graphs. A rectangular coordinate system is a pair of perpendicular coordinate lines, called coordinate axes, which are placed.. The electric power P (in watts) delivered by a battery as a function of the resistance R (in ohms) is : A free graphing calculator - graph function, examine intersection points, find maximum and minimum and much more. Save Graph. Sorry, your browser does not support this application", null, "## Steps for Sketching the Graph of the Function on eMathHel\n\nIntuitively, we expect the water height to decrease slowly at first, then to drop more quickly near the end.(d) As the value of x gets closer to `0`, the points get closer to the y-axis, although they do not touch it. The y-axis is called an asymptote of the curve. GFE has the following built-in functions. The function names are not case sensitive. Example: sin(x) is the same as Sin(x). All trigonometric functions operate in radians. Plot the graphs of functions and their inverses by interchanging the roles of x and y. Find the relationship between the graph of a function and its inverse. Which functions inverses are also..\n\nGFE is a free online function graphing tool that allows you to plot up to three functions on the same set of axes. In the functions you can refer to up to four independent variables that are controlled by sliders. This allows you to easily see the effect of changes since the graphs change in real time as you drag the sliders. Is given the formula of function of two variables z = sin(x) + cos(y). Develop the application, which draws the graph of this function in a separate form. In additional, you need realize the rotation of.. A simple to use online function plotter with a lot of options for calculating and drawing graphs or charts of mathematical functions and their score tables is a quadratic function whose graph follows. and is shared by the graphs of all quadratic functions. Note that the graph is indeed a function as it passes the vertical line test", null, "## Graphs of Functions (examples, solutions, videos\n\nThe aspect ratio (ratio of width to height) of the graph window is exactly 4:3. The initial range of values on the x and y axes are in the same ratio, so a graph of y = x will be at 45°, and circles would be round, not squashed into ellipses. However, if you change the axis limits, this may no longer be true. Graphing Calculator which plots 2D graphs and 3D functions. Offers a handsome formula editor, exporting features and more. Multiple graphs per plot We take a cone with \"easy\" values, say `h = r = 10`. This has volume `1000π/3\\ \"units\"^3`.\n\nA graph of a function is a visual representation of a function's behavior on an x-y plane. Graphs help us understand different aspects of the function, which would be difficult to understand by just looking at the function itself. You can graph thousands of equations, and there are different formulas for each one. That said, there are always ways to graph a function if you forget the exact steps for the specific type of function. JSXGraph is a cross-browser JavaScript library for interactive geometry, function plotting, charting, and data visualization in the web browser GFE can be used to plot inequalities by changing the relational operator in the pull-down menu to the left of the function. There are five possible operators: .relops {margin-top:40px} .relops td {vertical-align:top} = Equals The default. The function will be plotted as a line as usual. Greater than As above, but the line is drawn dashed.\n\nHome | Sitemap | Author: Murray Bourne | About & Contact | Privacy & Cookies | IntMath feed | Page last modified: 18 March 2018 A graph is a pictorial representation of a set of objects where some pairs of objects are connected by Mathematical graphs can be represented in data structure. We can represent a graph using an.. * If you are curious: the sine curve shown is sometimes called a sine wave. The slider a is controlling the frequency of the wave. See Sine wave. Download Function graph stock vectors at the best vector graphic agency with millions of premium high quality, royalty-free stock vectors, illustrations and cliparts at reasonable prices There is another asymptote in this curve: `y = 1`, which is marked with a dashed line. Notice the curve does not pass through this value.\n\nImprove your math knowledge with free questions in Graph a quadratic function and thousands of other math skills At each end of the x and y axis is a box containing the end values. To change them, simply edit them in place and press GRAPH or the Enter key again. If you just click-and-release (without moving), then the spot you clicked on will be the new center\n\nfunctions derivatives polynomials graphing-functions intersection-theory. functions graphing-functions. asked Apr 30 at 11:58 Normally, when GFE starts up it displays a default chart. You can alter what is initially displayed by attaching parameters to the URL of the web page. You can override some or all the controls to display whatever initial chart you would like.\n\nThereafter, the ball is coming down towards the ground and getting faster (the portion where the blue line is below the t-axis). Note: The large version is a copy of the normal-size one. Any changes you make to the large one will not be copied back to the original when you close it.\n\nThe graph of a function f is the set of all ordered pairs ( x, f(x) ) where x is in the domain of f. A function is increasing on an open interval if the function rises (positive slope) on the interval as you.. GraphSketch.com. Click here to download this graph. Beyond simple math and grouping (like (x+2)(x-4)), there are some functions you can use as well\n\nCreates a kNN or saturated graph SpatialLinesDataFrame object. Distanced constrained spatial graph dist.graph <- knn.graph(ralu.site, row.names=ralu.site@data[,SiteName Q3. (Application) Water flows out of a tank in the shape of an inverted cone (i.e. the water flows through the pointy end of the cone and the widest part of the cone is at the top). The volume of the water is decreasing at a constant rate. Create graph online and use big amount of algorithms: find the shortest path, find adjacency matrix, find minimum spanning tree and others (a) Note: y is not defined for values of x less than `-1`. (Try some in your calculator, like `x = −4`.)\n\nHere graphs of numerous mathematical functions can be drawn, including their derivatives and integrals. Draw Function Graphs. Mathematics / Analysis - Plotter - Calculator 4.0 Then plot the graph: Applications of Quadratic Functions to Real-World Problems. Learning Objectives. Here you'll learn how to write and graph quadratic functions in intercept form In this mode, there is a gravitation pull that acts on the nodes and keeps them in the center of the drawing area. Also, the nodes exert a force on each other, making the whole graph look and act like.. Inverse Functions: Graphs. A feature of a pair of inverse function is that their ordered pairs are When graphed the functions will be a reflection of the other over the line y = x as shown below\n\nGraphing a recursive function (self.math). submitted 5 years ago by [deleted]. I have a recursive piecewise function that I'd like to graph, but I can't find any graphers that support recursion Algebra. When we look at a function such as. we call the variable that we are changing—in this case. --the independent variable. We assign the value of the function to a variable we call the dependent variable\n\n## Coordinate Planes and Graphs, Functions\n\nHow do you graph a function using the first and second derivatives to identify critical points and One more subtle note we can take from a function's graph is whether for increasing [math]x[/math]-values.. The graph of a function is the set of all points whose co-ordinates (x, y) satisfy the function `y = f Since there is no limit to the possible number of points for the graph of the function, we will follow.. To visualize the relationships within families of complex functions, parameterize them with the variables t, u, s, r, or n. The tool will render a range of complex functions for values of the parameter.. You can change the range of the slider by clicking on \"range\" below it. A dialog will appear that allows you to set the range of each slider separately. GFE will check to ensure that the lower value is at the bottom of the y axis or the left of the x-axis. Negative number are allowed.\n\n## Graphs of logarithmic functions (Algebra 2 level) Khan Academ\n\n(a) Negative values for R have no physical significance, hence P is not plotted for negative values of R.\n\n• Audi g tron.\n• Vapaaehtoistoiminta tutkimus.\n• Kuparisonni.\n• Jäsenmaksulaskuri talentia.\n• Elgiganten vitvaror.\n• Rtk palvelu oy.\n• Homeopaattinen apteekki tampere.\n• Spekti keikat tampere.\n• Mitä laittaa snäpissä.\n• Sound blaster drivers.\n• Yvonne catterfeld trennung.\n• Ligamentti selkäranka.\n• Kasvatuslaatikko.\n• Biltema träskruv utomhus.\n• Vr mobiililippu lähijuna.\n• Merkintänauhat.\n• Hallitilaa siilinjärvi.\n• 0 9 lautapeli hinta.\n• Astoria kuohuviini.\n• Konepellin kiveniskusuoja.\n• Edullisin et lehti.\n• Lobbaus esimerkki.\n• Kuinka usein vaippa vaihdetaan.\n• Contura i51 hinta.\n• Studio elite kuvaukset.\n• Koiran vienti ruotsiin.\n• Dr oberniedermayr.\n• Parts of manhattan.\n• Audi a5 sportback viat.\n• Helsinki melu valitus.\n• Liiga pistepörssi 2017 2018.\n• Toimiston nimikyltit.\n• 2 panzer division ss.\n• Red cups tokmanni.\n• Std error mean suomeksi.\n• Orvokki ruukussa.\n• Vauva kääntyy mahalleen nukkumaan.\n• Vantaan seurakuntayhtym.\n• Suomussalmen vuokratalot leena kela.\n• Suomen fanituote.\n• Myydään autotraileri." ]
[ null, "https://kannte-koffer-glaube.com/images/_txdQqau2LxZQV99dnDG8wHaFj.jpg", null, "https://kannte-koffer-glaube.com/images/tKOiaSvcHTEA6LvZXZnTEQHaFd.jpg", null, "https://kannte-koffer-glaube.com/images/X989TbqStk5ndqgci5d0fwHaEK.jpg", null, "https://kannte-koffer-glaube.com/images/gXEePUt1v_aPXR1v06biGAAAAA.jpg", null, "https://kannte-koffer-glaube.com/images/J1PGoNNhCyk.jpeg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.90076107,"math_prob":0.973376,"size":18077,"snap":"2021-21-2021-25","text_gpt3_token_len":4051,"char_repetition_ratio":0.16217563,"word_repetition_ratio":0.03942428,"special_character_ratio":0.22553521,"punctuation_ratio":0.11163435,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9940671,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-24T05:12:23Z\",\"WARC-Record-ID\":\"<urn:uuid:e659f353-794b-42d3-81b7-2a9aaa1887a0>\",\"Content-Length\":\"37643\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:06359a82-38cf-446d-899d-bc548a3defdc>\",\"WARC-Concurrent-To\":\"<urn:uuid:b5090b7c-059c-4bd6-a04a-ff7fb69c5967>\",\"WARC-IP-Address\":\"5.61.58.33\",\"WARC-Target-URI\":\"https://kannte-koffer-glaube.com/pin/465489311459067364w4-63z250100jk\",\"WARC-Payload-Digest\":\"sha1:XKOD2QKELOHG7YUCVOTSSVPVEL6ATH5J\",\"WARC-Block-Digest\":\"sha1:QND6J7TQH6IPCSLO7QOGSZ73NHZOCRBA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488551052.94_warc_CC-MAIN-20210624045834-20210624075834-00365.warc.gz\"}"}
http://www.cut-the-knot.org/triangle/RelationsInTriangle.shtml
[ "# Relations between various elements of a triangle\n\n### 2S = ab sin(C)\n\nThis follows from 2S = aha because ha = b sin(C).", null, "### S = rp\n\nTriangle ABC is a union of three triangles ABI, BCI, CAI, with bases AB = c, BC = a, and AC = b, respectively. The altitudes to those bases all have the length of r.", null, "### r² = p-1(p - a)(p - b)(p - c)\n\nThis follows from S² = p(p - a)(p - b)(p - c) and S = rp.", null, "### 1/r = 1/ha + 1/hb + 1/hc\n\n2S = aha = bhb = chc. Therefore, a = 2S/ha, etc. On the other hand, S = rp, so that p = S/r, or (a + b + c) = 2S/r. From here, 2S/ha + 2S/hb + 2S/hc = 2S/r.", null, "### sin²(A/2) = (p - b)(p - c) / bc, etc.\n\nFirst of all, sin(A) = 2·sin(A/2)cos(A/2) = 2·sin²(A/2)/tan(A/2). Therefore,\n\n (1) sin²(A/2) = sin(A)·tan(A/2) /2.\n\nWe know that\n\n (2) sin(A) = 2S / bc\n\nand\n\n (3) tan(A/2) = r/(p - a).\n\nCombining (1)-(3) gives\n\nsin²(A/2) = 2S/bc · r/(p-a) · 1/2.\n\nTaking into account that S² = p(p - a)(p - b)(p - c) and r² = p-1(p - a)(p - b)(p - c), the latter leads to\n\nsin²(A/2) = (p - b)(p - c) / bc.", null, "### cos²(A/2) = p(p - a) / bc, etc.\n\nIndeed, from sin²(A/2) = (p - b)(p - c) / bc,\n\n cos²(A/2) = 1 - sin²(A/2) = 1 - (p - b)(p - c) / bc = (p(b + c) - p²) / bc = p((2p - a) - p) / bc = p(p - a) / bc.", null, "### cos²[(C-B)/2] = [(b+c)²(p-b)(p-c)] / [a²bc]\n\nThis is the consequence of the previous two. Indeed, cos²[(C+B)/2]=sin²(A/2).\n\ncos²[(C-B)/2]-cos²[(C+B)/2]=sin(C)sin(B)=4[ΔABC]²/(a²bc),\n\ni.e.,\n\ncos²[(C-B)/2]=sin²(A/2)+4p(p-a)(p-b)(p-c)/(a²bc).\n\nIn other words,\n\ncos²[(C-B)/2]=(p-b)(p-c)/bc + 4p(p-a)(p-b)(p-c)/(a²bc)=(b+c)²(p-b)(p-c)/(a²bc).", null, "### AI² = (p - a)bc/p\n\nSquare the obvious\n\nAI = r/sin(A/2).\n\nSubstitute there sin²(A/2) = (p - b)(p - c) / bc and r² = p-1(p - a)(p - b)(p - c):\n\n AI² = p-1(p - a)(p - b)(p - c)bc/(p - b)(p - c) = (p - a)bc/p.", null, "### bc·tan(B/2)·tan(C/2)\n\nSquaring AI = r/sin(A/2) and substituting sin²(A/2) = (p - b)(p - c) / bc, we obtain\n\nAI² = r²·bc/(p - b)(p - c).\n\nBy the incenter construction, tan(B/2) = r/(p - b) and also tan(C/2) = r/(p - c). Substituting these into the above gives the required\n\nAI² = bc·tan(B/2)·tan(C/2).", null, "### 1/r = 1/ra + 1/rb + 1/rc\n\nS = ra(p - a) = rb(p - b) = rc(p - c).\n\nTherefore\n\n 1/ra+ 1/rb + 1/rc = (p - a)/S + (p - b)/S + (p - c)/S = (3p - a - b - c)/S = (3p - 2p)/S = p/S = 1/r,\n\nsince S = rp.", null, "### ra + rb + rc = r + 4R\n\nS = rp,\n\nand also\n\nS = ra(p - a) = rb(p - b) = rc(p - c).\n\nFrom these we have\n\n (4) ra + rb + rc - r = S(1/(p - a) + 1/(p - b) + 1/(p - c) - 1/p).\n\nSimple algebra yields\n\n1/(p - a) + 1/(p - b) = c / (p - a)(p - b) and\n1/(p - c) - 1/p = c / p(p - c).\n\nAnd a little more effort makes a great payoff:\n\nc / (p - a)(p - b) + c / p(p - c) = abc / p(p - a)(p - b)(p - c) = abc / S²,\n\nby Heron's formula. To sum up, from (4)\n\n (5) ra + rb + rc - r = S·abc/S² = abc / S.\n\nHowever, abc = 4RS, so that (5) implies exactly what's needed:\n\nra + rb + rc - r = abc / S = 4R.", null, "### rarbrc = pS\n\nSince\n\nS = ra(p - a) = rb(p - b) = rc(p - c),\n\nwe immediatly obtain\n\n rarbrc = S3 / (p - a)(p - b)(p - c) = S3 / [S² / p],\n\nby Heron's formula. But\n\nS3 / [S² / p] = Sp.", null, "### r+R=R(cos(A)+cos(B)+cos(C))\n\nWe know that\n\nr + rc + rb - ra = 4Rcos(A), r + rb + ra - rc = 4Rcos(C), r + ra + rc - rb = 4Rcos(B)\n\nSo that 3r+(ra + rb rc=4R(cos(A)+cos(B)+cos(C)). But\n\nra + rb + rc = r+4R\n\nwhich combine into 4r+4R=4R(cos(A)+cos(B)+cos(C)), exactly as required.", null, "### r rarbrc = S²\n\nThis is an immediate consequence of rarbrc = pS and rp = S.", null, "### la = 4p(p-a)bc/(b+c)²\n\nFollows from la = 2bc cos(A/2)/2 and cos²(A/2) = p(p - a) / bc.", null, "### la = 2bc cos(A/2)/(b+c)\n\nApplying the sine area formula to triangles ABLa and ACLa and then to the entire ΔABC we see that\n\nblasin(A/2)/2 + clasin(A/2)/2 = bc sin(A)/2\n\nThis simplifies to\n\nla = bc sin(A)/ (b + c)sin(A/2) = 2bc cos(A/2) / (b + c).", null, "### ma² = (b² + c²)/2 - a²/4\n\nLet's use Stewart's theorem\n\nAB²·DC + AC²·BD - AD²·BC = BC·DC·BD\n\nwith D being the midpoint M of BC. Then AB = c, DC = a/2, AC = b, BD = a/2, AD = ma, BC = a. We have,\n\nc²·a/2 + b²·a/2 - ma²·a = a·a/2·a/2.\n\n(The above identity could be as easily obtained with the help of the Theorem of Cosines or the Parallelogram Law; here is an example.)", null, "### abc = 4RS", null, "Let AD be a diameter of the circumcircle of ΔABC and AH its altitude. Right triangles AHC and ABD are similar, for ∠ADB = ∠ACH. Therefore,\n\nIn other words,\n\n2R·AH = AB·AC = bc.\n\nAnd finally\n\nabc = 2R·AH·a = 4RS.", null, "### bc = 2Rha\n\nThis follows from the previous derivation or by substituting S = aha/2 into the final formula.", null, "### p = 4Rcos(A/2)·cos(B/2)·cos(C/2)\n\nBy the Law of Sines\n\na = 2R·sinA, b = 2R·sinB, c = 2R·sinC,\n\nso that\n\n p = R·(sinA + sinB + sinC) = R·(sinA + sinB + sin(180° - A - B) = R·(sinA + sinB + sin(A + B) = R·(sinA + sinB + sinA·cosB + cosA·sinB) = R·(sinA·(1 + cosB) + sinB·(1 + cosA)) = R·(2sin(A/2)cos(A/2)·2cos²(B/2) + 2sin(B/2)cos(B/2)·2cos²(A/2)) = 4R·cos(A/2)cos(B/2)(sin(A/2)cos(B/2) + sin(B/2)cos(A/2)) = 4R·cos(A/2)cos(B/2)sin((A + B)/2) = 4R·cos(A/2)cos(B/2)sin(90° - C/2) = 4R·cos(A/2)cos(B/2)cos(C/2).", null, "### S = 2R²sin(A)·sin(B)·sin(C)\n\nBy the Law of Sines\n\na = 2R·sinA, b = 2R·sinB,\n\nFor the area of the triangle we have\n\n 2S = ab·sinC = 2RsinA·2RsinB·sinC = 4R²·sinA·sinB·sinC.", null, "### r = 4Rsin(A/2)·sin(B/2)·sin(C/2)\n\nThis follows directly from", null, "### cot(A/2) + cot(B/2) + cot(C/2) = cot(A/2)·cot(B/2)·cot(C/2)\n\nThis is equivalent to showing that, for A + B + C = 180°,\n\ncos(A/2)sin(B/2)sin(C/2) + sin(A/2)cos(B/2)sin(C/2) + sin(A/2)sin(B/2)cos(C/2)\n= cos(A/2)cos(B/2)cos(C/2).\n\nLet's transform the left-hand side:\n\ncos(A/2)sin(B/2)sin(C/2) + sin(A/2)cos(B/2)sin(C/2) + sin(A/2)sin(B/2)cos(C/2)\n= sin((A+B)/2)sin(C/2) + sin(A/2)sin(B/2)cos(C/2).\n\nBut since (A + B)/2 C = 90° - C/2, this equals\n\ncos(C/2)sin(C/2) + sin(A/2)sin(B/2)cos(C/2) = cos(C/2)[sin(C/2) + sin(A/2)sin(B/2)].\n\nReversing the steps:\n\n sin(C/2) + sin(A/2)sin(B/2) = cos((A+B)/2) + sin(A/2)sin(B/2) = cos(A/2)cos(B/2) - sin(A/2)sin(B/2) + sin(A/2)sin(B/2) = cos(A/2)cos(B/2).\n\nCombining everything together we get the desired identity.", null, "### rR = abc / 4p\n\nr² = p-1(p - a)(p - b)(p - c) is equivalent to\n\nr = D / p,\n\nwhere D = p(p - a)(p - b)(p - c). Also,\n\nR = abc / 4D.\n\nMultiplying the two gives\n\nrR = abc / 4p.\n\nNote that the identity at hand also follows by combining S = rp with abc = 4RS.", null, "### AH = 2R·|cos(A)|\n\nIn ΔABH, if A < 90°, ∠ABH = 90° - ∠A. (This is because ΔABHb is right.) Applying the law of sines to ΔABH gives,\n\n AH / sin(∠ABH) = AB / sin(180° - ∠C) = AB / sin(∠C) = 2R\n\nfrom the lawa of sines applied in ΔABC. Thus\n\n 2R = AH / sin(∠ABH) = AH / sin(90° - ∠A) = AH / cos(∠A),\n\nwhich proves the assertion AH = 2R·|cos(A)| when A < 90°.\n\nFor the case where ∠A is obtuse, H falls outside ΔABC, ∠ABH = ∠A - 90° so at the end we'll get AH = -2R·cos(A), proving AH = 2R·|cos(A)| in this case also.", null, "### p² = rarb + rbrc + rcra\n\nAs we know, ra=S/(p-a). It follows that\n\nrarb + rbrc + rcra=S²(1/[(p-b)(p-c)]+1/[(p-c)(p-a)]+1/[(p-a)(p-b)]=S²p/[(p-a)(p-b)(p-c)]=p²,", null, "" ]
[ null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/triangle/RS.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.5822303,"math_prob":0.999997,"size":6241,"snap":"2021-31-2021-39","text_gpt3_token_len":2930,"char_repetition_ratio":0.16674684,"word_repetition_ratio":0.114660114,"special_character_ratio":0.48517865,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000045,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-24T02:15:22Z\",\"WARC-Record-ID\":\"<urn:uuid:9c2d5efd-802c-46a4-88d1-e80af15158ad>\",\"Content-Length\":\"27675\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:caf3b9dc-8ca8-4440-8f1e-c8177161ea54>\",\"WARC-Concurrent-To\":\"<urn:uuid:13a237ff-0517-40de-818c-56b6f06ac361>\",\"WARC-IP-Address\":\"107.180.50.227\",\"WARC-Target-URI\":\"http://www.cut-the-knot.org/triangle/RelationsInTriangle.shtml\",\"WARC-Payload-Digest\":\"sha1:SKSLUWCKUVUDLCAZX3X53RCGAPNABKXZ\",\"WARC-Block-Digest\":\"sha1:G7AOJD4L545S476XK2DYWBLE6VYT7ENE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057496.18_warc_CC-MAIN-20210924020020-20210924050020-00575.warc.gz\"}"}
https://www.softmath.com/math-com-calculator/function-range/simplify-expressions-and-use.html
[ "English | Español\n\n# Try our Free Online Math Solver!", null, "Online Math Solver\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\nBing users found us yesterday by using these algebra terms:\n\nSearch Engine visitors found us yesterday by using these keywords :\n\n• how can adults remember algebra?\n• what does letters mean in math\n• graphing equations and inequalities iep goals\n• Alebra math tutor in miami florida\n• Basic Algebra Study Guide to tutor\n• free online 2012 prentice hall algebra 1 textbook\n• free helpful step by step math websites\n• mathematic equations squared\n• pre-algebra calculator\n• turning point of a quadratic function\n• how to work square root problems\n• Algebra En Español\n• how to figure fractions\n• simple linear equation in architecture\n• simplification mathematics\n• zeros of simultaneous polynomials\n• homework-tangents\n• Algebra problem solving 1\n• practice college algebra online\n• do my algebra 2 problem\n• graphs of the 6 trig functions\n• basic mathematics 9th edition marvin L bittinger\n• 10-4 skills practice radical equations\n• algebraic fractions calculator\n• help with binomials factoring\n• college algebra practice math word problems\n• motion problems\n• Cube Root Chart\n• solving matrices having fractions\n• algebra equations crossword puzzles\n• prentice hall gold algebra 1 6-1 practice answer key\n• beginners algerbra final\n• math solver with step by step\n• Change to standard form\n• algebra 1 eoc prep answers\n• ALGEBRA 2 HELP - solving rational equalities and inequalities\n• whats teveasest way to learn pre algabra cant get it at all\n• square root problem solving\n• online copy of oleans-hanna algebra prognosis test\n• buckle down louisiana algebra 1 eoc answer key\n• examples of rings and fields in math\n• multi step inequalities solver\n• perform the operations 4+6x8 MAT104 Algebra with applications\n• algebra 2 prentice hall answers\n• summation problems in algebra\n• factor problems\n• how to teach dialations\n• gauss jordan solutions\n• what is the best calculator for algebra\n• set theory john von neumann\n• college algebra cheat sheet\n• parallel line calculator\n• Contemporary College Mathematics\n• algebra fast\n• algebra problem to simplify\n• algebra review worksheets\n• word problem calculator\n• coordinate grid\n• alegra solve for two unknowns\n• writing simple expression word problems\n• list used algebra formula or equation that we used every days life\n• if then math problems\n• MYTUTURSKILL\n• enter word problems in algebra\n• six trigonometric functions\n• word problem solver\n• steps to divide two complex numbers by their graphs\n• find the domain of rational expressions\n• free online algebra 1 textbook\n• basic algebra study guide\n• year 6 algebra\n• Free Algebrator Software\n• college algebra calculator\n• Electrical trignomic translations\n• EOC Algebra 2 Review\n• solving rational expressions\n• cooperative learning algebra equations\n• pictures of cartisian coordinate systems\n• test point method\n• Algebra Websites for College Students\n• alegbraic proof\n• answers 1302 college algebra UTA\n• multiple choice algebra test\n• inequalities calculator\n• Algebra 2 Multiple Choice Pre-test\n• Free Algebra Learning Software\n• algebraic thinking games\n• math problems on rings and fields\n• algebra 1 eoct test prep\n• absolute value activities\n• rewrite functions in factored form\n• gcd(315,825)\n• orleans hanna test\n• algebra with pizzazz d-37 code answer\n• easy algebraic equations\n• elimination method in algebra\n• maths refresher online for adults\n• solving my own fractions\n• algebra check up 2\n• online maths helper for finding problems with root\n• bittinger introductory algrebra help\n• Florida Algebra 2 calculator\n• Algebra 1 Multiple Choice Pre-test\n• differential equation d operator long division steps\n• simplify negative numbers\n• fractions with exponents calculator\n• page 525 answers impact math textbook algebra 1\n• algebra 1 an integrated approach homework anwsers\n• blank coordinate plane\n• prealgebra formulas\n• reducing fractions to lowest term\n• prentice hall algebra 1 answer key\n• Algebra 2 log multiple choice test\n• college algebra for dummies\n• what comes after college algebra\n• answer key to algebra 1 concepts and skills\n• an equation which contains a variable\n• geometry easier than algebra\n• hanna orleans test\n• equastion of a parallel line calculator\n• simplification calculator\n• transforming formulas help\n• graphing logarithms explanation\n• ALGEBRA WITH PIZZAZZ!\n• burnside math\n• step in algebra\n• algebra with pizzazz\n• how to name variables in algebraic motion problems\n• teach myself algebra free\n• Advanced Algebra Problems with Solutions\n• graphing systems of equations\n• calculator and showing the work\n• Free 9th Grade Geometry Help\n• how do you find the circumference of a circle 5th grade math\n• transforming equations\n• rudin chapter 2 solutions\n• algebra structure and method book 1 answers\n• algebra 1 concepts and skills answers book\n• what does it mean to solve an equation\n• calculator calculations\n• matrix multiplying\n• square root of 16200\n• algebraic properties\n• graphin inequalities\n• solving equations with the variable on each side\n• to algebra 2\n• algebra beginning\n• algebra lineal 1\n• cybered inc\n• tutorial algebra\n• computer algebra systems\n• on line caculator\n• inequalities and absolute values\n• answers to glencoe algebra 1\n• adding rational expressions with different denominators\n• basic mathematical equations\n• reducing fractions worksheets\n• writing algebraic\n• domain range of algebraic functions\n• algebra 2 concepts\n• the parabolic formula\n• online math help\n• math worksheets simplifying fractions\n• inequality math problems\n• rational numbers and\n• inequalities with absolute value\n• algebra 1 chapter 10\n• polynomials and their factors\n• prentice hall mathematics pre algebra\n• how to write linear equations\n• equation of a parabola in standard form\n• formula area ellipse\n• matric algebra\n• high school algebra review\n• system of equations matrices\n• solutions for linear equations\n• solving equations x\n• multiplying and dividing fraction\n• how do you solve simultaneous equations\n• coefficients polynomial\n• linear matrices\n• inequalities on graphs\n• factor polynomial completely\n• algebra website\n• Total - automatic matching\n• math book cheats\n• finding the value of x\n• solve linear equations\n• factor in mathematics\n• teaching square roots\n• fraction algebra calculator\n• helpwithmath\n• how to solve rational inequalities\n• algebra of sets\n• 2001 algebra 1\n• maths word problems\n• algebraic grid\n• x 2 y 2 1\n• hard math problem\n• computer algebra software\n• the system of equations\n• how to do inequality\n• saxon algebra 1 2 answers\n• lcm fernando\n• how to solve y\n• equation of graph\n• need help in math\n• worksheets algebra\n• college math tutorial\n• algebra ii software\n• examples of algebra\n• simplifying multiplication rational expressions\n• online calcutlator\n• lessons algebra\n• pre algebra worksheets\n• integrated algebra 1\n• college algebra practice tests\n• how do you subtract fractions\n• yx\n• algebrahelp.com/worksheets\n• graphing an inequality\n• algebra age problems\n• projects algebra\n• algebra 1 concepts and skills larson boswell kanold stiff\n• solve algebraic expressions\n• easy math problems\n• free printable worksheet sales tax\n• hard \"algebra problems\" std 9\n• \"solutions of polynomial equations by factoring\"\n• pre algebra terms and definitions\n• \"greatest common factor poster\"\n• math formulas for gre\n• graphing quadratic inequalities free calculator\n• LCM finder\n• examples of mathematics poems\n• linear combination method for linear equations\n• factoring trinomials worksheet with answer key\n• free printables worksheets about compare and order 3 digit numberwith answer key\n• solution of quadratic equation by extracting square roots\n• need a exaple of a non binomal perfect cube\n• number line with fractions\n• Multiply the two binomials below to produce a difference of squares. Enter exponents using the caret (^). For example, you would enter x2 as x^2.\n• 105mod25\n• examples of math poems\n• kumon answer book level d\n• solve algebra fraction problems free\n• Definition of pre-algebra\n• lial hornsby mcginnis begining algebra state exam\n• adding and subtracting real numbers worksheet\n• free examples of polynomials for 8th grade\n• sample of investigatory project in physics of\n• subtracting integers free worksheets\n• matrix and determinants 11th syallabus matric\n• first order differential equation calculator\n• how do you calculate the test standardized test statistic on a ti-84\n• order numbers worksheet decimal negative percentage fraction square root\n• rules in multiplyng and dividing rational expressions\n• negative numbers line\n• example of math investigatory project\n• how to solve inequality graph with solution set and set notation?\n• quadratic equations explained for dummies\n• algebramath.com\n• addition and subtraction of fractions worksheet\n• solve linear system equation jacobi\n• scott foresman math ninth grade\n• how to do percentages for dummimes\n• balancing chemical equations worksheet with answers\n• derivatives worksheet pdf\n• calculate line geometry math\n• worksheet-estimating mass\n• www.algebrator\n• online graphing calculator equivalent of ti 84 plus\n• number line\n• Science worKheets for SLOW LEARNERS\n• tricks of mathematics\n• Solve the system of equations. Enter your answer as an ordered pair.\n• free rational equations worksheets\n• quadratic equation by extracting the square roots\n• solving polynomial equations\n• distributive property\n• problem involving system of linear equation using by the algebraic expression with what is asked? what are given ? operation to be used? solution?\n• middle school exponent worksheets\n• Selection and Rationale for Pricing Methodppt\n• +EXAMPLES OF PROBLEMS IN MATH INVISTIGATORY\n• how do you change a decimal to a square root?\n• chemical equation predictor tools for java\n• subtraction of integers worksheet\n• college algebra software\n• Solve my Math 115 questions in personal financial management\n• boolean graph on excel\n• adding and subtracting equations worksheet\n• college algebra entrance test practice\n• negative exponent\n• the figure shows the graph of y=Ax^2+Bx+C.it passes through the points(-3, 8),(0,\n• sample commutative property of multiplication\n• investigatory project in physics\n• activity float calculation *.ppt\n• simplify using the mixed sign rule\n• 9th grade printable math worksheets\n• quadratic formula how to solve word problems\n• precalculus online calculator rational expressions\n• solvina a system of equation on my ti-83\n• how to solve complex polynomial equations using matlab\n• algebra 1 multiple choice test\n• short cut methods for solving arithematic problems\n• solve w=2xy+2xz+2yz for z\n• In many instances it is possible to use both fractional and decimal forms to multiply and divide. what are the advantages and disadvantages of using each form?\n• are there programs to do partial fractions on the ti -83\n• F1+mathematics simple equation exercise\n• MATHMATICAL COMPARISONS USING PERCENTAGES\n• worksheet for LCM and GCF\n• radical expressions calculator with variables\n• worksheet problem solving GCF LCM\n• algebra calculator show steps\n• examples of math trivia\n• math geometry trivia with answers\n• Algebrator\n• ALGEBRA 10TH CLASS\n• practice workbook .pdf\n• application of statistics sum of 8standerd textbook\n• how do you find out an equasion on a calulater\n• 26\n• addition and subtraction of algebraic fractions\n• lineear equation or not/explination\n• maths puzzles for 9th standard\n• online algebrator\n• bionomial therom pdf\n• gr 8 solutions\n• derivative calculator real 45\n• suare roots + ti-30xa calculator\n• am i good at math quiz\n• ALGEBRATOR\n• subtracting real numbers worksheets\n• rules for square roots\n• nice word problems on exponentiel functions\n• how to square root a fraction\n• example of crossword puzzle about rational expressions\n• \" distributive property word problems\"\n• +history of trivia of algebra\n• 18/4 simplify mathematics\n• combination and permunation examples 3rd grade\n• +tricky questions that involves using special products in math\n• algebra program\n• factor cubed polynomial\n• My Algebra\n• slope intercept form ti 83 program\n• free online solution for absolute value inequality\n• examples of problem solving in fraction\n• binary code conversion java\n• 8th grade free math worksheets\n• algebra problems\n• pacemaker pre-algebra\n• latest math trivia algebra\n• best cheat programs for ti-84\n• substitution method calculator\n• word problems of scientific notation\n• Free sequence Solver\n• 6th grade order of operations worksheets\n• basic on operations on rational numbers\n• how to easily slove applitude\n• graphing calculator ti-83 online * matrice\n• softmath com demos Entering_square_roots htm\n• simultaneous equations worksheets\n• free printable math quiz for 8th grade\n• \"literal equations worksheet\"\n• princeton hall math textbook\n• area ks3\n• types of college algebra\n• solve by extracting square roots\n• chapter 4 elementary probability theory test answer sheet\n• clothes line\n• math problems for 9th graders online\n• view #51 chapter 8.2 intermediate algebra fifth edition elayn martin -gay\n• logarithms for idiots\n• how to simplify 9x+9-1\n• installing algebrator work on ti 84\n• algebra simplifying division expressions\n• mathematics investigatory projects\n• gcf calculator with variables\n• history of the trivia of the algebra\n• negative Number line\n• square root equation calculator\n• free teach yourself algebra 9th grade print-outs\n• 9th grade math homework help with mean absolute deviation and the sum absolute deviation\n• examples of quadratic equation words problem\n• +Examples of Datailed lesson plan\n• sample of math trivia\n• online real number calculator\n• free integrated algebra worksheets\n• exponential form calculator\n• ti 83 plus solve complex numbers\n• synthetic division program ti 84\n• boolean algebra sample problem\n• chapter 1 in the algebra 2 book\n• 50\n• geometry prayers\n• softmath\n• \"solve eight off\"\n• trig identities worksheets\n• printable math worksheets 9th grade\n• how do you add subtract multiply divide integers?\n• examples of math trivia with answers\n• math sloverand steps for polynomials\n• ratio formula\n• matlab nodekstop\n• word problem with solutionof rational numbers\n• printable 8Th Grade Math Pretest texas\n• printable math gre worksheets\n• how to solve color cube problems analytical questions\n• Less common denominator of 5,12,15\n• (pdf)ppt sample example with solution on linear programing\n• GED Math Practice Sheets\n• module in intermediate algebra\n• finite mathematics\n• cartesian plane\n• free software that gives solution to mathematics problems\n• wrksheets adding and subtrating signed numbers\n• algebra substitution method calculator\n• free equation solver\n• example of real life problem of factor and factoring and pictures\n• algebrator\n• greatest common factor of monomials calculator\n• 8th grade math iwoa practice\n• how do i find out thr cube root of a number on the texas instruemnt ti-83 plus calculator\n• free printable math worksheets for 8th grade\n• prentice hall geometry workbook answers\n• completing the square method\n• successive way of finding GCF\n• free 6th grade entrance test\n• lesson plan on exponents in integers\n• linear inequalities in one unknown greater than or equa\n• how to use TI-84 plus for alegbra\n• how to combine like terms 4x-7x in algebra\n• \"absolute value function\" graph \"fun lesson\"\n• how are arithmetic operations similar oe different from doing opeations with rational expressions in algebra\n• 2nd order\n• slope percentage AND DEGREES TABLE\n• first order linear differential equation calculator\n• solve for x worksheets\n• Writing Linear Equations Worksheets\n• princeton hall mathmetics teacher book grade 5\n• (3A + 4B)(3A - 4B)\n• give a real life example of a situation in which there are two equations that are dependent\n• simplifying sums and differences of radicals calculator\n• free math 050\n• +how do you convert ineqaulities to solutions\n• cheat your way through pre algebra\n• special product word problems\n• lattice fractions\n• math trivia with answers mathematics\n• explaination of mathermatical nets\n• Divide Decimals Calculator\n• expressions using word phrases and variables/operations\n• Online Division Calculator Math\n• \"Why is it necessary to study and understand rational expressions?\"\n• gre practice test papers\n• worksheets for college algebra clep test\n• college algebrra by william hart 4th edition 1964 pdf free\n• teaching equivalent fractions\n• math poem algebra mathematics\n• solving radical equations online calculator\n• example of detailed lesson plan\n• how to compute laplace transforms using a ti 84\n• algbra1 structures and method book 1\n• introduction for math investigatory project'\n• iq test online free\n• maths test papers for lower secondary\n• Combining like Terms Worksheet Free prealgebra\n• how to multiply and divide fraction\n• online t-83 calculator\n• lowell lynde intermediate algebra, 3rd education\n• graph of a polynomial function\n• square root and exponent\n• solve logarithmic equations ti83\n• software to solve algebra problems\n• use ti 84 calculator online free\n• simplify the expression solvers\n• algebrator 4.1\n• what are the properties of real numbers,they description and examples\n• help with math.com/ printibles\n• algebra clock problems\n• practice test for multiplying mixed numbers\n• algerator\n• Example problem in radical expression\n• Algebrator software\n• simplify using only positive exponents\n• Laws of Exponents in calculus\n• function and relation graph\n• Linear Meters to Square Meters\n• deviding decimals calculator online\n• 7th grade math problems printable\n• Pearson college algebra worksheets\n• how to solving quadratic functions that have fractions\n• clothes line exponential\n• least to greatest decimals calculator\n• reducing monomial fractions\n• factoring polynomials with two variables\n• using algebra to solving questions primary school\n• solve the inequality, calculators\n• survey regarding the methods of quadratic \"equation do\" children like solving quadratic equation\n• finite math\n• +solving system of equations by subtitution with fractions\n• Explain, in your own words, how to use the zero-factor property when solving a quadratic equation.\n• transforming integers into radical forms\n• precalculus solving inequalities equations 3/x-8 >7/6x-4\n• square roots of exponents\n• circle graphs worksheets\n• distributive property worksheets 5th grade\n• examples of math tricks problems\n• substitution method calculator with fractions\n• kumon maths online\n• solving system of linear equations in two variables by elimination including fraction\n• +using numbers on a clock to solve equations\n• multipliying dividing integers worksheet\n• calculator tricks(problem solving)\n• +monimal calculator\n• ratios worksheets for 9th grade\n• holt geometry practice workbook answer key\n• What is the differance between TI-30XA and TI-30XS calulators\n• deitel, java exercise, a positive integer is prime if its divisible by only 1 and itself, for example, 2, 3, 5, and 7 are prime, but 4, 6, 8 and 9 are not. the number is 1, by definition is not prime. . Write a method thatdetermines whether a number is prime.,\n• domain and range worksheets algebra1 oakdale\n• how to find the variable in a fraction\n• electric phase sequence in electric arc furnace\n• algebrator trial\n• Free Printable Worksheets 8Th Grade\n• freshman algebra worksheets\n• \"put into radical form\" x^2\n• Algebrator Software Reviews\n• binary algebra\n• teach yourself algebra print-outs\n• 6\n• solucionario de algebra abstracta de fraleigh\n• 32\n• Explain why this statement is true: when simplifying rational expressions, we must cancel factors only, and not terms. Give an example using just numbers\n• free printable math test for 8th grade\n• symbols algebra\n• order of operations power dissipated by an 8.2k resistor if a current of 0.005 amps is passing through resistor\n• +Evaluating Algebraic Expressions(GED)\n• lesson plaN FOR Least Common Multiple5th grade\n• multplying rational expressions calculator\n• solving difference equations\n• use rational exponents to write √2:(8)*√4:(3) as a single radical expression\n• elementary algebra basic operations with polynomials\n• intermediate algebra for dummies\n• pre algebra math software\n• dividing numbers using sticks( mathinvestigatory project)\n• For all x > 0 and y > 0, the radical expression 3 x x − y is equivalent to:\n• class 7 math questions,pdf\n• inverse z transform ti 89\n• elementary algebra tobey\n• adding,subtracting, multiplying and dividing whole numbers test\n• icai cpt quantitative apptitute solution\n• mcdougal littell algebra 2 practice workbook\n• mcqs/ans simplification7\n• converting vertex form to genaral form\n• 60\n• number games for simplifying rational expressions\n• free online inequality calculator\n• texas Middle School Science Syllabus\n• solving for exponents with square roots\n• grade 8 math lesson online\n• merrill algebra two with trigonometry\n• 8th grade math i can printable out\n• converting mixed number fraction to decimal calculator\n• solve compound angles\n• +free adding and subtracting integers\n• algebra vocabulary, *.ppt\n• free printable 8th grade quiz\n• scavenger hunt unit 1 rational numbers pre-algebra worksheet\n• solving differential equations using matrix and laplace pdf\n• Algebra Step by Step Solver\n• degree to percent calculator\n• Polygon Area using matrices\n• test in mathematics regarding integers\n• doing for english work sheet for grade 4\n• square root property calculator\n• Algebrator\n• definition of prealgebra\n• CARTESIAN PLANE\n• Product Rule for Radical Expressions exercises\n• 1\n• best software to learn finite math\n• what is the orleans hanna diagnostic algebra test\n• +where can you learn maths for 1st year?\n• denominators calculator\n• teacher edition for algebra 1 glencoe 1998\n• squareroot of decimals\n• harold r jacobs algebra\n• algebra software\n• matametics for children age 7\n• Hands on Algebra Worksheets\n• larson precalculus with limits 3rd edition pdf\n• quadratic equation by extracting square roots\n• definiton of pre-algebra\n• simplifying rational expressions with square roots\n• scale 25.4 in decimals\n• matrics calculatir graphical\n• software college math tutor\n• Quadratic equation extracting square roots\n• long division powerpoint presentation free\n• how are math concepts useful in daily life\n• notes on algebra 1 9th grade\n• solving equations by using multiplying and dividing equations power point lessons\n• algebrator demos Graphing Equations\n• idiots guide to sientific calculator\n• what types of math methods like partial sum are there\n• Compound Inequality\n• math free radicals problems online with steps\n• expression divide calculator\n• free answer to my algebra problem\n• +100% free algebra problem solver\n• sample questions from the hanna orleans algebra test\n• algebrator\n• Graphing solutions of equations subtraction 7th grade\n• College Algebra Formula Sheet\n• algebratore for students\n• sabine's equation\n• free online algebrator\n• multiplying and dividing multiple signed numbers worksheets\n• free 8th grade mixed numbers worksheets\n• online science tests for 9th grade\n• understanding summation notation\n• algberator\n• prayer in math about linear equation\n• -6x + 6y = -18\n• add and subtract positive and negative numbers free workshee\n• multiply with exponets calculator\n• Two step equations and inequalities worksheet\n• Trigonomentry farmula\n• Free Algebra Elimination Calculator\n• Describe two real-life examples where rational expressions are used on the job. For ideas, look in the textbook or online and look around you at work and see what strikes you as being similar in your own life. What examples do you see? Describe two of them in detail. Make sure to explain what, how, and why the specific rational expression was used.\n• precalculus problem solver\n• primary six mathmatic\n• Show how to calculate the greatest common divisor by the step approach 44/52\n• isolating complex trigonometry variables\n• Elementary Algebra Worksheets\n• easy investigatory projects for first year high school\n• vertex form linear function\n• cheat sheet on solving system of linear equations\n• graph an inqualities poems\n• free example on how to solve for x and y in aljbra\n• online graphing calculator with table\n• freealgerbrahelp com\n• solve the equation (4m-2)squared-2(4m-2=15\n• +exsamples of subsitution when graphing\n• ppt on expansion and factorisation of a polynomial\n• what is the best way to figure out natural logaritms word problems related to time and rate\n• +How to graph a solution of an equation 7th grade\n• How is doing operations—adding, subtracting, multiplying, and dividing—with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type?\n• algebra pretest printable\n• math data printout\n• sample \"generalized probabilistic descent\"\n• strategies for problem solving workbook third edition answers\n• greatest common factor calculator with variables\n• softmath.com\n• free printable 9th grade math worksheets\n• elementary permutation\n• good programs to install in ti 84plus for college algebra\n• ppt on linear inequalities for class XI\n• properties of exponents calculator\n• writing equations of lines worksheets\n• difficult mathematical questions\n• Examples of Linear Relationship free worksheets\n• special product factoring formulas\n• standardized test statistic calculator\n• homework and practice adding integers page 34 lesson 2B\n• content\n• solve rational exponent calculator\n• pre-algebra with pizzazz\n• investigatory project in high school english\n• samples of trivia about math\n• example amazing and easy to make investigatory projects on\n• hyperbola examples\n• balance an algebric chemical equation calculator\n• 2variabel 3equation\n• green theorem calculator\n• free college entrance exams printable\n• solve linear function 8th garde style\n• solved exercises in implicit differentiation +pdf\n• polynomials sample problem\n• binomial theorem with exponents calculator\n• Free 9Th Grade Geometry Worksheets\n• sample word problems in converting fractions\n• equation solver software\n• Compound Inequalities Calculator\n• how to cheat on aleks mathematics 7th grade mathematics\n• solving permutation for kids\n• How do I rearrange a polynomial to a quadratic\n• 9th grade algebra lessons free\n• free 9th grade math worksheets\n• math investigatory topic\n• literal equations hart mcdougal\n• PRE-ALGEBRA COMBINATIONS\n• 4x + 6y = 62\n• kuta software practice with exponents\n• Learn Algebra online fast\n• MIDDLE SCHOOL MATH WITH PIZZAZZ BOOK C ANSWER How can you tell if a shark likes you? TOPIC 1-f: Greatest Common Factor (GCF)\n• equation with 3 unknowns\n• distance formula sums for 10th\n• Algebrator Word Problem Solver\n• solving quadratic equations by extracting square roots\n• hundredths grid\n• +merrill algebra two with trigonometry online\n• examples of math poem\n• rational expressions applications\n• thinking mathemathically answers 3rd edition\n• \"prime factoring worksheets\"\n• worksheet on exponential expanded notation\n• math quiz\n• how to converting mixed numbers to decimals\n• Special products and factors sample word problems\n• Simplifying by Factoring\n• mathemathical investigatory projects\n• +Compound Inequalities Solver\n• How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life?\n• examples of mathematics trivia\n• how to calculate radical formula\n• online differential equation calculator\n• java code for polynomial curve fit\n• prentice hall Student EXPRESS with Interactive Textbook CD-ROM world studies grade 7\n• understanding radical expressions equivalent to\n• calculatorsolving 4 equations guess seidel\n• algebraic fractions with variables and power\n• trivia of the algebra\n• investigatory project\n• alberta \"grade 9 math review\"\n• ode45 second derivative\n• simple conversion table\n• need help with this algebra 1 problem -16/25 divied (-4/5)\n• step by step integration\n• math investigatory project\n• least common denominator calculator\n• holt mathmatic worksheet and answer sheet . com\n• partial fraction decomposition calculator\n• common monomial factors worksheets\n• Algaebraic Equasions\n• investigatory project in math 4\n• how do you solve this equation 7(p+1)=9p\n• algebrator for physics\n• math worksheets for 3rd grade\n• Holt Pre-Algebra Worksheets\n• +work +sheet for equalities and inequalities\n• free compound inequality solver\n• prentice hall algebra 2 worksheets\n• simple algebra worksheets\n• factoring by grouping calculator\n• solve .07 to the 15th degree\n• definition of survey in math\n• best reactions about slopes in mathematics\n• algebra calculator\n• Boolean algebra question\n• Exact Cubic Equation Solver\n• permutations and combinations mark sheets\n• simplifying radical expression by rationalizing the denominator solver\n• how to solve elementary numerical operations\n• math calculator simp funcion\n• worksheets on combined operations of fractions\n• multipcation and division of rational exspressions\n• how are arithmetic operations similar or different than doing opeations with fractionssrational expressions lgebra\n• prentice hall algebra 2 answer key free\n• sample test in factoring\n• lcm and gcf worksheets\n• free kumon worksheets mathematics\n• easy questions for addition equations\n• simplify logarithms\n• plotting cooridates worksheet\n• accounting equations for find percentage\n• solve radical equations online calculator\n• graphing points to make a picture\n• easy quiz questions with answers in differential equation\n• What is a sign graph and when is it used? Give an example. Explain, in your own words, the test-point method and how it is used to solve a quadratic inequality. Be sure to show the connection between the test-point method and a sign graph.\n• www.trignometry .com for 10th classes\n• multiply and divide radical expressions calculator quick math\n• how to turn meters into square meters\n• ACTIVITIES FOR STD5 ICSE BOARD TOPIC-LCM AND HCF\n• middle school math with pizzazz book d answer key\n• algebra solver software\n• latest math trivia\n• real life algebra word problems\n• +rewriting a common formula A = 1/2bh\n• algebra checker\n• show interpolation +exampes with images\n• solve by elimination calculator\n• teach me arithmatic\n• Algebrator hyperbola\n• free printable 8th grade math worksheets\n• algebra substitution method with fractions\n• Online TI Calculator Emulator\n• Algebra trigonometry syllabus\n• useable ti-83 calculator online\n• hot to simplify 2x^2-36\n• pre-albebra step by step\n• Free Printable LCM Worksheets\n• example of investigatory project in mathematics\n• From your reading in section 10.6, describe a step by step process to solve radical equations. List each step provide an explanation of how to complete each step with an example\n• perpendicular symbol in excel\n• how to convert mixed numbers to decimals\n• free 10th grade printable worksheets\n• free worksheets working with positive and negative numbers\n• how to solve three exponential simultaneous equations\n• printable graphing linear equations worksheets\n• simplfying a radical expression calculator\n• math gcse questions\n• Algebra Elimination Calculator\n• algebra with pizzazz worksheets\n• trivia of algebra\n• lowest common denominator worksheets\n• successive way of find greatest common factor\n• Math Variable Calculator\n• product rule for square roots\n• sabine's equation formula and samples\n• 4Th Grade Long Division Worksheet\n• reduce rational expression to lowest terms calculator\n• evaluate exponential expressions\n• divide out common factors and simplify\n• free algebra books pdf\n• PRINTABLE PRACTICE APTITUDE TEST\n• fastest way to factor expression 64x3 + 27y3\n• free trinomial calculator\n• concering multiplying and dividing interers,which of the following statements is true?\n• \"example of mathematics prayers ( mathematical terms)\"\n• math projects\n• tricky questions that involves use special products in math\n• find slope for middle school students\n• outline of \"algebra 2 structure and method\"\n• adding subtracting multiplying and dividing fractions\n• mathematical equations used in refineries\n• which of the following is a quadratic function\n• mathletics instant workbooks\n• find common denominator algebra\n• simple math poem\n• elementary algebra practice problems\n• Free Math Trivia\n• At many colleges, the number of full-time-equivalent students, f, is given by f = n/15 where n is the total number of credits for which students enroll in a given semester. Determine the number of full-time-equivalent students on a campus in which students registered for a total of 25,350 credits.\n• ti84maths program asolver\n• plotting points to make picture\n• high school math Simplifier that SHOWS WORK\n• \"arithmetic practice worksheets\"\n• math mcqs problem solving with solution\n• solving equations when multiplying by a negative number\n• simplyfiy (2w to the 2nd power) to the third power\n• problem involving system of linear equation using by the substitution with agons\n• lowell lynde intermediate algebra textbook 3rd edition\n• permutations and combinations elementarypowerpoint\n• 26.3% written as a decimal\n• college algebra special product formula\n• simplifying expressions calculator for square root\n• free boolean algebra simplifier\n• algebra worksheet packets\n• real life picture of a hyperbila\n• solve each equation or formula for the specified variable\n• ti-84 plus complex root solver\n• kumon solution book level I\n• free 8th grade math worksheets\n• mathematics investigatory project for grade 4\n• expanded notation with negitive\n• MULTIPLYCATION AND DIVISION OF FRACTION AND THEIR RULES\n• elementary algebra for dummies\n• website that solves math problems\n• combination and permutation for kids\n• sample lesson plan ratio intermediate algebra\n• concept of monimial,binomial and trinomial and adition and subtraction\n• singapore standard math for secondary worksheets\n• highest common factor calculator\n• factoring trinomials\n• how to do radicals in geometry\n• similar fraction worksheets\n• solving quadratic equation by extracting square root\n• mathematical trivias\n• logarithms for dummies\n• algebra worksheets for 7th graders\n• non linear differential equations\n• 11th grade printable math worksheets\n• flow square root formula\n• worksheets on square numbers\n• iowa algebra aptitude test\n• algebrator demos\n• simplifying complex fractions worksheet\n• Variable Expression Calculator\n• texas instruments 84 interpolation program\n• Solutions of Quadratic Equation by extracting the square roots\n• +The difference between the cubes of two consecutive numbers is 547. What are these numbers?\n• ged math worksheets\n• +evaluating expressions wiyth more than two operations\n• cubic equations in real life\n• Solve pair of equation by reducing them to a linear equation 1/2x +1/3y=2\n• trivias on numbers for grade 3\n• softmath.com]\n• hands-on trig workbook\n• Solve any system using elimination calculator\n• bar graph science worksheet\n• mathletics instant workbooks for 5th grades\n• derivative calculator roots\n• what is the difference beween ti83 plus and ti 83 plus silver\n• manual de algebrator\n• system of linear equation age problem worksheet\n• solution of a quadratic equation by extracting square roots\n• college algebra cheat sheet\n• list of math formulas algebra\n• y11 3u parabola parametric worksheets with solutions\n• Traverse this string just once and find if it is palindrome or not\n• Linear * problems for high school\n• extracting roots algebra\n• examples of solving problems using graphs and charts on the hanna orleans algebraic test\n• polynomial formula calculator hyperbola\n• multiplying decimals calculator\n• (8n+2)/7=6\n• www. discreatemathmatics codes and groups chap solution.ppt\n• www.uses of mathamatics.nic.in\n• az algebra pretest\n• clep test college algebra\n• fraction number line\n• orleans-hanna algebra prognosis test\n• problem solving of linear equations.FRACTIONS\n• questions & answers to reading compass practice test for college students\n• decimal worksheet greatest to lowest worksheet\n• online usable algaba I caculater\n• sample test papers in algebra answer sheet\n• simplifying rational expressions calculator and that shows the work\n• slope equations\n• multiplying and dividing radical expressions calculator\n• real life exampels of a hypebola\n• definition prealgebra\n• how to solve quotients of radicals\n• tagalog version mathematical poems\n• solution for an irrational number expression using newton's method\n• math trivia question and answer\n• simplifying variable expression worksheet\n• +14.7 convert to mix number\n• Rational Expression Games\n• rules of negatives and positives when simplifying equations\n• texas ged print out practice test\n• How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions?\n• Equation Writer from Creative Software Design for ti 89\n• algebra standardized tests\n• Free 8Th Grade Math Worksheets\n• multiplication property of equality\n• mathematical investigatory project\n• free college algebra tutorial software\n• exponential functions\n• Quantitative Ability: questions on fractions, percentages, decimals, log base 10, algebra, probability and statistics\n• binomial fraction inequalities\n• games to teach numbers in english to adolescents. Numbers from 100 to 1000\n• sums for equation in algriba\n• number line with positive and negative numbers\n• applications of proportions worksheet\n• which is the relationship between the evaluating and solving process in linear and inequalities equations\n• ALGEBRA II PRETEST\n• glencoe mathmatics practice workbook 6grade\n• convert percent to degrees\n• Create your own radical expression, containing a numerical coefficient and two different variables,\n• free circle graph worksheets\n• how to solve reiman summ\n• algebra 2 problems simplifying the rational expression x^+5x+4 /x^-x-2\n• subtraction of integers worksheets\n• algebrator mac\n• cumulative integer review worksheet\n• form3 math fomula\n• Why must we always be mindful of the final value of the denominator in a rational expression? For example, consider the rational expression 3x/(x2 – 16). What values in the denominator must we be mindful of? Explain why.\n• Decompose my fraction\n• triangle method for finding percent\n• free ged math worksheets and answers\n• solving algebra problems with excel\n• multiply expressions calculator\n• greatest common factors worksheets\n• redcued fractions calculator\n• algebra pre assessment worksheet\n• 361002923\n• online printable graphing calculator\n• 7th grade mathmatical equation chart\n• multiplying expressions calculator\n• hex value 82 dcimal\n• mixed fraction to a decimal calculator\n• poems on graph an inqualities\n• what is identity of foil method\n• math trivia/tricks\n• free printable math worksheets for 7th grade\n• Algebra \"simplify exponential variables\"\n• What is the title of this picture factoring worksheet\n• site to solve algerbra math problems\n• linear metre calculation\n• free algebrator\n• Answers to Algebra 1 Textbook\n• Prentice Hall Mathematics Algebra\n• algebra problem solver\n• algebra solver\n• Step by Step Algebra Help\n• combining like terms in quadratic equation\n• algebra 2 homework solver\n• 3x-2y=-16\n• My Algebra\n• solve binomial\n• WHAT DOES QUADRILATERAL HAVE IN COMMON\n• prealgebra permutations and combinations\n• solving equations with two variables\n• simplifying algebraic expressions with powers\n• how to explain irrational number to another person\n• solve my geometry problem\n• Intermediate college algebra study guide\n• solve my algebra\n• all answers in the saxon algebra 2 book\n• College Algebra Problem Solver\n• quick learn algebra\n• my skill tutor\n• intermediate algebra help\n• math minutes algebra\n• how will learning patterns help students learn algebra\n• hotels in rangely co\n• 6th grade algebra word problems\n• algebra simple interest equation\n• online math reviewer\n• algebra properties worksheet\n• i need a calculator that shows work\n• investigating ellipses equations algebra\n• allebraic equations used in pharmacy\n• Accelerated Math Questions\n• algebraic pyramids\n• algebraic probability problems\n• all answers in the saxon algebra 2 book free\n• interval notation solve online\n• algebra I pretest\n• list of algebra formulas\n• free show me how to solve algebra\n• algebra 2 poems" ]
[ null, "https://www.softmath.com/images/video-pages/solver-top.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.78439766,"math_prob":0.9889867,"size":64982,"snap":"2019-43-2019-47","text_gpt3_token_len":15121,"char_repetition_ratio":0.23374066,"word_repetition_ratio":0.0257121,"special_character_ratio":0.20639561,"punctuation_ratio":0.021374548,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999876,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-22T13:34:59Z\",\"WARC-Record-ID\":\"<urn:uuid:aeff26a1-740d-4d67-9be7-8f49c3bc58d1>\",\"Content-Length\":\"203895\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ec820702-cccd-4c91-8f5b-cb9009a483e0>\",\"WARC-Concurrent-To\":\"<urn:uuid:b63cbb82-82d7-4572-8f23-1d9a07dbfe6a>\",\"WARC-IP-Address\":\"52.43.142.96\",\"WARC-Target-URI\":\"https://www.softmath.com/math-com-calculator/function-range/simplify-expressions-and-use.html\",\"WARC-Payload-Digest\":\"sha1:JN2VKQYCXO64J7NJRGHMGWGKWX77GVQ2\",\"WARC-Block-Digest\":\"sha1:HVN5XH6G6QJU72CAERBLIUIYDH2UJXZC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496671260.30_warc_CC-MAIN-20191122115908-20191122143908-00310.warc.gz\"}"}
http://stp.clarku.edu/simulations/harddisks/metropolis/index.html
[ "### Monte Carlo simulation of hard disks\n\nIntroduction\n\nThe application of the Metropolis algorithm for a system of hard disks can be stated very simply:\n\n1. Choose a particle at random and generate trial a change in its x and y coordinates:\n\nx(i) = x(i) + (2r - 1)δ\n\ny(i) = y(i) + (2r - 1)δ,\n\nwhere r is a uniform random number in the unit interval and δ is the maximum displacement.\n\n2. Accept the trial move if the trial position of the disk does not overlap another disk. Otherwise, the move is rejected and the old configuration is retained. A reasonable, although not necessarily optimum choice for δ is to choose its value such that approximately 20% of the trial moves are accepted.\n\nThe program uses units such that the diameter σ = 1.\n\nProblems\n\n1. The main quantity of interest is the radial distribution function g(r). Describe its qualitative r-dependence. How does g(r) change with increasing density?\n\n2. How does the form of g(r) compare to that a system of particles interacting with the Lennard-Jones potential at the same density?\n\n3. The pressure P of a system of hard disks is related to the value of g(r) at contact by the expression", null, ".\n\nBecause the hard disks rarely touch, it is difficult to obtain good statistics for g(r) at contact. Fit the values of g(r) close to r = σ to a second-order polynomial in r and extrapolate the values of g(r) for r greater than r = σ+.\n\n4. What does the phase diagram of a system of hard disks look like? Does the system become a solid at high densities? Start the system at a low density and slowly compress the system. We do so by first determining the minimum distance between the centers of any two disks. Because this distance cannot be less than σ, its value bounds the amount that we can compress the system. We multiply this distance by the parameter λ = scale lengths after every Monte Carlo step per particle. Start the system in a rectangular configuration and then compress the system by setting scale lengths = 0.95. Is the system a fluid or a solid at high densities? If its a solid, what is its symmetry?\n\nJava Classes\n\n• HD\n• HDMCApp\n\nUpdated 3 March 2009." ]
[ null, "http://stp.clarku.edu/simulations/harddisks/metropolis/pressurehd.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9179231,"math_prob":0.9909726,"size":2056,"snap":"2019-51-2020-05","text_gpt3_token_len":467,"char_repetition_ratio":0.12231969,"word_repetition_ratio":0.018817205,"special_character_ratio":0.23103113,"punctuation_ratio":0.08851675,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.997309,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-27T14:26:44Z\",\"WARC-Record-ID\":\"<urn:uuid:ce92800d-823e-4f4e-9263-eebb452e3744>\",\"Content-Length\":\"3521\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2c4b2ea1-57c4-4eb1-822f-fff2997678cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:a2f2affb-9981-46dc-b9e2-ccec0d1e78be>\",\"WARC-IP-Address\":\"140.232.1.51\",\"WARC-Target-URI\":\"http://stp.clarku.edu/simulations/harddisks/metropolis/index.html\",\"WARC-Payload-Digest\":\"sha1:PG37PZZGUX3EW6TCCZDFGB34XC3R6U7E\",\"WARC-Block-Digest\":\"sha1:YR4USJOS6QFLR5EXK5VGN4V723GV4FSR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251700675.78_warc_CC-MAIN-20200127112805-20200127142805-00158.warc.gz\"}"}
https://www.kylesconverter.com/time/weeks-to-sols
[ "# Convert Weeks to Sols\n\n### Kyle's Converter > Time > Weeks > Weeks to Sols\n\n Weeks (wk) Sols (sol) Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18\nReverse conversion?\nSols to Weeks\n(or just enter a value in the \"to\" field)\n\n#### Please share if you found this tool useful:\n\nUnit Descriptions\n1 Week:\n1 Week is equal to 7 days. In SI units 1 week is 604,800 seconds.\n1 Sol:\n1 Sol is a martian solar day, one full rotation of Mars from the perspective of the Sun. Approximately 88775.24409 seconds or 24 hours, 39 minutes, 35.24409 seconds; slightly variable due to orbital eccentricity. 1 sol = 88775.24409 s.\n\nConversions Table\n1 Weeks to Sols = 6.812770 Weeks to Sols = 476.8897\n2 Weeks to Sols = 13.625480 Weeks to Sols = 545.0168\n3 Weeks to Sols = 20.438190 Weeks to Sols = 613.1439\n4 Weeks to Sols = 27.2508100 Weeks to Sols = 681.271\n5 Weeks to Sols = 34.0636200 Weeks to Sols = 1362.542\n6 Weeks to Sols = 40.8763300 Weeks to Sols = 2043.813\n7 Weeks to Sols = 47.689400 Weeks to Sols = 2725.084\n8 Weeks to Sols = 54.5017500 Weeks to Sols = 3406.355\n9 Weeks to Sols = 61.3144600 Weeks to Sols = 4087.626\n10 Weeks to Sols = 68.1271800 Weeks to Sols = 5450.1681\n20 Weeks to Sols = 136.2542900 Weeks to Sols = 6131.4391\n30 Weeks to Sols = 204.38131,000 Weeks to Sols = 6812.7101\n40 Weeks to Sols = 272.508410,000 Weeks to Sols = 68127.1008\n50 Weeks to Sols = 340.6355100,000 Weeks to Sols = 681271.0077\n60 Weeks to Sols = 408.76261,000,000 Weeks to Sols = 6812710.077" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.78743994,"math_prob":0.95890784,"size":1333,"snap":"2023-14-2023-23","text_gpt3_token_len":526,"char_repetition_ratio":0.37697518,"word_repetition_ratio":0.0,"special_character_ratio":0.49587396,"punctuation_ratio":0.1462585,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9545448,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-25T20:36:04Z\",\"WARC-Record-ID\":\"<urn:uuid:43267336-8f04-4bae-a4eb-5791912cfd32>\",\"Content-Length\":\"18692\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:02f5d92d-67f2-4464-9937-9a4953f1c049>\",\"WARC-Concurrent-To\":\"<urn:uuid:dc4bd1ea-6c72-44c7-a5a2-9be16fdcac6e>\",\"WARC-IP-Address\":\"18.160.10.41\",\"WARC-Target-URI\":\"https://www.kylesconverter.com/time/weeks-to-sols\",\"WARC-Payload-Digest\":\"sha1:Z2LMWCRBSGH5MIQHW3SUYXGTOSKXBEQB\",\"WARC-Block-Digest\":\"sha1:M5YDUF7636WQE6CX5Y3NOF2CSZJCMIZ2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945372.38_warc_CC-MAIN-20230325191930-20230325221930-00134.warc.gz\"}"}
http://www.oalib.com/relative/3796171
[ "Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+", null, "", null, "Title Keywords Abstract Author All\nSearch Results: 1 - 10 of 100 matches for \" \"\n Page 1 /100 Display every page 5 10 20 Item\n Viacheslav V. Nikulin Mathematics , 2007, Abstract: Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing ground fields of arithmetic hyperbolic reflection groups are defined, and good bounds of their degrees (over Q) are obtained. For example, degree of the ground field of any arithmetic hyperbolic reflection group in dimension at least 6 is bounded by 56. These results could be important for further classification. We also formulate a mirror symmetric conjecture to finiteness of the number of arithmetic hyperbolic reflection groups which was established in full generality recently.\n Viacheslav V. Nikulin Mathematics , 2007, DOI: 10.1112/jlms/jdp003 Abstract: This paper continues arXiv.org:math.AG/0609256, arXiv:0708.3991 and arXiv:0710.0162 . Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimension at least 3 are defined, and explicit bounds of their degrees (over Q) are obtained. Thus, now, explicit bound of degree of ground fields of arithmetic hyperbolic reflection groups is known in all dimensions. Thus, now, we can, in principle, obtain effective finite classification of arithmetic hyperbolic reflection groups in all dimensions together.\n Viacheslav V. Nikulin Mathematics , 2009, Abstract: The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of V-arithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflection group is greater than N(14), then the field comes from very special plane reflection groups. In our recent paper (see also arXiv:0708.3991), we claimed its upper bound 56. Using similar but more difficult considerations, here we improve this bound. These results could be important for further classification.\n Mikhail Belolipetsky Mathematics , 2015, Abstract: This is a survey article about arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.\n Mathematics , 2006, Abstract: We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.\n Mathematics , 2012, Abstract: Following the previous work of Nikulin and Agol, Belolipetsky, Storm, and Whyte it is known that there exist only finitely many (totally real) number fields that can serve as fields of definition of arithmetic hyperbolic reflection groups. We prove a new bound on the degree \\$n_k\\$ of these fields in dimension 3: \\$n_k\\$ does not exceed 9. Combined with previous results of Maclachlan and Nikulin, this leads to a new bound \\$n_k \\le 25\\$ which is valid for all dimensions. We also obtain upper bounds for the discriminants of these fields and give some heuristic results which may be useful for the classification of arithmetic hyperbolic reflection groups.\n Mikhail Belolipetsky Mathematics , 2007, Abstract: We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.\n Mathematics , 2007, Abstract: We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in \\$\\mathbb{H}^3\\$, the commensurability invariants known as the invariant trace field and invariant quaternion algebra. Our scripts also allow one to determine arithmeticity of such groups and the isomorphism class of the invariant quaternion algebra by analyzing its ramification. We present many computed examples of these invariants. This is enough to show that most of the groups that we consider are pairwise incommensurable. For pairs of groups with identical invariants, not all is lost: when both groups are arithmetic, having identical invariants guarantees commensurability. We discover many ``unexpected'' commensurable pairs this way. We also present a non-arithmetic pair with identical invariants for which we cannot determine commensurability.\n Mahdi Izadi;Mohd Zainal Abidin Ab Kadir;Maryam Hajikhani PIER , 2013, DOI: 10.2528/PIER12112503 Abstract: In this paper, analytical field expressions are proposed to determine the electromagnetic fields due to an inclined lightning channel in the presence of a ground reflection at the striking point. The proposed method can support different current functions and models directly in the time domain without the need to apply any extra conversions. A set of measured electromagnetic fields associated with an inclined lightning channel from a triggered lightning experiment is used to evaluate the proposed field expressions. The results indicate that the peak of the electromagnetic fields is dependent on the channel angle, the observation point angle as well as the value of the ground reflection factor due to the difference between channel and ground impedances. Likewise, the effect of the channel parameters and the ground reflection on the values of the electromagnetic fields is considered and the results are discussed accordingly.\n Viacheslav V. Nikulin Mathematics , 2008, Abstract: An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective Picard lattices can be characterized in terms of compositions of their self-correspondences via moduli of sheaves with primitive isotropic Mukai vector: Their self-correspondences with integral action on the Picard lattice are numerically equivalent to compositions of a finite number of especially simple self-correspondences via moduli of sheaves. This relates two topics: Self-correspondences of K3 surfaces via moduli of sheaves and Arithmetic hyperbolic reflection groups. It also raises several natural unsolved related problems.\n Page 1 /100 Display every page 5 10 20 Item" ]
[ null, "http://www.oalib.com:80/images/arrow-down.gif", null, "http://www.oalib.com:80/images/oaliblog3.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8645426,"math_prob":0.89143586,"size":8047,"snap":"2019-51-2020-05","text_gpt3_token_len":1823,"char_repetition_ratio":0.16822082,"word_repetition_ratio":0.17568693,"special_character_ratio":0.20169008,"punctuation_ratio":0.10105581,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9772803,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-21T08:18:10Z\",\"WARC-Record-ID\":\"<urn:uuid:2b3d39ee-70e7-4c35-a7a0-a329017ad741>\",\"Content-Length\":\"73532\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5b28e31b-a22f-4c3f-a9f5-fe4ed592ac77>\",\"WARC-Concurrent-To\":\"<urn:uuid:1a8e4d1a-f706-4732-87b2-6c1cb12d7d84>\",\"WARC-IP-Address\":\"198.204.224.92\",\"WARC-Target-URI\":\"http://www.oalib.com/relative/3796171\",\"WARC-Payload-Digest\":\"sha1:6LZ7BDPJCOTLYAKSXRJJRZUJG52CYLAV\",\"WARC-Block-Digest\":\"sha1:2PVMSL2G4OP6NNQST2KQSOAO2SYMQ2A2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250601628.36_warc_CC-MAIN-20200121074002-20200121103002-00104.warc.gz\"}"}
https://dsp.stackexchange.com/questions/34424/question-about-ramp-filter-used-in-filtered-backprojection
[ "# Question about ramp filter used in filtered backprojection\n\nQuestion is this. First, a ramp filter (in frequency domain) is defined by $H(Q)=|Q|$. What are the responses of a ramp filter to (1) a constant function $f(r)=c$ and (2) a sinusoid function $f(r)=\\sin(wr)$? What does the response mean? Following is my work.\n\nMy work:\n\n1. First, take fourier transform of a function $f(r)=c$. It is $\\int_{-\\infty}^{\\infty}f(r)e^{-2i\\pi rQ}dr=c\\delta(Q)$. Then multiply ramp filter and take inverse fourier transform. It is $\\int_{-\\infty}^{\\infty}c\\delta(Q)|Q|e^{2i\\pi irQ}dQ=0$??\n\n2. Similarly, $\\int_{-\\infty}^{\\infty}\\sin(wr)e^{-2i\\pi rQ}dr=\\frac{\\delta(Q-w/2\\pi)-\\delta(Q+w/2\\pi)}{2i}$. So Applying the ramp filter and i.f.t gives $\\frac{w(e^{iwr}-e^{-iwr})}{4i\\pi}=\\frac{w\\sin(wr)}{2\\pi}$.\n\nIt this right?\n\n• Can you please clarify the math notation a little bit? Your first expression is like an integral equation not an evaluation of an integral. It is quite possible that your derivations are along the right track but with this notation it is unclear why. Also, what does your intuition say? What do you think might happen if you were to pass DC through a ramp filter? What is another name for the ramp filter? What does the ramp filter do at the end of the day? – A_A Sep 25 '16 at 17:01\n\nIf a filter has frequency response $H(Q)$, this means that its response to an input $e^{j2\\pi Q_0 r}$ is the signal $H(Q_0)e^{j2\\pi Q_0 r}$. In other words, a sinusoidal input of frequency $Q_0$ produces an output of the same frequency, but with amplitude $|H(Q_0)|$ and phase $\\angle H(Q_0)$.\nIn your first question, the input has frequency $Q_0=0$. The filter's response at that frequency is $|Q_0|=0$. Then, the filter's output will be 0: frequency $Q_0=0$ is completely absorbed by the filter and it does not appear at the output.\nIn your second question, the input has frequency $Q_0=w/2\\pi$. The filter's response at that frequency is $|Q_0|=w/2\\pi$. The output, then, should be $\\frac{w}{2\\pi}\\sin(wr)$." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.74430645,"math_prob":0.99910605,"size":735,"snap":"2019-43-2019-47","text_gpt3_token_len":274,"char_repetition_ratio":0.125855,"word_repetition_ratio":0.0,"special_character_ratio":0.34965986,"punctuation_ratio":0.11176471,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998944,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-13T10:48:42Z\",\"WARC-Record-ID\":\"<urn:uuid:fea3f1df-ee69-4795-91d1-cd961836cd70>\",\"Content-Length\":\"134790\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6963e47c-a725-48df-9b7f-161084009715>\",\"WARC-Concurrent-To\":\"<urn:uuid:37019a3b-9d93-4e06-86e4-cb5dd283c383>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/34424/question-about-ramp-filter-used-in-filtered-backprojection\",\"WARC-Payload-Digest\":\"sha1:XVFH67E2QAFM743G5XX36U2PTILXCZ7P\",\"WARC-Block-Digest\":\"sha1:2WHZZA2FLGZWV3HJM5UUMZ7RZ5RUMBEL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496667177.24_warc_CC-MAIN-20191113090217-20191113114217-00029.warc.gz\"}"}
https://homes.cs.washington.edu/~jmschr/lectures/Parallel_Processing_in_Python.html
[ "# Parallel Processing in Python¶\n\nauthor: Jacob Schreiber\ncontact: jmschr@cs.washington.edu\n\nSimply put, parallel processing is splitting up a task between many CPUs to make it work faster or more efficiently. In the big data setting this often means speading up complex analyses by splitting up the task across the CPUs and getting a speedup bounded by the additional number of cores added. This is made easier because most tasks on big data are embarassingly parallel, which means having many independent tasks that can be distributed to many cores easily. For example, matrix-matrix multiplication can be time intensive for big matrices. However, each row-column dot product is independent from each other and so can be given to a core without the need to communicate between cores mid-task. This is great for parallel processing.\n\nWhile languages like C, Java, and R allow parallel processing fairly easily, life isn't easy being a Python programmer due to the Global Interpreter Lock (or GIL). This is a lock on a Python process which prevents it from executing multiple threads simultaneously.\n\nWhat does that even mean, though?\n\nA process in a computer can be depicted as the following:", null, "(ref: https://web.kudpc.kyoto-u.ac.jp/manual/en/parallel)\n\nYour computer will allocate some memory for each process, which can be thought of as basically a \"program.\" Every program is isolated from the others, and no process is allowed to infringe on the memory space of another process. If a process attempts to infringe on a neighbors space, this can lead to everyone's favorite error, the segfault.\n\nInside a process there can be multiple \"threads\" of execution. These threads share the underlying memory of the process, and can each be assigned to different cores for execution. This makes parallelization nice, because a process can load up some data and then process it using multiple cores much many people might eat a birthday cake.\n\nHowever, having shared memory can cause problems. For example, imagine trying to sum a trillion numbers and saving it to a local variable \"x\". At some point, one of your lines of code will look something like x = x + item. However, if multiple threads grab the old value of \"x\" at the same time, add some number to it, and try to update the variable, you will get mistakes called \"race conditions\" which will cause you to get an incorrect sum. What's even worse is that the simpler the task, the higher the probability of these happening due to the frequency that these variables are being called. Lets take a look at a simple code example (without focusing too much on what the code itself says.)\n\nIn :\n%load_ext Cython\n%pylab inline\nimport seaborn, time\nseaborn.set_style('whitegrid')\n\nPopulating the interactive namespace from numpy and matplotlib\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\nimport numpy\ncimport numpy\nfrom cython.parallel import prange\n\ncdef int x, i\n\nwith nogil:\nx = 0\nfor i in prange(10000000, schedule='guided', num_threads=4):\n(&x) = (&x) + 1\n\nprint x\n\n2505506\n\n\nLooks like we're getting a very wrong answer, and a different answer every time the code is run. This is where locks come in! Locks can be acquired by any thread and prevent other threads from executing. In this case, a thread could acquire a lock on x, update it, and then release the lock. This means only one thread is operating on x at a time. We can simulate that with the following code:\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\nimport numpy\ncimport numpy\nfrom cython.parallel import prange\n\ncdef int x, i\n\nwith nogil:\nx = 0\nfor i in prange(10000000, schedule='guided', num_threads=4):\nwith gil:\n(&x) = (&x) + 1\n\nprint x\n\n10000000\n\n\nHowever, there can still be race conditions if multiple threads can read a variable but then acquire the gil to update it sequentially. In fact, we have exactly the same problem as before, where multiple threads can read a variable and then overwrite each other's progress. We're just doing it in a more orderly fashion instead of a chaotic fashion. See the following code:\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\nimport numpy\ncimport numpy\nfrom cython.parallel import prange\n\ncdef int x, i, y\n\nwith nogil:\nx = 0\nfor i in prange(1000000, schedule='guided', num_threads=4):\ny = x + 1\nwith gil:\n(&x) = y\n\nprint x\n\n275824\n\n\nUsing the lock seemed to solve all of our issues, so what was the problem? Well, if we only have one thread running at a time, then we're not going to get any speed gain! Despite having distributed work to each of the seperate threads, only one of them is running at a time because we're constantly putting a lock on the work the threads are doing. We can see below roughly what was happening, where only one thread was allowed to do work at a time because it was acquiring and releasing a lock.", null, "(ref: www.tivix.com/blog/lets-go-python)\n\nNow, the GIL is like a lock on a variable, except it's a lock on the entire Python process. This allows only one thread to be running at a time, no matter how many threads you create during the process of your program. This is a hotly contended issue amongst Pythonistas, but the general argument is that the Python interpreter was built to not be thread-safe because several speed gains could be made on that assumption, and since Python is pretty slow natively these speed gains are important.\n\nIt is still possible to do parallel processing in Python. The most naive way is to manually partition your data into independent chunks, and then run your Python program on each chunk. A computer can run multiple python processes at a time, just in their own unqiue memory space and with only one thread per process. This will be tedious, and you'll have to use another script to aggregate your answers. Pretty much, this sounds awful and you shouldn't do it.\n\nThis process can be automated using the multiprocessing module.\n\n## Multiprocessing¶\n\nThe simplest way to include parallel processing in your code is through the multiprocessing module which is built into python. The way this works is through the built-in pickle module, which is a way of serializing data, functions, and objects. In essense, you start up a pool of processes which wait for instructions from the main process. The main process will then send serialized data, methods, and objects, to the new process, and the new process will perform the instructions and send the result back.\n\nThe module has a relatively simple interface, where you write a python method, create a pool of workers, and execute that function for different inputs. Lets see it in action for the simple task of taking in a series of numbers and returning the number of items and their sum.\n\nFirst, define the method:\n\nIn :\ndef summarize( X ):\n\"\"\"Summarize the data set by returning the length and the sum.\"\"\"\nreturn len(X), sum(X)\n\n\nNow lets run this on a large amount of data in a purely sequential way to see what the answer is.\n\nIn :\nX = numpy.random.randn(1e7) + 8.342\nx0, x1 = summarize(X)\nprint x1 / x0\n\n/home/jmschr/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:1: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\nif __name__ == '__main__':\n\n8.34182145513\n\n\nLooks like we're recovering the mean fairly well, as would be expected given the large number of samples. Now lets time this:\n\nIn :\n%timeit summarize(X)\n\n100 loops, best of 3: 8.8 ms per loop\n\n\nSeems fairly fast given that we have 1e7 elements. But it is a simple operation!\n\nUsing multiprocessing in Python involves first setting up a pool of workers and then distributing the tasks to each worker involving a subsection of the dataset.\n\nIn :\nfrom multiprocessing import Pool\n\np = Pool(4)\nx = p.map( summarize, (X[i::4] for i in range(4)) )\nprint x\n\n[(2500000, 20853831.617965657), (2500000, 20855287.683435395), (2500000, 20856136.83326447), (2500000, 20852958.41664188)]\n\n\nThis returns a list with each element being the output of one of the jobs. We have to sum through each job now to get the total aggregate.\n\nIn :\nx0 = sum( y0 for y0, _ in x )\nx1 = sum( y1 for _, y1 in x )\nprint x1 / x0\n\n8.34182145513\n\n\nLooks like we're getting the same answer here! Now to time it:\n\nIn :\nn = len(X) / 4\n%timeit p.map( summarize, (X[i*n:(i+1)*n] for i in range(4)) )\n\nThe slowest run took 5.87 times longer than the fastest. This could mean that an intermediate result is being cached.\n1 loop, best of 3: 198 ms per loop\n\n\nThat looks like it's at least an order of magnitude slower! But we're using parallel processing, how could things ever be slower? The reason mostly revolves around the operation being too simple and the data being too small. Here are some of the more prominent reasons:\n\n(1) The cost of setting up the worker pool is very high given the cost of the original operation:\n\nIn :\n%timeit -n 3 Pool(4)\n\nThe slowest run took 14.03 times longer than the fastest. This could mean that an intermediate result is being cached.\n3 loops, best of 3: 23.7 ms per loop\n\n\n(2) The memory cost of using this is high, because you're copying your initial data at least twice. This is because one full copy lives on the original process, and you have to send a partition of the data to this new process, which all has to live in memory.\n\n(3) The cost of sending data across pipes can be higher than you want. Here is a speed comparison done by someone on StackOverflow:\n\nmpenning@mpenning-T61:~$python multi_pipe.py Sending 10000 numbers to Pipe() took 0.0369849205017 seconds Sending 100000 numbers to Pipe() took 0.328398942947 seconds Sending 1000000 numbers to Pipe() took 3.17266988754 seconds mpenning@mpenning-T61:~$ python multi_queue.py\nSending 10000 numbers to Queue() took 0.105256080627 seconds\nSending 100000 numbers to Queue() took 0.980564117432 seconds\nSending 1000000 numbers to Queue() took 10.1611330509 seconds\nmpnening@mpenning-T61:~$python multi_joinablequeue.py Sending 10000 numbers to JoinableQueue() took 0.172781944275 seconds Sending 100000 numbers to JoinableQueue() took 1.5714070797 seconds Sending 1000000 numbers to JoinableQueue() took 15.8527247906 seconds mpenning@mpenning-T61:~$\n\nThis can be made faster, but it shows that especially for large datasets the time spent just piping the data can be significant.\n\nSo, if a significant portion of time is being spent piping data, then we can get better improvement with more cores if we have a more complex task. Basically each core is speeding through the summation and gulping down data as fast as possible. If we had a more complex task then the core would be spending more time on it and not need to be requesting new data as often.\n\nLets look at the case of pairwise sums, where we take in a list of numbers $x_{1}, \\dots , x_{n}$ and return the sum of them all multiplied by each other, $\\sum\\limits_{i=1}^{n} \\sum\\limits_{j=1}^{n} x_{i}x_{j}$.\n\nIn :\ndef scalar_sum(X, y):\nreturn sum( x*y for x in X )\n\ndef pairwise_sum(X):\nreturn( sum( scalar_sum(X, y) for y in X ) )\n\n\nNow lets show the single process version time:\n\nIn :\nX = numpy.random.randn(1000)\n%timeit pairwise_sum(X)\n\n1 loop, best of 3: 221 ms per loop\n\n\nAnd a parallelized version. As a side note, we need a helper function to unwrap the arguments to the function since it has more than one function. It doesn't add a significant overhead to the program.\n\nIn :\ndef scalar_wrapper(args):\nreturn scalar_sum(*args)\n\np = Pool(4)\n%timeit p.map( scalar_wrapper, ((X, y) for y in X) )\n\n10 loops, best of 3: 84 ms per loop\n\n\nLooks like we're already getting a ~3x speed up when using 4 processes on this more complex operation!\n\nNow, lets go to a real world example which can be very sped up using parallelization: Doing Expectation-Maximization on a Gaussian Mixture Model.\n\nTo begin with, a multivariate gaussian $G$ of dimensionality $d$ is parameterized by $mu$, which is a vector of mean values for each dimension, and $\\Sigma$ which is the covariance matrix between all of these dimensions. The covariance matrix has a diagonal which is the variance of every dimension by itself, and each entry $\\Sigma_{i,j}$ represents the covariance between dimension $i$ and dimension $j$.\n\nA mixture model requires that its underlying components have two operations: (1) they can return probabilities of data given that component $P(D|M)$, and (2) they can be fit to data. The expectation-maximization procedure then iterates between these two operations, using Bayes rule to calculate the probability of each component producing each point, and then updating the components based on these weighted beliefs.\n\nMultivariate Gaussians have both of these operations. (1) The probability of a point under the multivariate Gaussian is as follows:\n\n\\begin{equation} P(x|\\mu, \\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^{d}|\\Sigma|}}exp\\left(-\\frac{1}{2}(x-\\mu)^{T}\\Sigma^{-1}(x-\\mu)\\right) \\end{equation}\n\nFortunately it's also implemented in scipy as a simple function for us. We can use this to create the expectation part of EM, which is calculating $P(M|D)$ for every data point and every component. We then normalize this matrix so that each row sums to 1, which defines the probability that each component generated that sample. Lastly, we do weighted MLE estimates to update the distributions.\n\nWe can see an example of it at work here:", null, "(ref: http://twitwi.github.io/Presentation-2015-dirichlet-processes/gmm2d/difficult-soft.gif)\n\nThe colors added to the set are a bit confusing, but we can pretend that they don't matter. Roughly, we believe that the data was generated from three components, and want to be able to identify the underlying distributions which generated the data. We start off with rough, and very incorrect estimates, and then move towards better estimates iteratively until we converge at good solutions.\n\nIn :\nfrom scipy.stats import multivariate_normal\n\ndef expectation(X, mus, covs):\nr = numpy.hstack([multivariate_normal.pdf(X, mu, cov)[:, numpy.newaxis] for mu, cov in zip(mus, covs)])\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ndef covariance(X, weights):\nn, d = X.shape\nmu = numpy.average(X, axis=0, weights=weights)\ncov = numpy.zeros((d, d))\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\ndef maximization(X, r):\nmus = numpy.array([ numpy.average(X, axis=0, weights=r[:,i]) for i in range(r.shape) ])\ncovs = numpy.array([ covariance(X, r[:,i]) for i in range(r.shape) ])\nreturn mus, covs\n\n\nWe now have the two components which we need for the EM algorithm-- the expectation step and the maximization step. We just need to repeat these two steps until we achieve convergence. Instead of writing a convergence calculator we're just going to run the algorithm some fixed number of times until convergence,\n\nIn :\ndef EM(X, mu, cov):\nfor i in range(50):\nr = expectation(X, mu, cov)\nmu, cov = maximization(X, r)\n\nreturn mu, cov, r\n\n\nGreat. So we have a function now which will take in some initial values, and iterate until convergence, and return those values.\n\nLets generate some data with 4 underlying components\n\nIn :\nd, m = 2, 4\nX = numpy.concatenate([numpy.random.randn(100000, d)+i*4 for i in range(m)])\n\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c='c', linewidth=0 )\n\nOut:\n<matplotlib.collections.PathCollection at 0x7f1eb1a22050>", null, "Now lets run the sequential algorithm and plot the results.\n\nIn :\ninitial_mu = numpy.random.randn(m, d) + X.mean(axis=0)\ninitial_cov = numpy.array([numpy.eye(d) for i in range(m)])\n\nmu, cov = initial_mu.copy(), initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 26.227670908s\n\n\nHowever, the calculation of the responsibility matrix in the expectation step is embarassingly parallel. We can either use model parallelism, where we break the model up across processes and have it analyze the same data, or data parallelism, where we break up the data across processes and have the full model analyze the partition of the data.\n\nIf we try to do this using the multiprocessing module, we will usually run into a memory error. This is because we have to create a new pool of workers each process, and pipe the data to each worker. The module doesn't have great shutting down of idle processes, and so in an iterative algorithm like EM you will frequently get several hundreds of idle processes all with a huge slice of the data taking up memory. Since we are implementing model parallelism, this gets especially bad, because each process will have a full copy of the data stored on it.\n\nHow do we deal with this, then?\n\n## joblib¶\n\njoblib is a parallel processing library for python which was developed by many of the same people who work on scikit-learn, and is widely used inside scikit-learn to parallelize some of their algorithms. It is built on top of the multiprocessing and multithreading libraries in order to support both (multithreaded will be talked about later) but has a significant portion of additional features. One of the biggest ones is the ability to use a pool of workers like a context manager which can be reused across many tasks to be parallelized. This means each iteration of EM can use the same pool of workers. Newer versions will also actively time the duration of the tasks being dispatched to the processes to create an optimal schedule for splitting up data chunks. Lastly, if the number of jobs is set to 1, it will work in a purely sequential mode, with no overhead of setting up a pool or dispatching data.\n\nLets see how to use it below:\n\nIn :\nfrom joblib import Parallel, delayed\n\ndef _expectation(X, mu, cov):\nreturn multivariate_normal.pdf(X, mu, cov)[:, numpy.newaxis]\n\ndef _expectation_wrapper(args):\nreturn _expectation(*args)\n\ndef expectation(X, mus, covs, parallel):\ntasks = ((X, mu, cov) for mu, cov in zip(mus, covs))\nr = numpy.hstack( parallel( delayed(_expectation_wrapper)(t) for t in tasks ) )\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ndef EM(X, mu, cov):\nwith Parallel(n_jobs=4) as parallel:\nfor i in range(50):\nr = expectation(X, mu, cov, parallel)\nmu, cov = maximization(X, r)\n\nreturn mu, cov, r\n\nmu, cov = initial_mu.copy(), initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 39.5285749435s\n\n\nIt looks like we're not getting a speed increase despite using parallel processing. This is likely because of the overhead costs of setting up the pool and piping data between the processes can be quite high. It might be time to move back to multi-threading, since we're having limited success with multiprocessing.\n\nWe did not immediately use threading because the GIL prevented multiple threads from being executed at the same time. However, it is possible to release the GIL if we use cython, which is a compiler for both native Python code and its extension, also called Cython. Lets look into parallelizing the pairwise sum problem first in cython.\n\nIn :\nX = numpy.random.randn(5000)\n\n\nLets first take a look at the raw python code and see how long it takes.\n\nIn :\ndef scalar_sum(X, y):\nreturn sum( x*y for x in X )\n\ndef pairwise_sum(X):\nreturn( sum( scalar_sum(X, y) for y in X ) )\n\n%timeit pairwise_sum(X)\n\n1 loop, best of 3: 5.54 s per loop\n\n\nNow lets keep the code the same but turn cython on and see how long it takes.\n\nIn :\n%%cython\n\ndef scalar_sum(X, y):\nreturn sum( x*y for x in X )\n\ndef pairwise_sum(X):\nreturn( sum( scalar_sum(X, y) for y in X ) )\n\nIn :\n%timeit pairwise_sum(X)\n\n1 loop, best of 3: 4.74 s per loop\n\n\nLooks like we're getting a pretty good speed increase without even modifying the code!\n\nNow lets use some static typing of variables to utilize the Cython extension language. Since scalar_sum is the primary workhorse, lets focus on just improving that one for now.\n\nIn :\n%%cython\n\ncdef double scalar_sum(double[:] X, double y):\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(X.shape):\n_sum += X[i] * y\n\nreturn _sum\n\ndef pairwise_sum(X):\nreturn( sum( scalar_sum(X, y) for y in X ) )\n\nIn :\n%timeit pairwise_sum(X)\n\n10 loops, best of 3: 27.3 ms per loop\n\n\nLooks like a pretty good speed increase there! Static typing is one of the main boosts in speed you can get from Cython, because it can be very expensive to have to infer the type for numerics if you have to constantly repeat the checks.\n\nNow lets cythonize the pairwise_sum component as well, to make the entire thing written in the Cython extension language.\n\nIn :\n%%cython\n\ncdef double scalar_sum(double[:] X, double y):\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(X.shape):\n_sum += X[i] * y\n\nreturn _sum\n\ncpdef pairwise_sum(double[:] X):\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(X.shape):\n_sum += scalar_sum(X, X[i])\n\nreturn _sum\n\nIn :\n%timeit pairwise_sum(X)\n\n10 loops, best of 3: 23.7 ms per loop\n\n\nNow lets remove the GIL. In order to remove the GIL we need to make sure that the code with the GIL removed obeys several rules:\n\n(1) Only statically typed variasbles of C primitives (int, long, double...)\n\n(2) Arrays must be represented using pointers instead of numpy arrays or memoryviews\n\n(3) No python object or methods at all\n\n(4) All functions called must be tagged with nogil at the end\n\nWe then specify when we want to remove the GIL through the use of a context manager with gil and with nogil depending on what you want to do.\n\nPassing arrays of data to the C level form the Python level seems like it might be a daunting task at first. However, numpy has solved this problem relatively elegantly. You can simply use the following to extract a pointer from any numpy array:\n\ncdef dtype* X_ptr = <dtype*> X_ndarray.data\n\nThe .data attribute extracts the pointer to the underlying data, and dtype is whatever datatype is being stored. For example, most numerics are stored as a doubles, so we can do the following:\n\ncdef double* X_ptr = <double*> X_ndarray.data\n\nOne last consideration is that X_ndarray must be cast as a numpy array. If we haven't explicitly cast it we must explicitly cast it now:\n\ncdef double* X_ptr = <double*> (<numpy.ndarray> X_ndarray).data\nIn :\n%%cython\ncimport numpy\n\ncdef double scalar_sum(double* X, double y, int n) nogil:\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(n):\n_sum += X[i] * y\n\nreturn _sum\n\ncpdef pairwise_sum(numpy.ndarray X_ndarray):\ncdef int i, n = X_ndarray.shape\ncdef double* X = <double*> X_ndarray.data\ncdef double _sum = 0.0\n\nwith nogil:\nfor i in range(n):\n_sum += scalar_sum(X, X[i], n)\n\nreturn _sum\n\nIn :\n%timeit pairwise_sum(X)\n\n10 loops, best of 3: 21.2 ms per loop\n\n\nNow we can parallelize this function by changing the range to prange. There are a variety of great scheduling techniques to assign chunks of data to the various threads, but guided usually works the fastest in my experience.\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\ncimport numpy\nfrom cython.parallel cimport prange\n\ncdef double scalar_sum(double* X, double y, int n) nogil:\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(n):\n_sum += X[i] * y\n\nreturn _sum\n\ncpdef pairwise_sum(numpy.ndarray X_ndarray):\ncdef int i, n = X_ndarray.shape\ncdef double* X = <double*> X_ndarray.data\ncdef double _sum = 0.0\n\nwith nogil:\nfor i in prange(n, schedule='guided', num_threads=4):\n_sum += scalar_sum(X, X[i], n)\n\nreturn _sum\n\nIn :\n%timeit pairwise_sum(X)\n\n100 loops, best of 3: 6.49 ms per loop\n\n\nHowever, a major problem is that we can't use openmp on Windows machines, so if you want to write code which works cross-platform, or just on Windows, you need to use a different solution. This is where joblib comes in again, because it has both a multiprocessing and a multithreading backend.\n\nWe can use the same scalar_sum code from before exactly, but we need to make a few modifications since joblib works on the python level, but releasing the gil requires you to be on the C level.\n\nIn :\n%%cython\ncimport numpy\nfrom joblib import Parallel, delayed\n\ncdef double scalar_sum(double* X, double y, int n) nogil:\ncdef int i\ncdef double _sum = 0.0\n\nfor i in range(n):\n_sum += X[i] * y\n\nreturn _sum\n\ncpdef double scalar_wrapper(numpy.ndarray X_ndarray, double y):\ncdef double* X = <double*> X_ndarray.data\ncdef double _sum\n\nwith nogil:\n_sum = scalar_sum(X, y, X_ndarray.shape)\nreturn _sum\n\ncpdef pairwise_sum(numpy.ndarray X):\ncdef double _sum\n\n_sum = sum( parallel([delayed(scalar_wrapper, check_pickle=False)(X, y) for y in X ]) )\n\nreturn _sum\n\nIn :\n%timeit pairwise_sum(X)\n\n1 loop, best of 3: 2.12 s per loop\n\n\nThere is a lot of overhead here with going between python and cython as individual points are passed. So lets chunk the data and send all of the elements of $X$ which it is responsible for summing.\n\nIn :\n%%cython\ncimport numpy\nfrom joblib import Parallel, delayed\n\ncdef double scalar_sum(double* X, double* y, int n, int m) nogil:\ncdef int i, j\ncdef double _sum = 0.0\n\nfor i in range(n):\nfor j in range(m):\n_sum += X[i] * y[j]\n\nreturn _sum\n\ncpdef double scalar_wrapper(numpy.ndarray X_ndarray, numpy.ndarray y_ndarray):\ncdef double* X = <double*> X_ndarray.data\ncdef double* y = <double*> y_ndarray.data\ncdef int n = X_ndarray.shape, m = y_ndarray.shape\ncdef double _sum\n\nwith nogil:\n_sum = scalar_sum(X, y, n, m)\nreturn _sum\n\ncdef double _sum\n\n_sum = sum( parallel([ delayed(scalar_wrapper, check_pickle=False)(X, X[i::num_threads]) for i in range(num_threads) ]) )\n\nreturn _sum\n\nIn :\nX = numpy.random.randn(100000)\n%timeit pairwise_sum(X, 1)\n\n1 loop, best of 3: 8.55 s per loop\n\nIn :\n%timeit pairwise_sum(X, 4)\n\n1 loop, best of 3: 2.62 s per loop\n\n\nLooks like we're getting a near-linear speedup when we add more threads. Great!\n\n## Expectation-Maximization Revisited¶\n\nNow lets go back to the expectation-maximization algorithm on Gaussian Mixture models. Previously we found that using joblib and multiprocessing to parallelize jobs did not help significantly, likely due to the high overhead of setting up multiple processes and then pipe data between them. Lets see if we can lower this overhead using threads instead of processes.\n\nFirst, lets generate some data again, and create baseline parameter estimates to start at.\n\nIn :\nd, m = 2, 4\nX = numpy.concatenate([numpy.random.randn(1000000, d)+i*5 for i in range(m)]).astype('float64')\ninitial_mu = numpy.random.randn(m, d)*4 + X.mean(axis=0)\ninitial_cov = numpy.array([numpy.eye(d) for i in range(m)])\n\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c='c', linewidth=0 )\n\nOut:\n<matplotlib.collections.PathCollection at 0x7f1eb1d91850>", null, "Now, lets use the same code which we used before. We're going to need to get this code down to the cython level so that we can release the GIL and use multithreading. The most important function to ensure that the GIL is released for is the log probability function, because it takes up the most amount of time. This means that instead of using the convenient scipy function which we used before, we have to rewrite it ourselves. If the inner workings of log probability calculations don't interest you, ignore it! Otherwise, we basically need to pass in the inverse covariance matrix and the log of the determinant of the covariance matrix. Using these, we can easily calculate the log probability of each point under the given parameters.\n\nFirst lets define the functions we won't change this entire time, the maximization step and the EM iterator.\n\nIn :\ndef maximization(X, r):\nmus = numpy.array([ numpy.average(X, axis=0, weights=r[:,i]) for i in range(r.shape) ])\ncovs = numpy.array([ covariance(X, r[:,i], mus[i]) for i in range(r.shape) ])\nreturn mus, covs\n\ndef EM(X, mu, cov):\nfor i in range(25):\nr = expectation(X, mu, cov)\nmu, cov = maximization(X, r)\n\nreturn mu, cov, r\n\n\nNow lets define the expectation step functions which we will optimize, and the covariance calculator for the maximization step.\n\nIn :\nimport numpy\nLOG_2_PI = numpy.log(2*numpy.pi)\n\ndef log_probability(X, mu, inv_cov, log_det, d):\nlogp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i, j]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ndef _expectation(X, mu, cov ):\nn = X.shape\nd = X.shape\nlog_det = numpy.linalg.slogdet(cov)\ninv_cov_ndarray = numpy.linalg.inv(cov)\nr = numpy.zeros(n)\n\nfor i in range(n):\nr[i] = numpy.exp(log_probability(X[i], mu, inv_cov_ndarray, log_det, d ))\n\nreturn r\n\ndef expectation(X, mu, cov):\nr = numpy.hstack((_expectation(X, m, c)[:, numpy.newaxis] for m, c in zip(mu, cov)))\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ndef covariance(X, weights, mu):\nn, d = X.shape\ncov = numpy.zeros((d, d))\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 3808.46620393s\n\n\nAlright, looks like it's taking a fair amount of time to run this calculation on the data. Lets step through the steps we took to reduce this down to Cython that we did before. First, lets just turn on the Cython compiler and see what types of speed increases we can get from that.\n\nIn :\n%%cython\nimport numpy\nLOG_2_PI = numpy.log(2*numpy.pi)\n\ndef log_probability(X, mu, inv_cov, log_det, d):\nlogp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i, j]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ndef _expectation(X, mu, cov ):\nn = X.shape\nd = X.shape\nlog_det = numpy.linalg.slogdet(cov)\ninv_cov_ndarray = numpy.linalg.inv(cov)\nr = numpy.zeros(n)\n\nfor i in range(n):\nr[i] = numpy.exp(log_probability(X[i], mu, inv_cov_ndarray, log_det, d ))\n\nreturn r\n\ndef expectation(X, mu, cov):\nr = numpy.hstack((_expectation(X, m, c)[:, numpy.newaxis] for m, c in zip(mu, cov)))\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ndef covariance(X, weights, mu):\nn, d = X.shape\ncov = numpy.zeros((d, d))\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 2470.94735408s\n\n\nGreat! We didn't need to do anything differently but we still get a fairly nice speed gain. Almost all python scripts which have a lot of numeric calculations will experience a speed gain of, in my experience, around 30%.\n\nThe next step for cythonizing our code is to include static typing. This allows the cython compiler to turn for loops into C-for loops, which are significantly faster. As a note, despute xrange being faster and more memory efficient than range for large Python lists, use range when writing in cython. Lets also pull the pointer arrays out of the numpy arrays.\n\nIn :\n%%cython\nimport numpy\ncimport numpy\nLOG_2_PI = numpy.log(2*numpy.pi)\n\ncdef double log_probability(double* X, double* mu, double* inv_cov, double log_det, int d):\ncdef int i, j\ncdef double logp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i + j*d]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ncpdef numpy.ndarray _expectation( numpy.ndarray X_ndarray, numpy.ndarray mu_ndarray, numpy.ndarray cov_ndarray ):\ncdef int i, n = X_ndarray.shape, d = X_ndarray.shape\ncdef double log_det = numpy.linalg.slogdet(cov_ndarray)\ncdef numpy.ndarray inv_cov_ndarray = numpy.linalg.inv(cov_ndarray)\ncdef numpy.ndarray r = numpy.zeros(n)\n\ncdef double* inv_cov = <double*> inv_cov_ndarray.data\ncdef double* mu = <double*> mu_ndarray.data\ncdef double* X = <double*> X_ndarray.data\n\nfor i in range(n):\nr[i] = numpy.exp(log_probability(X + i*d, mu, inv_cov, log_det, d ))\n\nreturn r\n\ndef expectation(X, mu, cov):\nr = numpy.hstack((_expectation(X, m, c)[:, numpy.newaxis] for m, c in zip(mu, cov)))\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ncpdef numpy.ndarray covariance(numpy.ndarray X, numpy.ndarray weights, numpy.ndarray mu):\ncdef int i, j, n = X.shape, d = X.shape\ncdef numpy.ndarray cov = numpy.zeros((d, d))\ncdef double w_sum\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 718.266939878s\n\n\nThat's a pretty nice speed gain! Now lets release the GIL for the important functions to get it ready for multithreading.\n\nIn :\n%%cython\nimport numpy\ncimport numpy\nfrom libc.math cimport exp as cexp\n\nDEF LOG_2_PI = 0.79817986835\n\ncdef double log_probability(double* X, double* mu, double* inv_cov, double log_det, int d) nogil:\ncdef int i, j\ncdef double logp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i + j*d]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ncpdef numpy.ndarray _expectation( numpy.ndarray X_ndarray, numpy.ndarray mu_ndarray, numpy.ndarray cov_ndarray ):\ncdef int i, n = X_ndarray.shape, d = X_ndarray.shape\ncdef double log_det = numpy.linalg.slogdet(cov_ndarray)\ncdef numpy.ndarray inv_cov_ndarray = numpy.linalg.inv(cov_ndarray)\ncdef numpy.ndarray r = numpy.zeros(n)\n\ncdef double* inv_cov = <double*> inv_cov_ndarray.data\ncdef double* mu = <double*> mu_ndarray.data\ncdef double* X = <double*> X_ndarray.data\n\nfor i in range(n):\nr[i] = cexp(log_probability(X + i*d, mu, inv_cov, log_det, d ))\n\nreturn r\n\ndef expectation(X, mu, cov):\nr = numpy.hstack((_expectation(X, m, c)[:, numpy.newaxis] for m, c in zip(mu, cov)))\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ncpdef numpy.ndarray covariance(numpy.ndarray X, numpy.ndarray weights, numpy.ndarray mu):\ncdef int i, j, n = X.shape, d = X.shape\ncdef numpy.ndarray cov = numpy.zeros((d, d))\ncdef double w_sum\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 63.3489141464s\n\n\nThat is a pretty massive speed increase! Now lets try using multithreads with openmp and see what type of performance increase we can get.\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\nfrom cython.parallel cimport prange\nimport numpy\ncimport numpy\nfrom libc.math cimport exp as cexp\n\nDEF LOG_2_PI = 0.79817986835\n\ncdef double log_probability(double* X, double* mu, double* inv_cov, double log_det, int d) nogil:\ncdef int i, j\ncdef double logp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i + j*d]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ncpdef numpy.ndarray _expectation( numpy.ndarray X_ndarray, numpy.ndarray mu_ndarray, numpy.ndarray cov_ndarray ):\ncdef int i, n = X_ndarray.shape, d = X_ndarray.shape\ncdef double log_det = numpy.linalg.slogdet(cov_ndarray)\ncdef numpy.ndarray inv_cov_ndarray = numpy.linalg.inv(cov_ndarray)\ncdef numpy.ndarray r_ndarray = numpy.zeros(n)\n\ncdef double* inv_cov = <double*> inv_cov_ndarray.data\ncdef double* mu = <double*> mu_ndarray.data\ncdef double* X = <double*> X_ndarray.data\ncdef double* r = <double*> r_ndarray.data\n\nfor i in prange(n, nogil=True, num_threads=4, schedule='guided'):\nr[i] = cexp(log_probability(X + i*d, mu, inv_cov, log_det, d ))\n\nreturn r_ndarray\n\ndef expectation(X, mu, cov):\nr = numpy.hstack((_expectation(X, m, c)[:, numpy.newaxis] for m, c in zip(mu, cov)))\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ncpdef numpy.ndarray covariance(numpy.ndarray X, numpy.ndarray weights, numpy.ndarray mu):\ncdef int i, j, n = X.shape, d = X.shape\ncdef numpy.ndarray cov = numpy.zeros((d, d))\ncdef double w_sum\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 36.5230062008s\n\n\nIt's almost two times faster! That's better, but we aren't seeing nearly the linear gain we would expect to see. This is because we implemented a data parallel algorithm, where the only thing parallelized is calculating the log probabilities. This is mostly because it's easier to implement. What if, instead, we implemented a model parallel scheme where each component is parallelized instead of the data?\n\nIn :\n%%cython --compile-args=-fopenmp --link-args=-fopenmp --force\nfrom cython.parallel cimport prange\nimport numpy\ncimport numpy\nfrom libc.math cimport exp as cexp\n\nDEF LOG_2_PI = 0.79817986835\n\ncdef double log_probability(double* X, double* mu, double* inv_cov, double log_det, int d) nogil:\ncdef int i, j\ncdef double logp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i + j*d]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ncdef void _expectation( double* X, double* r, double* mu, double* inv_cov, double log_det, int n, int d ) nogil:\ncdef int i\nfor i in range(n):\nr[i] = cexp(log_probability(X + i*d, mu, inv_cov, log_det, d ))\n\ncpdef expectation(numpy.ndarray X_ndarray, numpy.ndarray mu_ndarray, numpy.ndarray cov_ndarray):\ncdef int i, n = X_ndarray.shape, d = X_ndarray.shape, m = mu_ndarray.shape\ncdef numpy.ndarray inv_cov_ndarrays = numpy.array([numpy.linalg.inv(c) for c in cov_ndarray])\ncdef numpy.ndarray log_dets_ndarray = numpy.array([numpy.linalg.slogdet(c) for c in cov_ndarray])\ncdef numpy.ndarray r_ndarray = numpy.zeros((4, n), dtype='float64')\n\ncdef double* inv_cov = <double*> inv_cov_ndarrays.data\ncdef double* log_dets = <double*> log_dets_ndarray.data\ncdef double* r = <double*> r_ndarray.data\n\ncdef double* X = <double*> X_ndarray.data\ncdef double* mu = <double*> mu_ndarray.data\n\nfor i in prange(4, num_threads=4, schedule='guided', nogil=True ):\n_expectation(X, r + i*n, mu + i*d, inv_cov + i*d*d, log_dets[i], n, d)\n\nr_ndarray = ( r_ndarray / r_ndarray.sum(axis=0) ).T\nreturn r_ndarray\n\ncpdef numpy.ndarray covariance(numpy.ndarray X, numpy.ndarray weights, numpy.ndarray mu):\ncdef int i, j, n = X.shape, d = X.shape\ncdef numpy.ndarray cov = numpy.zeros((d, d))\ncdef double w_sum\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)", null, "EM took 30.6642620564s\n\n\nLooks like we're doing a bit better with a model parallel scheme than a data parallel scheme. This makes sense, because we can easily have each thread scan the dataset rather than constantly chopping up the dataset for the threads to see. Oftentimes data parallel schemes are easier to implement, whereas model parallel schemes can be more efficient.\n\nLastly, lets implement this with joblib. We're going to implement the model parallel version.\n\nIn :\n%%cython\nimport numpy\ncimport numpy\nfrom libc.math cimport exp as cexp\nfrom joblib import Parallel, delayed\n\nDEF LOG_2_PI = 0.79817986835\n\ncdef double log_probability(double* X, double* mu, double* inv_cov, double log_det, int d) nogil:\ncdef int i, j\ncdef double logp = 0.0\n\nfor i in range(d):\nfor j in range(d):\nlogp += (X[i] - mu[i]) * (X[j] - mu[j]) * inv_cov[i + j*d]\n\nreturn -0.5 * (d * LOG_2_PI + log_det + logp)\n\ncpdef numpy.ndarray _expectation( numpy.ndarray X_ndarray, numpy.ndarray mu_ndarray, numpy.ndarray cov_ndarray ):\ncdef int i, n = X_ndarray.shape, d = X_ndarray.shape\ncdef double log_det = numpy.linalg.slogdet(cov_ndarray)\ncdef numpy.ndarray inv_cov_ndarray = numpy.linalg.inv(cov_ndarray)\ncdef numpy.ndarray r_ndarray = numpy.zeros(n)\n\ncdef double* inv_cov = <double*> inv_cov_ndarray.data\ncdef double* mu = <double*> mu_ndarray.data\ncdef double* X = <double*> X_ndarray.data\ncdef double* r = <double*> r_ndarray.data\n\nwith nogil:\nfor i in range(n):\nr[i] = cexp(log_probability(X + i*d, mu, inv_cov, log_det, d ))\n\nreturn r_ndarray\n\ndef expectation(X, mu, cov):\nr = parallel([ delayed(_expectation, check_pickle=False)(X, m, c) for m, c in zip(mu, cov) ])\nr = numpy.hstack([ a[:, numpy.newaxis] for a in r ])\nr = ( r.T / r.T.sum(axis=0) ).T\nreturn r\n\ncpdef numpy.ndarray covariance(numpy.ndarray X, numpy.ndarray weights, numpy.ndarray mu):\ncdef int i, j, n = X.shape, d = X.shape\ncdef numpy.ndarray cov = numpy.zeros((d, d))\ncdef double w_sum\n\nfor i in range(d):\nfor j in range(i+1):\ncov[i, j] = weights.dot( (X[:,i] - mu[i])*(X[:,j] - mu[j]) )\ncov[j, i] = cov[i, j]\n\nw_sum = weights.sum()\nreturn cov / w_sum\n\nIn :\nmu = initial_mu.copy()\ncov = initial_cov.copy()\n\ntic = time.time()\nmu, cov, r = EM(X, mu, cov)\ntoc = time.time() - tic\n\nr = r.argmax(axis=1)\nplt.figure( figsize=(14, 10) )\nplt.scatter( X[:,0], X[:,1], c=['cmgr'[i] for i in r], linewidth=0 )\nplt.show()\nprint \"EM took {}s\".format(toc)" ]
[ null, "https://web.kudpc.kyoto-u.ac.jp/manual/sites/default/files/styles/large/public/thread_en.png", null, "https://lh4.googleusercontent.com/HXDr4afwx28XEZgogOWBMEcaU0updIy_BsRqOnq7kaGVq3kEyXMlwmrDTvi9ZlMRI7fdW4TT5sPO4z_9kSVxlhrUznOdvK_rHQtP6pfic8ABrVcm3lOWPEoMH8sDKK2fMhw1YLI", null, "http://twitwi.github.io/Presentation-2015-dirichlet-processes/gmm2d/difficult-soft.gif", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3X1wW/d95/vPAQGSoASSsGRTjkRSqh+Y25hSu55EknOz TlIriZNoMvljO92NpGZ7d3bubbZ1M1k58oOatrFkye6Oo6bb2+amvons3JnO3f7R64fGld3KTS1Z 2lUSifZOJdkRAcoJJfMBACUCJB7O/YM86DkH5wAgCZIg+H7NdCo8HRwyAP37nu/39/0apmmaAgAA AIAGEVjuEwAAAACAWiLIAQAAANBQCHIAAAAANBSCHAAAAAANhSAHAAAAQEMhyAEAAADQUIILefFT Tz2lH//4x8rn8/qP//E/qr+/X/v375dpmrr11lv11FNPKRQK1epcAQAAAKAiY75zcs6cOaNnn31W f/EXf6FEIqEvfvGL2rFjhz7+8Y/r05/+tJ555hndfvvt+o3f+I1anzMAAAAA+Jp3kGOapqamptTa 2qpCoaCdO3cqEonob//2bxUKhfTTn/5Uzz77rP7kT/6k1ucMAAAAAL7mvSfHMAy1trZKkv7bf/tv +vjHP650Ol0sT1u3bp3ef//92pwlAAAAAFRpwY0HXn31Vf31X/+1Dh48KHtSaJ4JIgAAAABYkAU1 HvjRj36k73znO/rLv/xLrV27VmvWrNH09LSam5t17do13XbbbWVff+7cuYW8PQAAAIBV4t577636 ufMOcm7cuKGnn35a3/ve9xSJRCRJO3fu1CuvvKLdu3frlVde0cc+9rGaniwa17lz5/gsgM8BJPE5 wAw+B5D4HOBfzDU5Mu8g5+WXX1YikdDv/d7vyTRNGYaho0eP6rHHHtNf/dVf6QMf+IC++MUvzvfw AAAAADAv8w5yfv3Xf12//uu/XnL/s88+u6ATAgAAAICFWHDjAQAAAACoJwQ5AAAAABoKQQ4AAACA hkKQAwAAAKChEOQAAAAAaCgEOQAAAAAaCkEOAAAAgIZCkAMAAACgoRDkAAAAAGgoBDkAAAAAGgpB DgAAAICGQpADAAAAoKEQ5AAAAABoKAQ5AAAAABoKQQ4AAACAhkKQAwAAAKChEOQAAAAAaCgEOQAA AAAaCkEOAAAAgIZCkAMAAACgoRDkAAAAAGgoBDkAAAAAGgpBDgAAAICGQpADAAAAoKEQ5AAAAABo KAQ5AAAAABoKQQ4AAACAhkKQAwAAAKChEOQAAAAAaCgEOQAAAAAaCkEOAAAAgIZCkAMAAACgoRDk AAAAAGgoBDkAAAAAGgpBDgAAAICGQpADAAAAoKEQ5AAAAABoKAQ5AAAAABoKQQ4AAACAhkKQAwAA AKChEOQAAAAAaCgEOQAAAAAaCkEOAAAAgIZCkAMAAACgoRDkAAAAAGgoBDkAAAAAGgpBDgAAAICG QpADAAAAoKEQ5AAAAABoKAQ5AAAAABoKQQ4AAACAhkKQAwAAAKChEOQAAAAAaCgEOQAAAAAaCkEO AAAAgIZCkAMAAACgoRDkAAAAAGgoBDkAAAAAGgpBDgAAAICGQpADAAAAoKEQ5AAAAABoKAQ5AAAA ABoKQQ4AAACAhkKQAwAAAKChEOQAAAAAaCgEOQAAAAAaSnC5TwAAAABOedPU0Xhcp1Mp7Wxv14Ge HgUMY7lPC1gxCHIAAADqzNF4XI9duSJJenF0VJL0aG/vcp4SsKJQrgYAAFBnTqdSZW8DKI8gBwAA oM7sbG8vextAeZSrAQAA1JkDPT2S5NiTA6B6BDkAAAB1JmAY7MEBFoByNQAAAAANhUwOAACoe43W UrnRfh6g3hDkAACAulerlsoLCS5qGZhU8/MsRyBE8IVGQZADAADqXq1aKs8lWHIv+E3T1OODg1W9 tpJqfp75BnYLCVSYz4NGQZADAADq3s729uKi27ptV+3Cvlxw4T5GwTR10BbU9IXDZY81l/Nx/zyX Jyf1xOx7nZmY0M72dp1KJqt+P7uFBCrM50GjIMgBAAB1r1JLZffC/mQioZZAoCTAKBcsuY+xPlh+ mfRmKqUPnjmjPV1derS31xHEPBmLOQKkfxgf1yvbthWfY53/8eFhXUyndTGdLj7fes0DnZ2O99se iZT/Jc2ab6CSN01NFQqO++Yyn4dSN9QTghwAAFD3KrVUdi/kT4yPSyrNZNiDpe2RiEzT1O6BAc/M yUgu57i9qaVF3S0tOp1K6WahoJFsViPZrA4ODpac3/PXrjle+2oioc9cuOAIvB7t7dXpVEoX02nP n+mnN244blcbLlTKevk5Go8Xf2+StCsandN8HkrdUE8IcgAAwIrnXtjb2QMgezByOBZzLMp3RaNl 3+O1RML3sWqyJV6BV7nzdgdZb05MVHwPSdrf3a2TiYTO37ihbWvX6uHu7qpe5/4ZWgKBOWViKHVD PSHIAQAAK549QzNVKDgyElYmw11O5c7cNBuGDm3Z4nmMStzZkj1dXY7yM7djV69KUjEAOZ1KaUck omeuXtWoK7jxew836+ezSuCkmcDqqaGhqjIq880A1er1QC0R5AAAgBXFb++HtZAvmKaOuB6XSsup 7mxtdRz3vo4Ofb2nR0fjcZ1KJrUrGlU8k/EtJ5OkkGHo/o6OkmzJo729MiQ9N1u21t3SoldtmaDr 2aweu3JFBdPU45s3F3+ub733Xsnxf6m1VXu6uhylY16/A/vPZ+fOqPj9/tz7nvZ3d+twLFb1HptK +6aApUSQAwAA5mW5NppX2vvht3/Hvdh/J5PRrmjUsU/miCtQ+ObmzXr+2jXfQCdrmno1kdBTQ0P6 ek+PnozFivtx9nR16X9+5CMKGIayhYI+e+GCXkskZNpe//y1a8Ug52g8rpFstuT4F9Np/WMyqUfl na2xfgd+5WHujIrf78/9e3OX81nP81Np3xSwlAhyAADAvCzXRvNq937Yg7DtkYgy+XzJc1oCAb3Q 31+87S5hezOV0r4NGzwzJO5zOBqPO0rU7A0Jnh4acmRyLKPZrHYPDGh7JKLnhod9j39ifFxH4nFJ 8jyX4x6v7QuHtW/DhpKMivtntErn3EEqe2ywkgUW8uJLly5p165d+sEPfiBJeuSRR7R7927t27dP +/bt0+uvv16TkwQAAPVnuRbB7lbKfq2VrSDsxdFRHRwc9Awy7Pt1DsdiOuPa3H9mYkIF09Q3N29W XzisvnBYD3R2lszM2R6JeAYax4eHVTBN39/NSC5XPL9LmYz/Dz17LHeAYrHaUEvS+mBQd7e2alNz s44PD+uXz57VocFBFcyZHNK0aTpea5XOWUGUxZ0B2tneXvw97R4Y0OFYrHhMoN7MO5OTTqf1xBNP aOfOnY77//N//s+6//77F3xiAACgvtVio/l8St7cj/o9u1zQdVsopIc2bSpmOexzbeysFtG7olHd 1dbm2GtyxJYlej2R8Cxpu5hOq+/MGf3bW2/17aLmpS8cLtnHczGdVndLS8XXjuRyGsnlHEHT44OD MmazSs0+v1/378trj82RKucRActt3kFOS0uLvvvd7+o73/lOLc8HAACsELXYaD6fkjd3K2W/1srl 2jM/tGlT2bk2bvb2z88MDUmGoXXBoP7dbbfpZCJRtr30O5mM/tjVUKCSq1NT6m5p0d3hsC7Zgif3 7Jy5sIKY+zo69NLYWMnjO1wZsYBhFBsxnE6ldCQe1xuuTJL990LAg3oy7yAnEAioubm55P7nn39e zz77rNavX6+DBw+q0zWtFwAANIb5bjS3Z28uT046Hqum5G17JOIIXtyLc4sVdP3B4KCytrKqtkBg QZ2/rPk1I9msvhGLVfWadKEwp/e4WSjo1USiZF+Be3bOXHxk7VpJ/zJH541EQpO234tX4VmljnR2 fgNYgeWwoD05bl/4whf0ta99Td///vfV19enb3/727U8PAAAaAD2vTLuEq/5lLz57QqxgrBfci3M u1taSrIMe7q65vy+S6FSaHRLoPql3D/OZmGeHhrSifFxR4AjScfee09db7yhT50/r9xsUOYOOpNV BlnHh4fZt4NlZZjmwj55f/qnf6poNKovfelLjvvfffdd/cEf/IGee+4539eeO3duIW8NAABWoK9O TupHtk5nvYahnkBA/U1N+nJzc8Uyp9+7eVP/ZMuMRCX92+Zm7Q2F9Fw2q4F83nGsv5ya0v85PV18 /v/R3Kz/bXZvy3ShoK9mMrqUz2tS0lRNf1J/zZK+HAzqOwvIzGwyDD3Y1KT/q8pjBCR1z/5uYxWW f9ubmvRf29r03UxGf25ra71RkrvwrtcwtCEQ0BmP7nWS9NvNzfqtKvYSAZXce++9VT+3pi2kf/d3 f1f79+9Xd3e3zpw5o7vvvrvia+Zysmhc586d47MAPgeQxOegkVllateHhyVbBuc/zM5oOZ1K6cTs fo6f/PjHvp+D8Pnz0mxplCSNS/qz6WldamvTqzdvSpJ+lM9r48aNerS3V79qmto0O+BzqlDQq+m0 /t90WutCIeVMU+/6LM4X07Sk5wsFhQOBOZeyWa6apr43h3MvyDu46QuH9bNMxlHSdyUQ0L333qsf Dg5KtoYM72lmQKn9uf233KK/ueeeYiOGy5OTjgxdPBLRvbY23XPB3wNY5pocmXeQ8/bbb+vIkSP6 +c9/rmAwqFdeeUV79+7VV7/6VYXDYa1Zs0aHDx+e7+EBAECDOeoatLk+GNS6UEivJxLFLmLWfo5P lzlOtd3Bjg8P60BPT7Gc7R1bm2VpYftbamFynsGNXdYjaKkmcDIkrQsGtW3tWg25AhxJKsy2ivba I+V+7s72dsf+LPsQUetxYKnNO8j50Ic+5FmKtmvXrgWdEAAAaEzuBbPV6ti9L+d0KlU2yPHrDuZe 7l9Mp3UkHlfeNPX7Hu2hG5U9wGkLBDyDKVMzv3+/rnAjuZweu3JFd5RpNOBuwy3NZOtM0yzOEdrT 1bWgJg8LNZ8W5WgMNS1XAwAAq0u1i8i8aWqqyszF5clJPZvP61dNUwHDKHmPr23apP8yNKQxVybG azF/KpnUmSUaUlqP5lsKZ3k3k9EtwWDJ71oqbcMtzWTrHrcFlAHD8PzfcKmCjfm0KEdjIMgBAADz Vu0i8mg8XmwxLKlk4bwrGlU8k9HF2ZKyi5I2xuN6tLe35D28Ahw/mXx+2cvSllMt+pq5f9fuDE65 luDHrl6VNFP+Zg1btX9OFjv4cWcPq2lRjsZAkAMAAOat2kWk+/6xXE4PdHYqnsloLJdTPJMpeY21 p8brtdX6B9fwSiyclcHJz+7bOT48XFJyaLmezeqxK1e0xtXq2vrfdLEzLe6BsOwPWj0IcgAAwLxV u4h0P0+ShqamdGk2uPHKtlxMp/XLZ89q0wLaDy98az8s9gxO3jT14IULjuycxavxwU3XbetzstiZ FivbZM8UYXUgyAEAAPNW7SLyQE+PTiYSjkXxqG3+isXdnviiqyMals/vbNyogmnql8+e1dDUlG93 uHL7gNyBknufVq0zLfaub1hdCHIAAMC8VbuIDBiGfrh1qz5ju/rvlb3xaomM5ReQHK2+5ysa/Jel p3uf1q5olEwLaoYgBwAALImAYajFtTfDS8gwdLtpKr4E54TqFKQ5BTh3trbqg2vWaHskIkPSc9eu FbNy1h4cd2laSyBAe2fUTOW/NAAAAFWyNqPvHhjQ4VhMhdnMjHW/u/uWl6xpakwqO6MF9aPVIzDp a2vTC/39eqS3V4ZhaNyVtTs+PKwdkYjjPpoCoJbI5AAAgJrx65Zlv1+S+sJh7e3q0kmfEqgbkm54 dFzD0vGbj+OW8Sgx3NHeXrbz2sV0WicTCX1z82admZigKQBqjiAHAADUbF6JX7csr65ZD/f06Llr 1+Z3wlh0c2nVbRcyDD0/W55WzquJhIzZvVqUqaHWKFcDAADFTMuLo6N67MoVHYnPb0eMu+TIuu2+ /2I6rQ2nTtE5rQFlTbPq/11PjI/P+7MGlEMmBwAA1GxeiV9L6f3d3XpmaMjRUW2+mQKsPH3hsPZ0 dXl2aDs+PCzTNPWmrWyNzA4WiiAHAABUNdTTXtK2fXbTuLWfYn93t47G43p+tvxsT1eXY7H6tCvA wephSDJNU4akv926VZ8dGHC0jr6YTuvxwUFJzn1cwEIQ5AAAgKqGeno1FbD+7c7SHJxdtD4y23Tg 2NWrjmO1BQK+wyTRWExJlzIZPT44qG9dvarf2bhR8UzGt6TtVDK5tCeIhkSQAwAAqhrqWa6EzStL 82Q8LtM09fuxWMljO9au1Y8mJhj+ucqM5HL6RiymO1pafJ8zbftMWK3HF9oQA6sPQQ4AAKiqu5q7 pK2SyUJBx957z/Oxv5/nnh/UP0Mz2Zty3p2a0q5oVC2BgC5PTjqyOs22z933p6f1Zx4tyYFKCHIA AFjl8qapBy9cKO6T8FpM5k1TBdNUXzgsaWbPjaSKrYLdQyDR+FoMw3N2jtvg5KQCgYBGXZ8Ra8bO 6VRKA9ms4zGvbGKt2p+jsRDkAACwSvgtBo/G446N4FLpYvJoPF7cZyNJBdPUP6VSGs/ldGdrq+4O h7Wzo0PfGx7Wu7Yhnuy6WX2qCXAk6fLUlOP23a2t+s3bb5dpmo7BsXZeDTH8BtBidSPIAQBglfBb DHpdHXcvJt3P+fZ77xX34VzPZrUlHNYjswvLY++9p3Q+r1bD0Gg+X/OfA43JMAx9vadHHzp71nF/ Xzisu9rafBti1Kr9ORoLw0ABAFgl/BaD7oBmVzRasph0P2fSFbz8UyKhDW+8oYODgxrJZnWzUNC/ 8rjqDvgxJX3wzJmS8see1lb9zT336NHeXs8yNL8BtFjdyOQAALBK+M3CsbePtubffOGttxwlbe4W 08/+4heOsrS0aSrt2lsRsz0OVBLPZDxL3U6Mj+tIPO5bglZN+3OsPgQ5AACsEn6LQXv76MOxmKOk 7R/Gx/Xxzs7iNPq/ueceBQxDp5JJR5Dj5VKZhgSAW7m9PFbW0W9fGXtw4EaQAwDAKhGY3fNgLRKP xOMlnajcJW2vJhJ6NZGQ5NzHc19Hh14aG1u6k8eqdnlyUodjMRVMs9gAw/55pMMa3AhyAABYRSp1 oqo0C+f48LD2d3erYJpaEwjoZoH+aVg8YUlpSRfTaT125UqxhbnFCsrpsAY3Gg8AALCKuDM1x4eH tXtgoHiV/EBPj3ZFo76vv5hO63MDAzo4OEiAg0V3W4VsjLWvjA5rcCOTAwDAKuLO1FxMp3UxnXZc /f7h1q06Mlv6sz0SKRn4ef7GjSU/bzSukGHoX7e3S4ahCzduqL2pSYl8Xql8XnHXPp29XV0yDKNk X5lfUw2sXgQ5AACsIvbmA5cnJx3ByzNXr+pUMqkd7e2yrp8HDENfuu02/X4sVnxepKlJ112T6IH5 ypqmXksmi7ffd3Xps9zZ2qpHfNpI02ENbgQ5AACsIn6d1CRpJJvVS2NjjoYCL46O6o7WVscxKnVV AxZDKp/3bSawnB3WaHpQnwhyAABYpQ709Oj48HDJ8EU3ghrUg21r19b8mLUIUGh6UJ8IcgAAaHB+ C7mAYaintbVikAMsp6Ckj3d26oV77tETg4N6/to1SdKeri496lO+Vq1aBCg0PahPBDkAADS4cgu5 5goLxDtaW0syOb/U0qLY1JTyi3CugNunb7lFL27dqsOxWHFGjiQdHBxccJlaLQIUmh7UJ4IcAAAa XLmFXLmhnutDoZJZE9GmJv1saqrWpwj4ujg5qYJpegYgC82a1CJAoelBfSLIAQCgwZVbyFkLslPJ pC5OTuodW9ZmJJvViKuL2nie/A0Wz691dGhgctLRve+dTEZH4nHPQbULzZrUIkBZzqYH8EeQAwBA gyu3kLMWaIdjMUdGpy0Q0CTDPrHE/j6ZVDhQOqv+icFBfaKzUw90dmpoNpO4p6trwVkTApTGRZAD AECDsRoNnEomNW2aajYM3dfRob+55x7fTdrusp9yAU5AEuEPFoMp789e2jT18vi4JOnQli0EJqiI IAcAgAZjbzRgsbI01uLQ3nFteySiTIUytLZAQFnTVNY0CXCwrOhehmoQ5AAA0GD8FoGnU6licGOf j+Pe5+CF0jXUi53t7QzgREUEOQAANBivDdrW/U+62vACK8VtoZAe2rRJB3p6dMTVFv1kIqEfbt1K oIMighwAABqMvWOafU/OgZ4e/fLZs1Udw5AUDQa1IxLR2YkJjeRyi3jGQGUPbdpULLd0ZytPjI/r SDzuuVeHrM/qRJADAECDmU/HKHc3NVPSWC6nj3Z2amdHB9kfLJu7Wlr05Q98wNFJzStb6VemWW4Y LhpXaY8+AADQsPZ2dXne77fn5lQyqa/39GhXNKpbg0G1ebT3BRZTT2urTqdSOhyL6YnBQe0eGFDB NPVAZ6fjeVOFgnYPDOhwLKaCaRbvLzcMF42LTA4AAKvII729MiUdu3q1qhK0qUJBTw8N6cRs+15g qb2WTEpyNsh4cXRUD3R2qi8cliR1t7QUP6PubM32SMTx2u2RSPHflLI1LoIcAABWkYBhKGAYVe+x +emNG7pw8+YinxUwd68mEr6PnUomdTgW0+lUqqQ9uj2EoZStcRHkAADQYCpdnZ5LuQ4NB7ASTZtm yawoy5sTE8V/U8rWuAhyAABYIaotral0ddqvxTRQ79YFg9re3q5Lk5N6J5Mp3t/d0qK9XV16c2JC O9vbdWq2xM3LzvZ2x7/t3wX7Y1jZCHIAAFghqi2tqXR12upSdTqV0lShwH4brBijuZyypukIcKSZ 0rVPRKN6ob9fknQ4FtNLY2PFx3dFo2oJBIoXByz274L7MaxsBDkAAKwQ1ZbWuK9OW12n7NkfKzjK Fgrq/Kd/8u2uBtSb8zdueN5/fHi4+Pn2Cl68sp7zabeOlYEgBwCAFaLa0hq/TI17MnzeNPW5gQEC HKwo7U1Nup7Nltx/MZ3WZy5cKH6+5xq80GmtsRDkAACwQpQrrXEv0PZ3d+vpoSEdu3rVcYwT4+P6 9Pnzam1qUjqf12tlOlQB9ejucFj//vbbdSqZ1JlUytEc48T4uI7E4/PKztBprbEQ5AAAsEKUuzrt XqCdTCR899qUa73r+b6SyPWgXryTyeijkv6//n4dsX3uLadTqXllZei01lgIcgAAaADuBZnfvoX5 IMBBPbmUTuuxK1dUME0Zmum4NmrL5ly6eVMPXrjgOxzUD53WGgtBDgAADcC9QNu2di1d09DQjr33 nkY89uZcymR0ydV9rZqsDJ3WGgtBDgAAK5C7HOfh7m5Jctx+amioOPHdXqK2PhhkyCdWPK8Ax081 WRk6rTUWghwAwKq2UjsqPRmL6eDgoKSZcpyCaerxzZsdz7EWbLsHBhz3rwuFHEHOna2tJXNHgHp1 azAoU6o6UN8VjZZt0rFSvvOYG4IcAMCqlTfNedXuz+d95rKoqub5z1+7VnLbHeRY3KVse7q6FDCM isNA72ht1Qfb2jRVKMy5WQGwWH4lEplTKWazYeiI7ftUME3HBQKJLmqNiCAHALBqHY3HSxZLi9FR aa6taWvdyvZAT48KplkMjF5PJNQSCOi+jg69USZ4CRqGDK5wo478WkeHmn0+k+uDQa0LhdTd0uII yqdN0/F96guHHa+ji1pjIsgBAKxaXoubWnRUcmdiTiWTJe9bLltTTSvbvV1denz2arQk5UxTn79w Qfd1dJRkfgKGoYBh6GI6LUnF///S2JjubG31/TkuptPF5wL14PTEhPzC7pFcTiO5nPZ0dekT0ajv 98+NLmqNiSAHALBqucu43LX78+XOxOyKRkvet1y2pppWto/09ur1ZLKYiXo3k9G7mYxeGhtzHMvi d7U6lc/P+ecDlstkoXJD82+/954e2rRJf3PPPQoYhg7HYsXvhTRzgcCYLdecbxc19vXUP4IcAMCq 5dUyttJCpZrFjTugaDYMHdqyxfGaL7z1lu9rqmllGzAM37Kd48PDMk1Tb05MFF/vDpwstJpGo7me zRYvIDza2zuv73kltS4pRe0R5AAAVq35tIytZnHjDiju6+io+BwrW2MPorZHIiqYpr7w1lvaHolI ks7YApdp0/Q8x4vpdLGUzXoPa6F3KpnUtGmq2TB0X0eHHu7u1mcHBgh0UPeCkubS+Ny6cLAYraGr KSnF8iLIAQA0vGpLS/KmqSdjseIG/b1dXXqkt9fx3GoWN9ZG/+eGhzWWyxUzK4/09srUTKB0KpnU rmhUIUlZzQQfh2MxmaZZEqD4/dsvk+N2OpUqLvTsv4uCaepwLKZYOi1DknfIBNSHnGbanf9ielo3 qyhbW8y9NtWUlGJ5EeQAAFaM+dbBV1tacjQeL7aWlaTHBwdluK4Cuxc3U4WCCqbpudHfmro+kssV jyWpeC7SzD4gK4vy0tiY1odCFX8eaSZw2dHe7thr4Me+APP6XQArRXxqSt0tLXrXY65TUNLHOzuL nQNrsb/OTzUlpVheBDkAgBVjvnXw1ZaWeN3vvu9AT49OJhLFwOTE+LiOxONVbfT3uu/8jRuO29VO cd8eiej1Mu2f+8Jh3dXW5liA5U1Tx4eHqzo+UI+mTdMzwJFmMj2vJhLFBiKL2QhgMUrgUFsEOQCA FWO+dfDVlpZ4bc53P9drw7+7RW3eNDXlUU5jHcv+HlvXrPEdtNkXDmtPV5fOTExoRyQiU9KbqZSm Z2felGvv3OPRGvpoPE5LaDS8E+Pj+uWzZ7VvwwYd6OkplojSCW11IcgBAKwY862Dr1RaYpXBnUom 9UBnp4ampiTN7Mnxeu4/T0467juTSulwLFZcPLmHjK4PBvV7mzZpf3e3norHi8MI93R1qWCavkHO vg0bSq4WH47FHOVudg90dqq1qUlThULx/e0ZLzZHo5H0hcPqaW31bJpxMZ12fE/ohLb6EOQAAFaM +dbBVyotsZfBSTNByUObNunhnh4dcV0BPhqPl5TLjORyjpa17mBiR0eHHtu8WYdjMccAz4BhFJsc FN87FNKO9nbfYKxcuVk8k9Fv3n675/BRqTRI7AuHtW/DBv3f772nd6anfY8LLIc2w9CkTwdBSTJN U/d3dCjhPK+yAAAgAElEQVSeyehyOi2vVgTVlo2i8RDkAABWjMWqg3cvekZyOR0cHNQ/2oZtWsFB uQXS6VTKs1TNyjhVU243mc/L9FjYTRcK+tDZs3rHZz+CJF3KZPTYlSta19TkuP/y5KQOx2L62qZN OplI6KcTE+oIBnXnbEZp7+236xuxmO9xgeVwoKdHfxGL6T2fx8dmG3qU41UiSie01YEgBwCwKtk7 tXntn5FKmwIcu3pV29au9T3mjkhET8ZiJaVqBdNUwTQ9y+22RyKOjm6ThYJeGhvTS2NjOplI6KX+ fj09NKRnrl6tuinBaD4vSWoLBDRZKBRLd/5+bEyvzWZ53s/l9E4mo5fGxvTNzZv1QGenb9kcsBx+ cP26fqmpSe/Nfp7d1oVCGsl5T85ZHwrpq5s2ObKhdEJbXQhyAACrkrtEzQoI7NqbmnTdFlhcz2Z1 YnxcD3R26qc3byqRzTqGE5pSSfmZlRV6Mh7XppYWPWBrcWvt0QkZhrIe2ZsT4+P6XBWDOv1e7/55 /tEnC/XctWsaKpMhApbD0NSUMq7Pdcgw1NHUpN/duFEBw3Bkcu5sbVUqn9e2tWv1cn+/goFA8TEr A5w3zZISVJoQNCaCHADAquQuFdvU3FycayNJhuRbGjY0NaVr992nL7z1liMzc2Ziwvf9JgsFXUqn dSmdVl84rB3t7XrwwgW9ViF74s4meWnSzEDRSvI++xsup9MMAkXdmSwUZBVRWoF81jQ1ksupKRDQ gZ4eGYah06mUtkcikma+gzvb230Dl/m2ocfKE6j8FAAAVpa8aepwLKbdAwM6HIup4LG4d9fl792w QYe2bNH64Mz1v3KL/ovptJ6MxUqOsbO9Xf/uttsqnt/FdFoHBwcrBjiSlKtisrv7arcfvyMR4KDe uTOVp1Op4h69F/r7FTAMHRwc1Iujo3rsyhUdicc9jzPfNvRYecjkAAAaTrmrtfZ20buiUTUbRnE6 esAwdOzqVc9jhgMBpW0Bx5PxuB7p6dE3N28uXj0+0NOjJ2u8gX/MZz8CsJpdnpzUE4ODMiS9OTGh y6627n7By3zb0GPlIcgBADQc9wLnVDKpw7FYscmAfY/LoS1bHAGQex9OketK8s1CQY8PDhZn01je LFOyBmBh1odCGslmi9lQP37By3zb0GPlIcgBAKwI9m5oO9vbtb+7W08PDXluIHZfrZ02Td8BmvaA 6Gg87rsPJ+1TEmZ1JHtxdFTHh4erKi8DMHdW5vWlsTHPx/vCYd3V1lY2eFmsNvSoPwQ5AIAVwV2C djKRKJlhYy1e3Fdr3cMx7exXfBdan38xnV7Q6wHMCM1esLDvxWkJBLSzvd03yOluadHlyUldnpxU wTT1aG8vndNWMYIcAMCK4A5A3F3H7I+7r9YejsUcCyOr1Wx7U5P+aXxcu8bHNTQ1pdEq59AAWFxe LdGtDM2zv/iF3rVlXNcFg/pXkYijDNUqZQvMdl+jXfTqQ5ADAFgR3CVo29audSxqvGrwvZoMTJtm 8XXXs1nf8jQAiyegmf01nvvfbMKSPnnLLZo2TZ1KJnUkHlfQFahkCgXFPb7Hz1+7Vsyu0i569SHI AQCsCAd6elQwzeKwzf+1vV33d3TozYkJbY9EVDBN7R4YKF6xzZmmPnT2rCOI6QuHl+v0AdgUVHqh wkv/7OBcq1T1pbExuXMxNwsFz1LRn7kCH9pFry4EOQCAFSFgGAoYRnEx841YTLuiUf1w61Yd8WgZ fTKRKMnSsGcGqB+Dk5NqCwQ0WaZZh6nS4MRvrlNfOKzRXE4js9khd8kb7aJXF4aBAgBWDPdi58T4 uI7MdlxzP8+9Z8euLxwuyepw1Q9YWpenpsoGOJL0TqHgG5w0uW7v27BBOzyee2swqENbttAuepUh yAEA1K28aepwLKbdAwM6HItpeyRS8hxrU7Hd5clJtTe5l0D/YmhqSptaWnR3a6vuamnRLcGgcjU/ ewALtcYwdKCnR4e2bNH6UMjx2Cc6O3VoyxZ9ft26YhDjFRD9SiRCp7VViAtXAIC65W4bfUdrq0KG 4ShDsc/EOD48rIvpdLEsza8UZrJQ0Guz820ALL51waB+de3a4lypahmmqS+89ZZ2trfrvR079Pm3 3tL5Gze0be1avdzfr2DAeb3+QE9P8e+ApZngZlUiyAEALAv3cE+v9q7uMjR729iQYai3pUVvJBI6 opnFzelUyrG4aWtqqlgOA2DxrQ+F9PLWrfpfzp51fI8rGZI0NDpa3Gv3d9u2lX1+wDC0b8MGx/Df +zo65nXOWNkIcgAAy8KdpZFK27u620bbZU1T72QyeieT0cvj4zqZSOj+jg7H80eYewPUhaGpKfX/ 9/9eVYBzV0uLAoGAfpbJOLK21XZHcw8DZi/O6rSgIOfSpUv6yle+oi9/+cv60pe+pOHhYe3fv1+m aerWW2/VU089pZCrfhIAAKl0weK1gLEvVv755s2yM21OjI/LNE31hcMaqmJDM4ClM+nT5tnLeKGg kampkvunCgVHm3i/PTbuYcBYneYd5KTTaT3xxBPauXNn8b5jx45p7969+tSnPqVnnnlGf/3Xf63f +I3fqMmJAgAaiztLY20YtpoNWFdh93d36+mhIRUKBY3lchrL+bcImGu9P4DlFQ4ElHZdkPDKwK4P BoszdV4cHdXJREItgUCxGcmZiYmKwQ9Wl3kHOS0tLfrud7+r73znO8X7zp49qz/6oz+SJH3iE5/Q s88+S5ADAPDkV1Ly/elp/ZmtjO1kIuE7MNCQ/8wMAPUpKKl5timIO8Dxsy4U0ojtAoc94LH4lb1i dZp3kBMIBNTc3Oy4L51OF8vT1q1bp/fff39hZwcAaFh+JSUD+bzj9qlk0vcYBDjAypOTlKsiuFkf DGpNPq//0NsrQ9Ljg4MVX1Ptvh00vkVrPGCa/KcHADB3/U1N+pEt0Lk5z70164NBTRYK7M0BVoC+ cFh7u7pkyll69pMf/1j3bt6sgmnKMAydTqU0VSj4Znf9Bodi9alpkLNmzRpNT0+rublZ165d0223 3VbxNefOnavlKWAF47MAic8BpC/PVgkM5POKFwqKVXHRzKtsbaTM3h0A9eWTuZw+M1tu9qAkjYzo JyMjkv7lvwufnv2/gmnqruZmDeTzuqepSTJNvVUoqL+pSbvef1/nZl+H1a2mQc7OnTv1yiuvaPfu 3XrllVf0sY99rOJr7r333lqeAlaoc+fO8VkAnwNImvkc/Nf77pMkHY7FHPMu/FA7AKws64NBx4WI ofZ23dvfX/I8v/8ufHhRzw71aK4XQecd5Lz99ts6cuSIfv7znysYDOqVV17RH//xH+vAgQP6q7/6 K33gAx/QF7/4xfkeHgAAR3OCHZGI/svQkMZde3YA1C93MHNbKKSHNm1SwTR10LbHhjIz1Nq8g5wP fehDeu6550ruf/bZZxd0QgCA5ZE3TR2Nxx3dzmrZirXS8a3Hfzg5qc/EYjrQ0+PI0BiGoRQBDlBX ok1NMiQl83m5v52fbG/XJ2+5xdEw4KFNm/Rob68KpqnA7B6b7ZGITNPU5y9c0LRpqtkwdF9HB0M8 sSCL1ngAALCyHI3Hi6Vhi9GK1ev4X+/pKQY+9s3EP7KVqNlfE6jZ2QCohY92duqF/n596vz5kmYA n7jlFj3S21tsGLA9ElHBNEsGenqVpb40NiZpZg8OMB8EOQAASaWtV2vditXr+E/GYo6SlUrvz94b oL5YZWYhj8eejMd1oKeneLHEHszYL6T4/a05nUoR5GDeuCgGAJBUWhNf6xp5r+M/f+1a2ee7X9Ma 4D9bwHJxf/se6OwslpRlPZ4/WSjoswMDxdvumVfWbb+/NezTwUKQyQEASHJu8rdKSRbj+KeSSU2b pk4lkxp1tXleHwrpg/m8Wtrb9czQkCYLBUWbmorNBtKFgoKaGSYIYHE1SfpkNKp4JqOL6bSsiVPr gzPLx3gmoydjMT3S26uQz/698zduFPfbnXFlbKZn28O7/zbY9+T8hHbQmCeCHACAJClgGDXdg+N3 /HJtoX9lzRpdTiYVSySK9026nkOAAyyN5kBAH2tv1w8yGcf9Vre0kVxOjw8OyjAMZX3mWW1bu9ax H89x/NnAaLH/9mB1IsgBACwpd/19Xzisu9rayk4xB7D00oWCfj8Wq/i848PDuqO11XFfs2Ho/s5O vdzfry++/bbn6+7r6KjJeQJeKG4GACyJvGnqcCymy5PO3My+DRv0Qn+/WthvA6xIF9Ppkj0539i8 WX+3bZuCgYDn3pq+cJgW0VhUZHIAAItqulDQ5wcGdCqZ1M1CoXh/XzisfRs2FBc6O9vbix2XAKws zYahQ1u2eO7pO9DTo5OJhCNTu2/DhprO4QLcCHIAAAtSacjn5wcGPMvQxmfr+vOmqSPxuE4lk9oV jSqdSunT3d0ypOL8nNeTSd+afwC1dUdLi5oMQ1empkq+dyGf/Tf3dXT47qsJGIZ+uHWrjrj+TtTS Yg8zxspDkAMAWJBKQ0R/OjHh+brr2aweu3Kl5Arv/x6ambjx3Gx76S91dck0Tb3maj8LYHEk83k9 tGmT7wwru5BhqNkw9A/j43q4u1tBn7LTxW4usNjDjLHyEOQAABak0hDRjmBQ79taRQckFWyPn79x w/H872ezStsWV79fxUILQO2M5HK+M6zcWZysaSprmno1kdDtp07pq93dy5JFWexhxlh52OUJAFiQ SkNE+9raHLfDriu929auddxO1/DcANTe+mBQn1+3Tmtc3+WRXE6PXbmiI/H4kp/TYg8zxspDJgcA sCBeQ0Tt9fHTriu/VvMBq/HAw93dempoSMeuXtX1rNfcdABLbW9XlwzD0OlUSm+mUhqxfTfXhUJ6 ob9fnzp/3nO/3XJkURZ7mDFWHoIcAMCCeNXauwd+7opGdf7GDUcQc2c4LEn64ttva2d7u77ygQ/o G1XM5ACweOxdD62Ss0ODg3rcVja6t6tLkvRyf78+69E5cTmyKAwUhRtBDgCg5k65mgQ0G4Ye2rTJ EficmZjQS2NjkmY2Cj/Q2bmk5wjUM0PScvQTvKutrRgs2DOyu6JRNRuG7uvoKGZJgoGA/m7bNhVm OySSRUE9IcgBANScu0Rt2jSLC5/jw8O6mE47yl8k6cLNm0t2fkAl0aYmjefzS/JeawIB7Whv12uJ RPG+5QpypgoFFUxTAcNwdCyTpENbtujrPT0lAQ1ZFNQjGg8AACqaLhT0qfPn1fXGG/rU+fPKFQpl n9/s6qzUbBjFhdBdrkYEFncDAmA5LVWAI810G/xoJFJyn1tfOKz1wequT7f5tHKWShd/9m/rifHx YuMAr45lVuDz4ujoojYZyJumDsdi+urkpA7HYiowJwtzRCYHAFCRfaDnifFxfXZgQH+7dWuxlGV7 JCJD0psTE9rZ3q4d7e3FUjRJ2tHericGB/X8tWsa9Wgu0BcO6+X+fj144YJetV3NBlaDdKGgw0ND FZ/39kc+ogcvXPDc7O/2ic5O3dfRUfx+mqapH1y/LkkyTVOXMpnic28NhRz75azgZmd7e3HmjHV7 qVo127NIP5r9/2SLMBcEOQCAityzbM7fuOE5fM/69xObN+vQli3FkhbTNB0bl932dHXpqaEhDU1N Lcr5AwtxR2urfjE1pUmPbMIDnZ1qCQQ0VSjopzduaMQ2E2ouKr0qoJmFvz3A2RWN6mPt7fp9j4Yd Vomo1TzgcCymi2nvBu3b1q51HNdqHODVsexIPF4S+CwG5t5goQhyAAAVuRdB29auLbvoeHNiQi/0 9xdv7x4Y8H3urmhUkhy1/0A9eTeT0Z2trXrHlv2QZjKQr2zbVgwkdg8MOAKAhXDvybklGCz5zr2e SMg0Tf1Rb6/OTEzo4uRk8RytsjMr++F+bV84rLva2rSzvV0Pd3frSDxeHABqmmZxX447e3Kgp0cF 0/R8bi15ZZGAuWBPDgCgopf7+7UrGtVtoZB2RaN6ub9f2117COzsC5K8aWqqzB6eN5JJ/VGZLA9Q DwzT1B2trY77RrNZx36RWi7Eb3HtvXlo06aS40+bpl5NJPSjVEovbt2qD65Z43jcHti4X7tvwwa9 0N+vR3t7FQwEFDAMXUyndTGd1uODg757bQKz++uqee5CHOjp0aEtW/SxpiYd2rKFjm2YMzI5AICK rFaxdn7XbXdFo44FibvEJiDnpurJCk0MgHpweWpK39y8Wf+YTBY/zyO5nA4ODhYzHgd6enQykahq z0wlD23cqKZAoKQts9fxrXLS7ZGII/thvxBRaVjmXMrDlqKUzPqdfnpkRPeyFwfzQJADAJiXNycm HLdvC4X00KZNjn0AUukCiJAGK9W333tPUY/uZtZnPGAY+uHWrfrls2d9979IpaVoIcNQ1rbfZ1c0 qsc2by4pAcubpuKukjlJKsx2Isu7LhiYtmNWavNcTXmYNTfn8uRkyWuBekO5GgBgXtwLm4c2bSrO 0Ng9MFAs42EBhEZxPZv1DF7sn/GAYWjfhg1lj7POFSi5A5wfbt3qucflaDzu+f4juZweu3JFf/rz nzvut7qpVcMqD/v8unW+5WFWsxHrHPrCYUrJULfI5AAA5sWr/OVwLKaDs/trXhwdlWmaemT26rE1 BNTSFghQqoa6tq6pSdvWrtU/JJMlgznXB4NaFwppT1dXySLfuv1GIqE3JyY0Zuu4dmdrq/Z2dekb Hh3RJKklEJCpmW5o7oGb7qzomkBAN23fofQCvk/VDPR0v/9dbW20dUbdIpMDAJgXa1FkbV4OGEax 45LlW1evSpqZb/E/P/KRYic1ib04WF6thlHxSu9oPq+/9whwJGldKKR/3r5dj3uUlVnfjZe2bdN9 HR2Oxz64Zo0e37xZ39y8eWa4ZyjkeHxne7vvwE13VtR9bPfje7u6KvyEc+M+Plla1DMyOQCARTOS yxXb2JpSyX6CJklLN1ce+BcZj5k3i8Frr4u9Q5nl7tZW9YbDOpVM6h1XSZqVQbFnT7dHIirY9ujs 7erS13t69NTQkG9zgYWq1LwAqCcEOQCAmtnT1VUsV7NYCzSv/QRbPGaPAMvJ3QTAz54qsyT7u7t1 MpHQ+Rs3tG3tWj3c3S2ptPTLMAzfrmxWxsReUmYvDbVeHwwEHOVj+dmGBO6yt/mqpqQNqBeUqwEA aubR3l490NnpuG/HbBtbr2GEb3/4wyWzR4DlEg4ElProR3VoyxatCZQukcKGob5wWH3hsCQV5+OU 8/TQkE6Mj+t6NqsT4+N6amhIUuVSrzWBgPrCYT2xebNnxqSaNs5+ZW/AakCQAwANyLqCa+9ythSv DRiGPubaJ1BuUOIfX72q36zxvgFgvtKFgn7l3DlJ0qaWlpLHb29uLg7BPFjlEEy/YMTdzcy9f+Zm oaCL6bSM2dI2t2r2xyzFPBugXlGuBgANyLqCK6m4H6DaMpOFvFaS/h9X29ofXL+ug7Y2s1aXtYvp tB67cqV4VRyoB9bn8oHOzpLyyp9NTTluHx8erlgK5jd/xl36VTBNmZKOxOOOjml+gUk1+2OqmX0D NCqCHABoQAu5grtYV3+tRd3pVMqxeBxyLRyBenDh5k2tD4U0ks36PscK1l8cHVXBNIttnu1BT7Wb 9a1mBDddXQf9ApNq9sfQKACrGUEOADSghVzBncvkc/eCLm+a6m5pcQQx5mz5m/Wc7ZGI4/i0kkY9 ul4muPHy/LVrxc+9PQM6l836XvvWFhKY0CgAqxlBDgBU4LegX27lzmshV3Crea1fSdvReFyvJhKO 517KZPTYlSs6mUio2TD0z5OTc/9hgWViL6c0TVOXquwGOJ8MqPsCw74NG+ribw2wEhHkAEAFC92j sljKnddCruCWe60VWB2bHfJpsRZ05RZ2fu1xgXrW09qqv9u2TdJM22brO2e3KxrVv+7ocLR0ns/+ F8rLgNohyAGACuq1Q9FinpdflsgeWNldnpzU4VispBQNWOlCUnHWzI5IRN/cvFlvplKaNk01G4bu 6+goBiPuPTlzRXkZUDsEOQBQQb12KFrM8/LLErkDqTWBQLHV7WNXruiJzZt1aMuW4oLQlHRmYkJT hQKZHKxIZ2/c0Muzn90XR0e1KxrVD7du9Swjq5QBrbeSV6CREeQAQAX1WkKymOfllyVyB1abXE0G TqdSenHr1pLjFUxTXW+8oZFcrmbnCCwWax/OxXS6pLvaifFxHYnH55RxqdeSV6CREeQAQAX1WkJS 6byquXrs9xy/LNH+7m6dTCR0/sYNbVu7VgXTdAQ507bBoe5j3xIKOYKccCCgNsNQxjTVYhgay+cX /DsBamFPV5fOTEyUzMmxzLU0tF5LXoFGRpADAMuk1iUs04WCPnfhgk6nUgo3NWnbmjV6bbbTmd/V Y78rzFZW6FQyqWnT1KlkUodjMZmmWSw7OzE+rjbX+f50YkKHYzHt7+7W5wYGis99cXRUd7S2Op6b LhRkLSFvSrqztVXxqSlHoAQsB0OlWUu7uZaG1mvJK9DICHIAYJlUU8LiDoT2d3fr6aEhz8Docxcu FNs33ywUigGOxeqIZj/GZVc7Z+sKs5UlsneTemlszNFOV5ImXQHJ+7mcHrtyRc/+4hd619VqN1Wh VG08m1WWAAd14Llr1/TWhz8sSSX7y+yloeUuVNgf2x6J6InNm/Wm6/UAFg9BDgAsk2pKWNyB0MlE wpEdkWYCo7xp6vVksuz7Xc9mi/Nq/JoAuK8wu8+p3PR3O3eAI0mVitFGKVdDnbiYTutIPF4MWAzD 0MO2iwNH4nEd6Onx/H62BALa2d4u0zT1+GxL6RdHR3Voyxa90N+/XD8SsOoQ5ADAMqmmhMUdZJy/ ccPz8aPxuGcWZFc0qvM3bjimt7uPIc1stN63YUPJFeaSkp0FZFrSNB3ACvL8tWvFPTleFxiODw+X vMb+uDvryT4cYGkFlvsEAGC1OtDTo0Nbtujz69bp0JYtniUs7sBn29q1jttThYJ2Dwx4Lrh+rbNT P9y6VQ9t2lT2GJJ0V1ubHu3tdZTaHI7FdCqZ1K5oVJ+75RYd2rJF65uby/5M64PBkr03Fu8t3MDK 4L44cDGd9m1M4IV9OMDSIpMDAEvIq4bf1Ewm5gtvvVVS1+9uE/1wd7eemi2ZyeTzvmVn1iwPUzPt m62ryt0tLQppZpP/O7aSMmuYp9/Qz7ZAQJcnJ5V3ZXLuaGlRb0uL/n72KvVILqdbgvynBSvbHa2t 2tPVpYOz5WbSzMUBr+9bXzisu9raSmZB7enqmtNwUGbpALXFf4kAYAlYC5jjw8OOEhiLXwMCrzbR 1u0PnjnjuH99MKgdHR3FBgVHXO8nyfHvXdGo4plM8Yr0Y1eu6PjwsPZ0den4L37hOPZkoaBLHvts 3p2aUtK1l+bq9HQVvxGgfn3Qltl0X2Bwf6d6ZjOX93d06F93dDiaE8wlSGGWDlBbBDkAsATcmRGL V52+131WkGS1dG42DI26mgCsC4X0Qn+/8qapBy9c8M3yWFoCAd3V1lYSBNmvXlcjXSg4bk/abv9a R4cMw9CFmzfVv2aNTNPUPySTooca6tnJREKfuXBBL/f3y5jNbH7x7be1s71db334w8Vsqj17s9Dm AszSAWqLIAcA5mC+JSV+CxarTr9SAwK/IMkuZ5raPTBQUjbjx+u952PaFeTYnb95szgA1N3SGqhX N2e/Q7efOqVfjUQcgYy9g9opV0fDhQQmzNIBaosgBwDmwKuk5OuzrWTLBT7bIxHHAubu1lb95u23 O+r0y9XuuxdTXt7NZDxbN7u1BQLa1Nysgmlqf3e3TiYSOplIzHtGTbmm0iN0VMMKNpLLlVwwsAc8 u6JRx2MLCUzc+++YpQMsDEEOgFVnIRt8vUpKqqmlN91DM6endezqVZ1MJPRyf39x1o27AYHVlOBM DUtXrP01BwcH9b1f/ELvTk35Pnd9KKSHNm6UJH37vfccraiB1e6nExPaFY2q2TB0X0fHggITr/13 AOaPIAfAqrOQDb5eJSXV1NL/4Pp1x+3xQkGaLYn57MCA/m7bNs/zklSxTM2LISloGBWzM+UCHEna 0d6uxzdvljSzCJvPuQCN4LZQqKTD2vuzmZ5DW7YQoAB1hiAHwKqzkA2+9pKS7ZGICqapy5OTjufM tWTFmr/hPo/DsZg2tbTM6VgWU5p3+Zndq6Ojan79dRVMU73NzYo2NWnc1U0NWA1+Z+NGPdrbqyPx uI5dverIatIkAKg/DAMFsOq4g5C5BCVWSckL/f0KGIYODg4Wu5P1hcO+Qz33dnX5HrO9qanYMMDu ZqFQMmywLRBQyDAUXqL5GRnNBEt5ST+bnibAQUPzG2QrSa8nEvrCW29Jmgl47GgSANQfMjkAVp1a bfB1X729a3a2hp19/88DnZ0ampqSaZrKm6ZS+bzykt7JZIqDOUMeJWbW/Jt/vnmz+Dz3zpiAJP8e ZwCq8W4m45gfZffqbHfAF0dH9cTmzTq0ZQtNAoA6RpADYNWp1QZf9/6c7ZGIDsdijoWPu/VzXzhc 7Kp2xKMttFeJWTKf15lkUqNlOpUR4AC10WwY2tPVpSfjccfMJ7s3JybmPQ8HwNIgyAGwIi2kQ1qt uDNCBdMsaRzgzvZcTKeLz6m2jj9rmnqfVszAkpg2zYoDcSlPA+ofQQ6AFWkhHdJqxZ4RypumPnT2 rONxK/jxGrb5zNCQ1oVCS3KeACprMwx9tLNTft/KXdFocQgo5WlA/SPIAbAiLaRD2mI4Go+X1PBn 8nnlCwX1hcMazWYdgzFHcrnibfbTAMsnpJk9bpOmqRPj43qgs9PxeF84rH0bNixLthjA/BHkAFiR vObV1EK5Mji/x/KmqePDwyXHejWRKG5WlmY6o3nV+BPgAMvIMCTbXrgh1+yovV1dzMABViCCHAAr 0lw6pM1l/065Mji/x56MxUqyOF78NjEDWD6V5km9OTGxRGcCoJYIcgCsSHPpkFbt/h2vjMzpVEp5 0+AyF98AACAASURBVNSTsZiOxOOOx45dvaqTiYTeSCbn8yOgRgzNDD8FyglKqqZ9x6bmZsdFix2R yKKdE4DFQ5ADoOFV2r9jZXqODw977qv5zPnzjrIzy/VsVifGx33fd00goB3t7RrKZDRm24OD2iLA QTXs3747WlsVNAzPDOz5mzcdtyt9vuqh0yOAUgQ5ABpepf077lk2dl7BTbVuFgp6bQGvB7A4hqen 9UhPj0xJz1+75gh23BcjzlQoV6uHTo8ASgWW+wQAYLHt7+7WrmhUt4VCuiUY1LeGhvSp8+eVm90j U8vObCHD0K1Brh8B9exmoaDHBwf1j8mk7gyHtb5MO/dKTU3qrdMjgBkEOQAaWt409bmBAZ0YH9f1 bFZjuZzez+V0Ynxcnx0YkFS6iFlfZZASMgy5i1Kypqlta9fW4tQBLLIT4+N6aWxMI9ms4/4HOjv1 +XXrdGjLloozcdx/PxgUCtQHLjcCaGhH43HffTPnb9yQVNqp7eHubj01NOS5R8fOryvTT27c8G0X DWD5VPu9vL+zU49v3lzVMefS6RHA0iHIAdDQypWObF2zRpJ3p7ZHe3t1OpWqqjW022gup1uamjQ5 51cCWKi+cFh3hsOaNk39JJXSSD5ffOzjHR36aGenTqdSmioUfC+AVNqHYzeXTo8Alg5BDoCG5m46 YHe/a7K5u0vSjkjE97WVjNkWVgCW1o72dhmS4pmMRmwXKj7a2VkMSAqmqSOz33d3wDNVKKhgmnRJ A1YwghwADc1eSnJ5ctKRmXFfrX0yFtPBwUFJM12S/rC3V4e2bNGpZFIXJyf1TiazZOcNoHohw1DI MDRZKOhiOl38Hlv6wmHt27DBUUpmz8AUTFOfuXChGOicGB/XkXicDA2wghHkAGgI9izM9khEhmYm ldvnVhyOxRytoq0Nwtawzz+KxRzHfCIeV0cwqHXBoPZ2dSlgGDp29SrzboA6kzVN3z1yknR1akqF Mo8HDEMtAWcvJqvU1WsOjikxGweocwQ5ABqC16wK+78f7e313SB8NB4vufIrzSycRrJZjWSz+kYs pjtaWzVOgAOsODcLBR0cHHRkb9wXRjKuElPrIojf3xZm4wD1jSAHQEMo12DAeixgGPp6T4+OxuM6 lUzqMxcuqNkwdHmyuhYB71KuBqxox65elTRTxuoXvEjSrmjUcVHEzutvDbNxgPpDkAOgIZRrMGCf W2Ff2ABYXa5ns8Xvf7nApCUQKJafuf+2WH9PvO4DUD8IcgA0BPtVV2tPzulUStOmqVPJpA7HYjrQ 08MVV6CBhQ1DbYGAMqapHZGI7u/s1A+uX9fVqSndtM3HsUpWq7kwUm4ODrNxgPpFkAOgIXjNqrA3 GnhpbExS+YyPl5BhqCMQUCKfF7txgPpxd2urxnI5RyOQtGkqPbu35rVkUp+IRvXP27d7Nh3xujBi b1Zi8ZuDwx4coL4R5ABoWF619H9zzz2S5NkWek0g4LjaK802H2DmDVB3esNhXbLNtlkfDJZ0Pnzu 2jU9tnmzZzaGIZ5AYyPIAdCwvGrp7Qub3QMDjiDHv8EsgHqyKxpVs6tl87pQyLe9OwENsPoQ5ABo CF6zLNxXb/d3d+twLFa8vSMScQRBk64sDoDld1dLi3rDYQ1NTUmS9nR16es9PfrcwEDJc+9oadG7 s8+TpO6WFhVMkxk2wCpEkAOgIXi1g320t9dx9dZel//i6Ki+uXmz+sJhXUynl/6EAVQlWSjo/s7O 4p6ZgGHoaDyuE7ZSNUnF7/Gdra3FDO2riYSOxONkcYBViCAHQENw77+xOqrZMzvu55yZmNCeri7P QaAAlp6h0rLR69ms4zv64uio+sJh32OkXHvo6KgIrE4EOQBWBK9yNHsJinv/zZlUqthR7cXRUR0f HlZPa6vjmG8mk3ozmVyaHwBAWSHD0P0dHXo1kVjQcdqbmnQ9my3eZoYNsDoR5ABYEfzK0SzW/pvj w8O6mE6XbEC+mE7rYjqt9cGZP3sjrtazbkHDUM6kFQGwVLKmqVcTCe2KRtUSCOj9REJnfDob7u3q kmEYOp1K6dLNm7pkayBydzisf3/77cywAVY5ghwAK4JXO2g7q3vS6VSq7B6bcoGNHQEOsDxaAgG9 0N+v//4//oc+OzWlEVtWZk0goEd7e4uZ3Lxp6sELFxxBzkc7O9mDA0CB5T4BAKiGu+TEfjtvmjoc i2n3wICmXB3SQnRVAlYU67sdMAz93saNjsce6enRo729xVJVdwOCXdEomRsAkmqcyTl79qweeugh 3XXXXTJNU319fXr88cdr+RYAVimvYX7WPh2rRM1ilbtsj0R0cnxcr7HvBqhrd7a2KpXPa9vatXq4 u7t4/yO9vcWyNK/SM3dGtyUQoF00AEmLUK72kY98RMeOHav1YQGscl7D/Owtoe2scpfDsZhvgBOU VF3hGoBauCUY1JirXLQvHFZPa2sxG3NifFxPDQ0Vv+uVhnh6DfytVqVmJgBWtpoHOSZ17ACWiF9r WGuhU6517K7OTl3OZHQlk5H31mZgZfBqu7yU7x0OBKoapLt97Vr9bGqqZM/c+Rs3HLft39tKgYhX hrdalZqZAFjZah7kvPvuu/rt3/5tJZNJfeUrX9F9991X67cAAEmlV3H7wmHt27ChuNBxP26XMwxd 3L5dX3jrLd/nACtBk2EoYJqaXqTjByT5hTCmZvbJBAxDp5JJTRUK+vtEwvP5OcPQvg0bHNlXryYh 9mxMpUCkUqannErNTACsbDUNcnp7e/Wf/tN/0oMPPqihoSHt27dPJ06cUDBIEzcAted1Fdd9lfdk IlEyGV2aKYs5Eo+XDYSAlWA+nQDDhqG0z+vcj0WDQUWDQb1j62Bmd2ZiQi/09xdvf/DMGc/gJZ7J FPfbnE6ldHly0vG820Ih/c7GjTJNU7sHBtQzNaWYq9zUHYgspORsIaVuAOqfYS5ifdm/+Tf/Rt/6 1re00dUdxXLu3LnFemsAK1zeNPX96WkN5PPqb2rSl5ub51UvXzBNfW/2OPFCQTHbn7xew9CDwaC+ m82yPwerSo+kuM9jzdKcskK/3dys32xu1venp3Uhl9Ogaeqqz9Ki1zD0uVBIX25u1vemp/Vn09OO 40hy3Le9qckxK+e3m5v1Wy0txdvPTk2VHMP+eDn2vw0L+RsDYOnce++9VT+3pimWF154Qe+//75+ 67d+S++//75GR0fV1dVV9jVzOVk0rnPnzvFZgONzcDgW05/Nlqn8KJ/Xxo0bfctS8qapJ2MxPX/t mqSZQYGP2NrMfnj2ee5GBTHT1J/bZnAAtVau1KsarYahzCJci7y7s1PxRMLzMdMwpArvuT4Y1LpQ SHu6uvRob6+OxOPF72s5MdPUn01Pa+PGjfp2T482urIwX3jrLcmWXVnf0aFDHR2+mZo/GBhwPD8e ieheW1apkg9XfgqWGesDWOaaHKlpkPPJT35SX/va1/Taa68pl8vpD//wDylVAzAv7rKUY1evSpJn OcrReFwHBweLtx+f/fdjmzc7nnegp6ek3TSwmBYS4EhyBDhe3cnma2hqSutDIcegTUuzYSjrEeQ8 0Nmpn9y4odFcTiOz/yfN7IuZ636W06mU534adwnZfR0di9ZdDUBjq2kEsmbNGv35n/95LQ8JYBX4 /9u79+C46vv+/69ztKvdlSWtVjaWqK1buCj9EtlJ+RXfmhAIJgmXyXR+Q4am2G06k+lMf6FpmmIM NqT5BgsbOk2ZJP02GcgvMTTDNGQyrYGSmPyCS2ob83UaW/AtBhxrVybIRrJutla33fP7Q9plz9mz N2klrVbPx0yn2asO9mp9Xufz/rzfibr6F0ZH9alwWDubm9NOXs5PTmrXmTOKW1bypCpxZdftBOsf zp7V0ZERbaqt1T1NTXq0p0eHh4ZmtX8BKAWbamu1ORjUN86edQ0nqa6srNRvJiYyhqxsQX9Tba1u CIV0eGhIE5alSsPQ5mBQccvSi47Vn3/o6ZEh6a3RUdf3SrSIjoyN2X5mpjCSus+ueWQkZ7e0fLur 0S4aWH5YZgGw6FI7KL088/8TJyuPnT2r8ykndE+dO5c8WXq2v18vDQ4q4rIhum9qSs/29+vZ/n59 o6cnedUZKDWZStqu8Pt1OuWzvXEmGBh5BPW3J9J31QRMU02VlXrT8ftytd+vC7GYorGYNtXW6t/X rZPHNG3BIG5ZyXLQVP2xWHLl1GlrKKQX1q2TaRiKW5b2OkKGm9TVnePHj+cMIvl2V6NdNLD8EHIA LDq3Vq6pJy9uAz8T3DqnORFwUMoyrbZ8sKpKf3b55ToyPKwNNTU6NDiYtpJSiBuCQZmmmRZy/uTy y11P+N2CQSF8ppkMKXNp9VwMtIsGlh9zsQ8AAJylK6m3dzY3a09bm25buVJ72tq0LUczE6BcbKyt 1f0tLTrQ0SHTMLIGHE8epVdb6urSfte2hkIZV1XmGgRKaX9Mtu8YAOWJlRwAiy5xkvVCJKJPNTfb TrqcV4DjliVjZk/OeDyecSVnpcejlR5P2lVrYKkw9P5ekkTjjUyy7TUzJV0VCChmWbIsS+2BgKT0 LoRO2WZIbQ2FdGhwUBMpP3eFaWpnc7NemdkLl2s/zULKd+8OgPJByAGw6BJB5pN9fbo2R0lL4pTK mjlhW+XxuJaj9U9N6ctr1+rJlD08wFLy5MwemEx7XvIV13SjgQcd72MYRtY9L6nBYENNjQwp2cxj Z3OzPnXypO0iw+ZgULsdHQ1LxWKXywFYeIQcAEtK6j6BXI6OjOiuhgZbe2lgqTgVjSaDTsJqr1fr q6vllfRmNKq3M6xUejO0gU6VqxwtVzB4vqNDt3R16cTFi1pfXa3nC5hPAwDzjZADoGTELEud4XDG Nq8xy9L+3t68329Tba0sWkajjHxp7dpk8IhbVtpqSsL1wWDOJgUbamqy/r7l4jFN/Wz9+sL+AwBg gRByAJSMH0xMJKemu7V53ReJZCw9W2GauhR/v0/VKo9HX1m7Vuv/9/+exyMGiuOmujr5KyrS9pl9 bvVq/XJ4OLlasqOpKfmYaRh6Yd067Y1EdHhoSOPxuHrGxyVJHw0G9fG6Oh0ZHk7OutlUWytLSu6Z iVuWrXua2wyqpTxLhtk4wPJGyAFQMrpiMdvtXG1fV3k8Wun1SpKafD7bleu+qSlVvfzynCfOAwvB X1GhAx0dafNk4paVDD0HBwb0SE+PLfinlpR1hsPJ0PLVcFh72tr07Lp1GX/m7V1dttvOGVTS0p4l w2wcYHkj5ACYs1xXTPO9otpRUaGXU4KOW9vX1G5PH6mpSZ4AnopG05oQEHCwVIzH47q9q0sbamoU tyy9eemS/r+BAY3H7Z/iRNB3/k7d09SUVsqZa89Ntu5p+by+1DEbB1jeCDnAAivHEopcV0zzvaL6 p5WVWrNmTcY2r842sIeHhmyPjzpWgoBSdqXfrw+uWGErUcs1dDMR/J2/Uy8NDqaVcm6qrc36feP8 fbIsy9bJLdcsmVL/LnOGOGbjAMsLIQdYYOVYQpHrimm+V1RzdXNythDYWFur5y5cSN4ezdBkwBSr Oig97VVVOtDRkVY25qbSMPTV1lZbMEl14uJF+3sHAtrZ3Ky9Wb5vss2gymeWTKl/lzEbB1jeCDnA AivHEopcV0yLdUXVeVL1UGur9rS1qTMctjUdcCLgoBS9HY3q5hMnFM5jjtPHgkFJ0mdee02bamu1 sabG9ju1vrra1rBge2NjsolAqmzfN4XOksnnvRdztYfZOMDyRsgBFlg5llA4r5je09Rka02b6Ag1 1yuqzpOooyMjOtDRof29vQz8xJJRZZoajcd1Khq1fW7bAwFta2hQzLL0z+fO6ezEhAxNf0d8NBi0 BfyvzwT81N+xR3p60n7H5vP7Jp/3LvXVHgDli5ADLLByLKFwXjFN7fJUzBMb50nVeDyuuGVpW0PD nKfCAwtlNMuq49GZ9s7/vWGDbcXDWdL2ykzAT+X2Ozaf3zf5vHc5rlwDWBoIOcACWw4lFPN1YnNP U5P+33ffTU55PzgwoE+dPKlKw9DWUCg5CyRmWXqkpydrCRtQahIrO4lGAj7TTIaH2a7IJL5vEmVj iXK3YpSN5fNdVo4r1wCWBkIOgKKb7YlNzLKyTmB/tKcnGXASUvch7GlrS57Q/XJ42HUSPFBKrvT7 1V5VpbcdpWvObmuFrMi47YNZrLKxcly5BrA0EHIAFN1sT2x+MDGhf8xwIhazrLQ5IE6PnT0rSbYB ikCpqvd4dGqmLO3mEycy7is7Mjxc0AqwW6BZrLKx5bByDaA0EXIAFN1sT2y6HHNuUk/E9kUiaSeB V/r9tpWd85OT2nXmjFaYZsE/G1hIVaapv1qzJnm7MkvpWKElXm6BhrIxAMsNZwIASkZHRYXtduqJ mPPErT0Q0H9fd532tLVptddre4y9OCh1o/G4HgyHtTcSkSRtnmkRnbA1FNKt9fXaGgrp8NCQOsNh xTPMgXJya+G+s7lZe9radNvKldrT1kbZGICyx0oOgAUXsyw9HA7rqXPnJEnbGhp0X0uL/rSyUmvW rHFtRT3uCC7bGxvlMc3kilGiPCcVQ0BR6hLh3a3EM3WQ53MXLqQ1I8jUOMDtvSgbA7DcEHIAJC3U 4L59kYgeSGn5vLu7W4Zh6JOOE7GHurttz7uprk7+iorksSWO9z8HB3Wl3693JyZsqzgEHJS6xKqL Wwhxrl46mxFkCi0EGgAg5ABIkW8HptmGocTrEg0CUh0ZHtYnHfclVnoSesbH9caGDcnbqfN4UnkN Q5N5lvYAi+VKvz85KNeNcx9NKubNAEB2hBxgGcg3lOTbgSlXGMr081Jf57Sptlbq6yvovyvT8U0R cLAEvD02pkd6ejKuuqSWnY3H47aOgTQOAIDsCDnAMpAtlKQGEue+l7dGR9UZDidDSmIvTWKzdEJn OCzLsnRfS0tamHm2v19xy5JpGGkrOF7DUKVhaGNtrSbjcf3fFy/K/8oruquhQfe3tOiuhgZbudrn Vq+2zdHZUFPjeqU7W8S5qa5Oh4eHs06dBxbK4aGhjI+llp3FLUt7HRcOAACZEXKAMpapPMzZmjl1 dWVrKKTI2Fhy+nrisXubm/Xpkydd589ciseT+2r+pqlJf9/TY3t8/7vv6q3x8bTXTVqWJi1LPx8c 1M8HB6fvjEb1QHe3/mNoSM93dMg0jOSJnWVZtvBUZZoFNReoMk39Jhol4KBkTFhWXiut7LMBgMIQ coAylqk8LFtr5sjYmAampmz3HRke1r5IJOeAzSPDw7qtq0v9jte/Mzlpu20o+2qLNL3JujMclsc0 ZVmWXhoc1ImLF23PKTSsjMbj+o1L2AIWSpVhaDSlnLLSZeVTytxUAACQH0IOUMacpTCrvV7dvWaN 4pal206e1IRlKZwyTFOS69T1TbW1eW103lRb69pUwLn7J98dMw9FIgU3EAgYhqLsyUGJ2lJXZ7tY sDkYTPvdSvwOzVd3QwBYDhgGCpSRmGWpMxzW7V1d6gyH0/bYrK+uliQ90N2t5y5c0MGBAb3pEmoS Vnu9ycGB2TY6G5I+UVenHU1NyZ+RarabpGfTIa3KNNNCFVAKTEnPd3SkDeV0/n6cn5zUrjNn0va+ AQDyR8gBykii7OXZ/n7tOnNGEccqTaVhpLVlzmZ9dbXun2kmsLO5WVtDIdfnWZJ+Pjio/3nmjN6+ dCl5v0fSVT6fPhoM6qHWVrUHArP5z0rzibo6VZn2r6/E7f5YLO+VImAh1Xk8Mg1D984EmyPDw9ob iWhHU5P2tLVptddre75zhcd5ESPOiiUAZES5GlDiCplJ4zwpMhzP2xwM6u0sKzdO/zk4qA++8oq2 NTTovpYW+czs10Ue6umxBYwpSW+Nj+ur4bDaAwFta2iQNfO+LyQaDRTI1PR/p3M/Ds0EUOouTE2p MxyWaRgZ9+Ck7qFzrvCwdwcA8kfIAUpcISc2zuGBTT6f7mpo0CsjI8mAFLcsW1vmbEYtS6eiUe3u 7lZnJJKz7CzbdeXE++xpa9MxRwMBN5WGodqKCvU5mhjERaDB0vXUuXO6qqrKdl/i4kTqXBy3NtH5 zrECAFCuBpQ854nM/t7ejGUqzpKyFwcHZRqGDnR06N7m5uk5G0NDutLv12qvV58IBnWFz5fXcYzG 4++3eZ6DI8PDuuAILm4+Wlvrur8HWOo21NTYbh8dGtKemQsP97e06EBHR7JMNJXzIsN4PE7pGgBk wEoOUAKylaQ5V2dORaPqDIe1u7U17X1Mw0grKdvf2yvLsvTkuXNpndN+nmUQ4XzZUFOjnw8MKJpj NeYXQ0N5z79J8BrGrJoVAAulf3JShxwXC/qmppJzprKVn6Wu9IzH48kubZSuAUA6VnKAEuBsGJDa VWlnc7NWeezXIxLNA9w2IjuvEifKxNxaQy8E5+6hB7q707q+uSk04BiSKgg4KHF9U1N6McOKaK7y s8RA0AMdHWkXMyhdAwA7VnKAEpCt1t40DK30em17U/onJ3V7V5fGYrHkCdOz/f36xcCAPhYMLsgx r/J40vbLOGUa+jkfO2osSWM5nwWUrkJarTtXeGfbph0AyhUhBygBuU5YtjU0aHdKs4C+qSnb8xNe HBzUf+Wxqb8YLOUuD2NdBZAqJMVc7l/p8ciQtNLr1baGhrRGA9nkalIAAMsdIQcoAaknLBtqahS3 LN128qTG43H1jI9Lkj4RDOrsxITOjo/rUpZyr36X1RVTxV89cfs5ANLDv1vAkaRNwaAOdHSk3Z9P 23gzx/4dAFjuCDlACUg9YekMh22zMhLmsqeGhsvAwsm3+UWiO5ozyDwcDifbvD/b3y/LsrTLpdEI ACAzGg8AJSRmWdrf25vXc1d7vXqotVVX+/15Pd9rGKrKMcwTwMKo93h0cGDAtdlIorFIwpOO2wCA 3FjJAUrIvkgk7xWbu9eskWEYMgxn/zJ3k5Zlu8I8HyVsAPJT4bhNdzQAKC4u6wJ5cmvXXGzOE51V Ho+8Ls/bGgrJkLTrzJlZl7ERcID5l+kf2Q87Wr2/NTqa/F65q6HB9pjzNgAgN1ZygDwlZtlI8zd8 z9llbaV3OuI4WzVHxsZ0uKg/GcB8cF5MaA8EtL2xUTuamvRIT4/29/bqVDSqU9Fo8vvl/pYWmYZB 5zQAmANCDpCnbLNsnPLpjuQmcTKTeuLj5lQ0qqkMHdYoQwNKU3sgoP9z3XXJ74L7W1p0ZHjY9nt+ ZHiYzmkAUASEHCBPhQzfy3fVJzUMbZgpX3llZCSv44lMTLje7zdNjWZpMQ2geK7w+TQUi2lgaipj q+iE7Y2NaRc7GOoJAPODkAPkaWdzs+KWlex8ZFmW4pblukLjturjtrrjFobyNZVhTxABB1g4FYah c1u2aG/K77LTyooKraqslGVZmozH9WhPT/J7YEdTkySGegJAsRFygDyZhiHTMJKlJbu7u2VkKCtx uzrrFmiylbyt8ni00uvNWLKWre0BJWvAwnhzbEyd4XDye+DI8LDeGh21/d72x2Lqj0a1u7tbh4aG dHBgQNL87e0DABBygILkuy8ncTU29ersZ157Le21zjCUqm9qSh+urtbZ8XFdKnB1hoADLJy9kYhM w0juvcs00FeSTly8aLu9v7e34L17AIDcaCENFMBZL5+pft65yhKzLI07gkripKY9EMj4814cHCw4 4AAornqPR4Es4eNSPG4b6LmzuVl72tp028qV2hoK2Z67vrradvtUNOo6EBQAMDes5AAFSKzQHB4a 0oRl6fDQkDrD4bQrsM7StJcGB5MlKtL0nJudzc2yJDX7/bOedQNg/g1MTdkuXFzh8+n0+Hja8xIr u6nd0eKWpb0pe/ESraPdytoYCAoAxUPIAQqQOHlJLUd57sIFSfa6eufJirNExWeaybKW1PADoPQ4 V2Y9pnsRhNvKrls76MRtZ1kbndUAoHgIOUAenJ3RDg8N2R53hhrnXpv11dW2MJM4mcnnyq2h7E0G ACyu1V6vvrR2bcGd0dz27gEAioOQA+TBWX7mrLN3XoF1lrV5JF3p92s4FtP66upk29gNNTU5W0cT cIDScaXfr/7JSdt966urbas1uYYBOx//1w99iIYDAFBkhBwgD84Vl0rD0J62NttJjNuJjdvsjIMD A7rm1VcVtyz91qWuH0DpMSW1+Xx6e2ws7bFKR0DJNQw432HBAIDZI+QAeXCWn50aHdWrIyPJVRln 29hcc3DepNEAULK8M6FlMmXgblxybTYgSZuDQdvtXK3m821FDwCYPVpIA3m4p6lJW0MhrfZ6Ve/x 6O2xMZ2fnNTBgQHd0tUlyf3EhY3EwNLzAb9fH8vzd/cKvz9tL82Gmpqst/NtRQ8AmD1WcoA8PNrT k7ELWqJzmnO1563RUW2oqVF7IECLaGAJafL5FHEpS3PTOzGRtp/GubvGeZuGAwAw/wg5QB6ylZMk hvslTlT29/bqVDSqU9GoHuju1sqKigU5RgDF4TNNXYjF8nruaDyum0+c0PMdHcnW0kdHRmzPcd52 aysNACguytWAPDjLSa70+7Xa69XWUEjPd3RIev/E5aqqKttz+/M8WQJQGjYHg1rpye8aoCXZylYl ytEAoBSwkgPkwa28xNJ0l6Q/fP11W5tYZ9kagNK1yuPR3WvWqMIwdGR4WBOWpcNDQ2ry+QoqMz00 OKjOcFg7m5tdvy9ytZUGABQXIQfIg1t5ibOb2kuDg/KZpjbW1OhrLS365jvvqG9qajEOF0Ce+qam 9MPz57W9sVEba2v1QHd38rGtoZAODQ5qwso9rWrCspLfB/e67LGhbTQALCxCDlCA1Kuxb42O2h5L NCZ4tr9fN9XV2QKO1zBs7WgBLJ4q09RoPJ68fSoa1a4zZ9QeCNie5zNNXV9XZ2s6ssrj0UdqauSx LL01NqbI+LgtBB0ZHnYNNLSNBoCFxZ4coACJk5dn+/uzlrI4T2AIOEDpqDLd/+nrn5y03d5U5buZ IAAAIABJREFUW6vnOzqS7eO3hkJ6d/Nm/fu6dfqDUEgfXLFC19fVpb0mn3by7NMBgPnFSg5QALer r+2BgGKWZZuEfinlKjGAhVEhKZ82H5nKSPumprQ1FJLPNLWptlb3NDXpkZ4e+UxTX1q7NrmPJrVU VVLyNRtqamRZVtoqb2qbaNpGA8DCIOQABcjUVGCIvTfAoqr3eHQhy+/hyooKraqslKSsq7A+09SB mY6JmfbdOUNM4jXO8NMeCGh7Y2MyHLEHBwAWDuVqQAF2Njdrayhku+9UNKr3coQceigB8ytTwFkx U5rWH4vpVDSqJp8v6/uklpEdHhqyPXZwYMC1VDXxGudK71VVVbq/pYUuagCwCFjJAQpgSfpYMJic ht43Oan+PFZx2JEDLI61jlbQPePjGZ+7yuNR3LIUtyyZhpG1q1p7IKCrqqpspWfOlV723QDA4iHk AAXYF4nYWsw6NzBXmabWVlbqzZT9OQDmZqXHo+FYrOAGHltDIV0fDGp3yu9sNn1TU3qguztZWlaZ ZQVme2NjWvkZ+24AoHQQcoACOMtRRh0NBkbj8az7AgDkb4Vp6v6WFu1sbtanTp60tXJOtcrjsTUT SN0LI0nGzKDPTbW1iluW7UKFm8Tv+eZgUM9duJC8P7UpgVuAYd8NAJQOQg7gkG0yeabGA6kYAAoU h88wkr9/zlWVKsNQk9+vbQ0NilmWvhoOJx+7q6FB9zY3a2/K7/G/fuhDMg0jWYp2ZHhYG2pqZEh6 8tw5W0lboszMbWWG/TUAsDQQcgAH5yC/7737rnonJhQwTf0/v/M7eqi1VUdHRvTGpUu2ttHAUued CQH5tGFeCBdiMX3q5Em9sG5d2qrKrtbW5KrJ7V1dttc9de6cJCVXbJ7t79f+3t7k6o5zteW+lhZb IEqEG1ZmAGDpIuQADs6StNMzQeZSPK6vRSLa09amAx0duu3kSUIOysqkZanN59OZLJvzF9rBgQHt jURcV1USq67Ols6nolE92dubdl/i4oUzuMw2zGRb9QUALC5aSAMOG2pqsj6eWq8PlJuIS8DJdNru lXS131+Un+s1DFWZpuvPOjw0lLbSYhpGctXVbe5Npr1xbgN9Zyvx85/t79euM2e0NxIp2nsDAOaG kAM45LoOm6jXv6epSas8LIaivLitRHyirk7tgUDa/ZOa3tTvdIXPp6v9fq30ePL+R2bSsjQaj7u2 W5+wrLQwEbMs7Xes1qSq93q1NRRKzslJKGZbZ2dgKmaAAgDMDSEHcDg6MpLxsRuDQcUtS7d3denW ri6aDKAkeedQMjVpWbrC75fXMOSV9AGfTz7TVKyA9s2nx8fVEgiof2pK8dxPz+qmujqFHSs1R4aH tS8ScV3BSWj2+XRwYECXZjogtgcC2tPWVtS2zs7AxFwcACgdXIYGHLJ1UHtnYiJn+1mvpq9wA4sl 33kyiX8AnFHdYxj6ZH29xuNxHRwY0G+y7NG5q6FBpmHosbNndX7y/U/+iYsX057rbPWcTaINtFvL 5021tWmrJlf7/dre2KijIyPaVFurw0NDtsevqqoqehMB5uIAQOki5GBJm4+Nv4kTlcNDQzo1Olpw cwGvaWoyPtfr18D8yxQ3TkWjWVdJpOnBtzubmnR/S4ssSS8NDtrm2Kyvrk6ba/OltWtdA9EK00yu uEhSi2Go6/d/X4/29Oib77xje4/2QEA7Z9pDp16MaAkEkgEn8XhqN7b5WGWh+xoAlC5CDpY0Z7tn Kb1zUqESJy6d4XDaIMCPBYM5V3KcA0KBcpEYhpmYL3N0ZER7IxHFLcsWaLaGQnq+o0P7IhE9OdPO +a6GBt3f0pK8CJH4vZWkQEWFLeTc6vXq0Z4e23MStjc2ypyZnyNNr6IkVpyk978HWGUBgOWNkIMl bT43/jrfyzczfV2ansPRMz5OoEHZyFRKlgg2qSulneGw7eKCsymBzzTlMU3tam3VrtbWtPdMBI79 vb06FY2qb2ZVZ5XHo5Ver6xYLK3cLHEsbjNsnHNyjgwPs8oCAMscjQewpM3nxl/ne43H4/rMa6/p P4aGdCoaJeCg5OVTuLna69XXW1u10utNe2xrKKTnOjqSe2ASqza5Libk+j1MBJCrqqps9/dNTelU NKr/NTGhCZd9RT7TdC1HpQEAAMCJlRwsaXMtSYlZlh4Oh5MT0rc1NOi+mZKaTOUwToVspgYWUj7t B2orKvTUuXNpe3BuqqvTC+vWaa9LSaizOce2hgYZhlHw72G2Jh+VhqGtoZDt9y5TeKE0DQDgRMjB kjbXkpR9kYhtj83u7m4dGhpKK89xlsOkqq2oULCiQqdLaEo8kK9sjTU+89premt01HbfkeFh/euH PpT833Np+JHtQsLmYDDZQCBXeKE0DQDgRMjBsuZWduPcwHx/S0vWK86/GR/XTXV18phmzo5UQDEZ ym+1ZjZeHBx0vX9jTY0tVMQsKy2I5Bt4Ut8nnvI+zSMjyffJFF7mo7MiAKB8EHKwrGULL9L7IWhn c3PyJOySy16cXwwO6sZQiJCDBeUxjLxn4hSL86fl0+Ewn0CSGmiOHz+eM7DMR2dFAED5KHrIefjh h3XixAkZhqH7779fHR0dxf4RQNEkwktiT06Tz2e7gp3YA2AahkzDcA04khTT9AqQTxJFa1go8xVw su0z++Y77yT3rJkz+3BSua2OOgPJS4ODaSWhqUGoeXxc6+JxPdrTkzEYzVdnRVaIAKA8FDXkvPrq qwqHw3r66ad1+vRp7dq1S08//XQxfwRQVKZhaHdrq3bPtLlNLZnZUFOjuGXp9q4u1wnqbgg4WEwr PR71F9AEI9Ee2rkf5ktr1+o/hoZcm22cn5xMBha3Uk635gDOAOJWEpoahCTpra4u1+el/pxcP3c2 WCECgPJQ1JBz5MgR3XTTTZKkK664QsPDw7p06ZJWrFhRzB8DFFWmK7cPdXcnmxI829+vK3w+2+tW eb3J+R5AKRgoMOC8sG6dTMOwhfvE78D9kvZGIjo8NKQJy9KvR0b0Xsr7p5ZyJm5nag6QrSz0sbNn JSntIsKJixdtt51Bab46qs3n7C0AwMIpasjp6+vTh2a67khSKBRSX18fIQclzXnlNm5ZMg1DeyMR 2/Oc3dMIOCg1+Uxu8kr6eCik5zs6kmVYmTb4p96XOgBUspdy5lrpyNZFLbEytDUUsr1mfXV11vbR 89VRbb5WiAAAC2teGw9YC7whFpgN55Xax86eZe4NljSPpCsCAUnp+8wmNV0u9khPT0EhYS4rJ25d 1B47e1bnUy4UVBqG9rS1JburPdbRoUcce3IWAjN3AKA8GFYRk8i3vvUtrV69Wp/97GclSTfddJP+ 7d/+TVWOqdYJx48fL9aPBmbte+Pj+seJicU+DKBo6iS9WFMjaTpUfH9iQk9PTOhCynNaDEPNpqmO igr9aWXlgm+ud/7e/UVlpf7M51PMsvSDiQl1xWKLdmwAgNJ07bXX5v3coq7kbNmyRd/61rf02c9+ Vq+//roaGhoyBpyEQg4W5ev48eOL9ln4iGXp58eOzbn982qvV9WGod8QmLDI/q+6Ov1tRYU2zASd yMiIrnWUiYUtS+FYTC/HYlqzZo3ubW5e0K5iH7EsrXH5eZ3hsP5xpiwucWxs/F+eFvPfBZQOPgdI KHRxpKgh5yMf+YiuueYa3XnnnaqoqNCDDz5YzLcH5oVpGNre2Gjbb1BlmhpNaRe9yuPRdTU1ejMa 1XAspnUrVigWj+sXKaVuf3H55XpkZhM1sBiqTFMbq6uT5WnOzf5X+v0ajsUUtyxbSeaR4eEF7yqW aU8NG/8BAMVQ9D05f/3Xf13stwTmnbMO/wfvvqs3x8aSj6/0erWlrk7Pz1wJf3FwUF7HVe4nz5+3 BSNgoY3G43p5ZCTj42+nfKZTbaqtLZlwwcZ/AEAxzGvjAWCpcF5VtixLu2faR0vStoaGtBa3zkGM v8lwAgkspHwHhLYHArqqqipZKrY3EimJcLGzuVnvvPOOIjU1bPwHAMwaIQfLRiGTzO9raZExM809 8dxPnTyZ9f3pJYhS5jUMWwDa3thoC/Y7m5sVtyw9de6cpOmgn2invpBMw9Cf+Xy6tqNjQX8uAKC8 EHKwbBSy58A0DNtG7L2RiLwLdqRAYQylh2xnqLk+GNQNoVDG1simYcg0jGQDjt3d3TLmaRYNAADz jZCDZaPQPQfOUHSl3z9vxwbMhdsqYpvPpwuxmKKxmDbV1urf162TxzSzvk+p7MsBAGCusv+LByyC mGWpMxzW7V1d6gyHFS/SKCfnHoNMew4SP/8xR6e0TJu2gVL05tiY+iYndSke1w2hUM6AI+X/OwIA QKljJQclp9BWtvnutck1yTzxPvt7e3POzFnt9Wp9dbVt7ghQCi7zeFTv9do+w84VmcRn/fDQkCYs S5WGoc3BoHY0NSWfz6Z/AMBSRshByZlrWZnkHooyzeVwe59UboHm7jVrZEj6z8FBjRZppQkohg/X 1OjjdXW2z3JiRSZbkH/uwgVJ8zsbBwCAhULIQckpdE5GsfYRZHrdX65Zo/taWrQ3ZbXI2WIaKBWV hpFx1TJTkE9gDw4AoFwQclBycpWVOc1meKBbiZvzfRL29/bKmDlxTJTB3eZoJ11pGGr2+XLu23Hr ggUU08RM22e3FZlcIYY9OACAckHIQcnJVVbmVGgoktxL3BJzQvZGIroUjyef++bYWPK5ieOacJSo TViW3h4b09ZQSOFoVG9mCDsEHMy3yixzbZxB/mq/Xy2BQHJPDntwAADlgpCDJa/QUCS5l7gl5oSk BpxMr8k0MycyNqarqqrUPzWl/qmpgo4JKIbNwaDtdmqTgfF4XO2BgCRpW0OD7mtpWfBhnwAALARC DpalTCVu2cp5Ukt5JjM851Q0mrMzGzBf2gMB7WxutpVjjsfjrl0ALcm2zyxTV0IAAJYiQg6WldSr 2ltDobQyHWf42RoKyWeaaWVwbiVBqzwe9bF6g0V0V0ODHuru1r6eHo1mWJFMeOrcuWQgz6dVOwAA SwkhB8uKs7vUnrY224ld6v6eDTU1MiQdHRlJe5+NtbXJlrvSdMD5cHW1XhwcnL+DBzJY5fXqy2vX Km5Z+mo4nNdrLMe+ssNDQ/NxaAAALApCDpaVXO2mU/f3dIbDeQ8l7Zua0ouDgwpVVGggFnv//SRl v54OzN1Kj0c7m5v1mddec338pro6+UzTNvjzFwMDtgYZzmYaAAAsZYQcLCuFtJvOFoiOZti74zxR JOBgPngNQ5Mpn7VT0aj2RiIZ26B/vK5Ou1pbbfc5V26ydWUDAGCpIeRgWcm33XTMsjTu2NOQOjX+ jdFR19cFKioydmcDimXSZdXl8NCQ/q2jQ1PxuB6KRGzPOTI8rM5w2Pa53xwM2kounV3ZAABYygg5 WFbybTe9LxKxdaTaGgrZpsafzjAHZ/2KFXppcFAx10eB+ZMYAvpgW5s8pmnbezZhWa5zoaTC5ksB ALBUEHIAF85SNZ9pJtvrurWZXmGa2hwMurbqTcUeHcyXExcvqjMc1l+vXatfDAxohWkqUFGhL61Z k1ZemZgLRTc1AEC5Mhf7AIBS5Nyrk3o70z6e/3LpwuZEwMF8OT85qV1nzqjj1Vf14uCgLsXj6puc 1A96e7XR8Zl9a3RUneGw4jQbAACUKVZyABfZSnl2NjfLsiw9ee6cesbHNRqP69LM/6XySRpfyIPG srPK41HU8dmLjNs/dW+PjcnQdLv0/b29yYG1ifI1VnMAAOWIkINlK3UqvHPie7ZSHtMwtKu1Vbta W7X6l7+0DV30SEqMAyXgYL5tqK3VhGXZyiSrKyp0wTGU9ujIiA50dOjI8HByAKjkXnoJAEA5IORg 2UodDDrbie9Bj0fvpZxQUo6GhZSYe5NqZUWFQh6PrTlGosTSrYV6trAPAMBSRcjBspVrMGg+2quq 9HbKySQhB3NV7/HIisc1kEcr8nA0KsMRSN4aH9f/bGlRhWmmlVu6lWHuLULYBwCg1BBysGwVMhjU KXH1++2U0p9UlYahjwWD+mgwqB+eP6/+yUn1OUqIADcXpqby/mJ+M0Mr838+f15vbNggafqzujfL Sk0xwj4AAKWGkINlay5zQlJL3aTpDeCpIWbCsvTi4KC6x8ZsKz1APtzi8CqPR/1TU8q3H9pEPK7b urp0eGgo2ZjAbaVmLmEfAIBSRcjBsjWXOSHOq90bamu1ORjUY2fP6vzkZPJ+Ag6Koco0C1oJbPL5 dOvJk3pxcDDtMednl6GgAIByRMgBZsF59XtzMKj7W1r00uBgzoGgkhQwTUXz2HMBSFK2NgDtgYDu amjQocHBZKh5cXBQK0z3MWjOlRqGggIAyhEhB5iFTFe/nZ2uMqmpqCDkIG/OGUyS5DUMPdjSovtb WmQahl7p6rI9HjBN2+tWeTz6clMTKzUAgGWBkAPMQqar35uDQT134ULO19dWVNjK2oBC3RwKaXdr a/K2c3Xx7jVr9MvhYZ24eFHrq6v1fEeHPBlWdwAAKDeEHKCIElfJnXtznN4eG1O9x6ORqSkRdTAb m4NB22231UXm3QAAlitCDjBLmYYoJlZ4UruvuXFOpQecVno8+r2aGv3XyIit8cCVfn9a2Rl7awAA eB8hB5ilfVmGKKZeVR+LxVy7XAG5fHjFCvlcmlS8OzGhz7z2Gis2AABkQMgBZinbEMXUq+pxy9L/ OHZMpzIMDs0mYJpSPK7CX4ly8POhIdf7L8Xjera/33XuDQAAkNiFCuQpZlnqDId1e1eXOsNhbayp sT2eaYiiaRja3tg4q595QzConZzAIouvdXfr5hMnNEW3PgAAkljJAfLkLE/7emur9rS15RyiGLMs WZal9kBAlmVprd+vo8PDGs3jpPToyIhecawYofx5DUMtPl9ew2QnLEsHBwZ0S1eXfrZ+/Zx/dqa9 ZgAALCWEHCBPzvK0V0ZGdKCjI+fr9kUi2t3dnbzdEgjYAs6Vfn/Gk1maEyxPk5aV7MCX6TNQISmW cvvExYtF+dnZ9poBALBUEHKAPDnnkGQqT3NyhiPnyWh7VZU+f/nlNClAmgtTU9oaCslnmtpYUyNL 0+F6U22tfjEwYPusrK+uLsrPzLbXDACApYKQA+TJbQ5JPpzhaH11tQ4ODCRvT1hWsiTooe5uQk6Z usLvlyxLp8fHXR+vMk0Zmm4qkMpnmq4rhjuamnRLV5dt2GcxzDbMAwBQSgg5QJ5mO4fEGY4SJ6eJ oHNwYED/49gxbW9s1FGumpelK/x+vXHddZKkW7q6dGhwUBOWZXvO5tpa/XT9en3q5ElbCM4UMjym WZQ9OE6zDfMAAJQSQg4wz0zD0L3NzcnN3I/09KjSsZH7VDSqXWfOaGsoZLvfkGQ/FbZb6fHoL9es 0Q/Pn59Vi2osjNNjY6r75S/VWFmp9kBA19fV2YKMNL1iYxqGXli3TnsdG/8XEkNFAQDlgBbSwBw4 20rHLfdIktjM/Wx/v3adOZN2FT/BK2lrKKQV5vSvZraAI0mrvF6ZhqE/Xr1aqzxcs1gs+fQeuxSP 6/TYmJ4fGNDBgQFVmfav383BoKTsf+f5ft4AAFjuOCsC5sCtE1Xqqk3iSrxz83alYWhPW5v29/ba VmAmpbQr/Nmcikb1QErnNiyO2USNRIe99kBA2xsbtbO5WTHL0qdTytWc3c3ofAYAQH4IOcAcuHWi cp6IvjQ4qIijRfTmYFD3t7RoZ3OzrTTpcIYJ94VYYZppm9dRuq6qqkoGlc5wOC3kJj5jMcvS/t5e 18cAAIAdIQeYA7dOVM4Tz9ST1tSr9lL6/ofOcFjPXbjg+rPqPR4NTU3ZZqO4ubyyMq8hkph/V/j9 MuJx/XZqSoakxspKDUxO6kLs/b/F8Xhct3d1ZQy5icYD+yKRtH1XdD4DAMAde3KAOdjZ3Kw9bW26 beVK7Wlr087m5qwnnomr9pkmyO9sbk5rPrDK49HXW1v13pYt+lpra9pjqa7IMlgU88eUdJnHoyt8 Pq1M+Ts5PTamz69Zo0sf+5gufuxj+rPLL7cFnHqPRwcHBjLu1doaCtm6naVqDwTofAYAQAas5ABz 4NaJKvWk1Dncc0NNTc738zk2pPdNTek/hoZ0v6Qdzc06NDSkX4+MKOjx6OqqKk1alioNQ5uDQf3g 3XeL8x+GgsQlvTc1pfemptIeSw0n/+mYgXTB8fzI2Ji+3tqaHPiZmJ8kpa8abm9szBiWAQBY7gg5 QIFilpXWWCD1ZDM1+OxxDPfM55TUeTIrTZe87Y1Ekv9bmj6pTqza7Glr0/0tLWl7NtzkakuN4koN tm/maPN9KhqVaRiuwz+ZXwMAQP4IOUCBCulwdXRkJOttNzubm/XS4GDGDehuEo/d1dDg2m0tYJoy NN3Ri4CzsFKD7XAs146qzH/PzK8BACB/7MkBCuTWUS0T5/6cfDaKJwZCOvfmbKqtzfj6DTU16gyH dXR4WFtDIa32em2PR+PxZMtiFMZrGFrt9eoKvz/jc1Y5/rxTpQbb9dXVtseu9PvVHgjY7kv9O2Yu DgAAs8NKDlAgt45qmcy2xCgRdPY6yuISDg8NaSJlL07cspKrS9L0hvVc83ZMTW98HyUAZXV9MKjr 6+r0Dz09GZ/zV2vWyDAMHRke1ng8bvuzT/18PN/RoVu6unTi4kWtr67W8x0dMg0j498zc3EAAJgd Qg5QoEKCy1xKjDK91u2+27u6bLczDRtN5TNNbait1dvRaMbnLDUeSYZhaHIWKx4Vkq09tynphpmA 41YC2B4I6KqqqrR9WXHLyhhaPKapn61fn/ZeqX+nidWbI8PDemt01PY85uIAAJAfQg5QoFLcG+Fc Xdo4s3pwZSCgZr9fvx4ZSev8FY3HM87kcTI13UGs1E1JUpaAU+/xyGMYOj85mfaYc7dMXJJpmjqa IVhsb2xMCyf7IhHbKttspK7eODlL2bI1wAAAYDkj5ABlILFakDjBfrK3V2+mzMvJp3wtG0PT+0dM yfa++bhyHmf3eDQTbPJ0YWqqoD+LgwMDuqmuLu3+1Pk1CW7hJBEiCwnFbvNwUleM3H4epWwAANjR eAAoA4nVpc3BoA4ODKQFEa+yb46XpgeL3rZyZVrDA2l6lePtsbG0uS65bA2F1F5VVdBrCtGapRlA JpGxMdfgkknP+Li+3tqq9kBA7YGAHmpt1Qvr1qWtmmQqJSu0xMy5x2t7Y6MOdHSkDZEtpAEGAADL DSs5QBk5PDTkev+kpJUej/pcyrScPhoMKh6P6+jISFrLabeQ482wB+ZKv1+VhqGJAvbH+CXFCthT 015VpbZAwLYyk6u07lQ0qiafL9nVrG9iQv1ZWjv3T05qd2urdre2Zj0Wt/lGifsLke+er0IaYAAA sNwQcoAlIp89GJkCRaVhZJyhk9A3NaVn+/tdT9QTnOHhar9fr193nW7p6korAXt7bCxZprbK41Ff HqtAn6+s1I/i8byeK0mbg8G0FQy3gLPCNHUppYNc6oDWK/3+rCGn3pPf16SzZDDR+a7QoZ357vli OCgAAJkRcoAlIp89GJk2u28OBnVPU5N+0Nubtj9mhWlqrc83qw5rf3L55TIMQ5Ece25Wer05g8sq j0fHp6bUl2c76yv9fu1sbtbeSCRrMJOULONzk2tA57bGxryOZ6EbUpRiAwwAAEoFIQdYItz2YDhX dzbW1to6prUHAtre2JgMA24NABInypk6emXSHggk39cZkJzNBu5qaJBpGOoMh20rKqn6pqbUV8DP /+34uB7q7pZpGGoPBNLKzm6qq5PPNDVhWfJYlq70+zUci6m2osJ2bNkGbN5UVydD0y266WAGAMDS QcgBlgi3PRjO1Z2HWlu1p63NtaTNbWO6s0vYkeFhbayp0Td6erKWcEnTG+LNmQGYqdoDAb32+7+v R3p60o7DsiztzlIy55QIJhdjsbSBpaOWpa+Gwxlf2zM+rma/P20F5/zkpLaGQoqMjelUNJpcYWoP BNQ/OWlbceoZH08eLx3MAABYOgg5wBLhtgfjM6+9ZnvO0ZERHejocH29MyRtDYVsXcJST94tybZ/ 5xPBoHrGx3VhakorvV5ta2hIHo/zfbc3NspjmmlhIDazYpLY8P+51atVYRh68tw520rQ1lBIPtO0 haOHuruz7idycyrLkFOfaeqqqqq0x/9q7dqsIYwOZgAALA2EHGCJcNuDkanDlluTAreQZEnqDIfT VlwS7YrzGTSZbQN86oDMNy5d0unxcdt/z67WVt3X0qK9M8faPDKib6YEr5hlqTMc1tHhYdvqy1wl /pxS/+xORaOyJNtKmHPliQ5mAAAsDYQcYAnLFDCcZWwvDQ7qhXXr0kJSZzjs2sygkE3t2Z7rNiAz 4alz57S7tdX2+uPHj9vClPP1X29tlSHpyXPnJL2/GnRkeFhHh4ZcS+xS9+JcHQhoS11d8s9pf2+v LTS94lgJi1uWDEfYAwAApY+QAyxhmQKGs6zq4MCA9kYiac8txkBJ56rRPU1NenRmP85bo6MFvc/3 xsf1tymb/J3HkwghuxwzazrDYVvDBWm6LC51T875yUl9/vLLbX8G2xsbbSHKuVJTjA5mMcvSw+Gw npoJZtsaGnSfY7AnAAAoLkIOUIbcBlPu7+1NKz8rxkBJt1WjTO2aU21raEh7n3+cmJBSZvXke3xu zQ/+z3XXpe1Zcnak21hTo6+3tuqVkZF5W6nZF4nY9hPt7u6WQftnAADmFSEHKEM7m5vTwkZiI35q WVoxBko6A8aJixfTnnO1369mv189M3tyEqsZqYHDuepzeGhI/zZTOpbr+NyaH2QKcc5QtqetLWOz hmJwWx2jgQEAAPOLkAOUIdMw9MK6dfrUyZOuqyqJk+xilGM5g8S6FSv04uCg7TlXr1jhGiRS9wQ5 TVhW3seXKazl05FuvgOH26oaDQwAAJhfhBygTJmGIZ9puj5WzJNsZ5CYisfTQk6+ZWZdOeO5AAAM gklEQVSpKjPsWXHrHJcpDBXSkW6+7GxuVtyybHtyaGAAAMD8IuQAZcx5Qt8eCGh7Y2NRT7KdQeL2 ri7b4+2BgO5panJtVe22ypGwORh0vd9ZbiYVNqCzGCV6hTANQ7tbW7Xb0SwBAADMH0IOUMbcTujn u6uXM7jc1dCgW7u6kmVzmfYEbayp0TvvvKOe2tqs4WOuHeGKUaIHAABKGyEHKGPzfUKfz9BRy7LS 9gVl2hN0vL9f1+ZoArDQ5WYAAGDpIeQAmLVMpWPZytekuQWTuZabZdrTAwAAygchB8Cs5VM65lx5 2RoKzWkfzFxXp+a6pwcAAJQ+Qg6AWcundGwx9gVlM9c9PQAAoPQRcgDMWj6lY6W20Z89PQAAlD9C DoBZK7UAk4+FbiENAAAWHiEHwLKyFIMZAAAojPs4dAAAAABYogg5AAAAAMoKIQcAAABAWSHkAAAA ACgrNB4AsChilqV9kQhdzgAAQNERcgAsin2RiHadOSNJybk1n1zMAwIAAGWDcjUAi+LI8HDW27nE LEud4bBu7+pSZzisuGUV8/AAAMASVrSVnJ/85Cd67LHH1DxTcrJlyxb9+Z//ebHeHkCZ2VRbm1zB SdxWX1/er3dbCWL+DQAAkIpcrnbLLbdox44dxXxLAGUqsQcndU/OfxUQcua6EgQAAMoXe3IALArT MOa08uK6EgQAAKAih5xjx47pC1/4gqamprRjxw797u/+bjHfHgCS3FaCAAAApFmGnB/96Ed65pln ZBiGLMuSYRi69dZbdffdd+v666/Xr3/9a+3YsUMHDhwo9vECgKS5rwQBAIDyZVjW/LQk+oM/+AO9 /PLLMgwj43OOHz8+Hz8aAAAAQJm59tpr835u0crVHn/8cV1++eW69dZb9eabb6q+vj5rwEko5GBR vo4fP85nAXwOIInPAabxOYDE5wDvK3RxpGgh5/bbb9c999yjp59+WrFYTHv27CnWWwMAAABA3ooW choaGrR///5ivR0AAAAAzIq52AcAAAAAAMVEyAEAAABQVgg5AAAAAMoKIQcAAABAWSHkAAAAACgr hBwAAAAAZYWQAwAAAKCsEHIAAAAAlBVCDgAAAICyQsgBAAAAUFYIOQAAAADKCiEHAAAAQFkh5AAA AAAoK4QcAAAAAGWFkAMAAACgrBByAAAAAJQVQg4AAACAskLIAQAAAFBWCDkAAAAAygohBwAAAEBZ IeQAAAAAKCuEHAAAAABlhZADAAAAoKwQcgAAAACUFUIOAAAAgLJCyAEAAABQVgg5AAAAAMoKIQcA AABAWSHkAAAAACgrhBwAAAAAZYWQAwAAAKCsEHIAAAAAlBVCDgAAAICyQsgBAAAAUFYIOQAAAADK CiEHAAAAQFkh5AAAAAAoK4QcAAAAAGWFkAMAAACgrBByAAAAAJQVQg4AAACAskLIAQAAAFBWCDkA AAAAygohBwAAAEBZIeQAAAAAKCuEHAAAAABlhZADAAAAoKwQcgAAAACUFUIOAAAAgLJCyAEAAABQ Vgg5AAAAAMoKIQcAAABAWSHkAAAAACgrhBwAAAAAZYWQAwAAAKCsEHIAAAAAlBVCDgAAAICyQsgB AAAAUFYIOQAAAADKCiEHAAAAQFkh5AAAAAAoK4QcAAAAAGWFkAMAAACgrBByAAAAAJQVQg4AAACA skLIAQAAAFBWCDkAAAAAygohBwAAAEBZIeQAAAAAKCuEHAAAAABlhZADAAAAoKwQcgAAAACUFUIO AAAAgLJCyAEAAABQVgg5AAAAAMoKIQcAAABAWSHkAAAAACgrhBwAAAAAZYWQAwAAAKCsEHIAAAAA lBVCDgAAAICyQsgBAAAAUFYIOQAAAADKCiEHAAAAQFmZdcg5duyYNm/erEOHDiXve+ONN3TnnXfq c5/7nL72ta8V5QABAAAAoBCzCjk9PT36/ve/r2uvvdZ2f2dnpx544AH98Ic/1PDwsF5++eWiHCQA AAAA5GtWIWf16tX69re/rerq6uR9k5OTeuedd3TNNddIkm688UYdPny4OEcJAAAAAHnyzOZFPp8v 7b6BgQEFg8Hk7fr6er333nuzPzIAAAAAmIWcIedHP/qRnnnmGRmGIcuyZBiG7r77bm3ZsmUhjg8A AAAACpIz5Nxxxx264447cr5RfX29BgYGkrfPnTun1atX53zd8ePHcz4HywOfBUh8DjCNzwEkPgeY xucAszGrcrVUlmVNv5HHow984AP61a9+pd/7vd/Tz372M23bti3ra52NCwAAAABgrgwrkVIKcOjQ IT3++OM6c+aM6uvrddlll+mJJ57Q6dOn9eCDD8qyLK1fv1733nvvfBwzAAAAAGQ0q5ADAAAAAKVq 1sNAAQAAAKAUEXIAAAAAlBVCDgAAAICysigh59ixY9q8ebMOHTqUvO+NN97QnXfeqc997nP62te+ thiHhUXyk5/8RB//+Me1fft2bd++Xd/5zncW+5CwwB5++GHdeeed+qM/+iN1dXUt9uFgkRw7dkyb Nm3S9u3btW3bNj300EOLfUhYQG+++aa2bt2qf/7nf5Yk9fb2atu2bbrrrrv05S9/WZOTk4t8hFgI zs/Bfffdp9tvvz15jpB67ojy9cgjj+jOO+/UHXfcoYMHD87q+2DOLaQL1dPTo+9///tp7aM7Ozv1 wAMP6JprrtFXvvIVvfzyy/roRz+60IeHRXLLLbdox44di30YWASvvvqqwuGwnn76aZ0+fVq7du3S 008/vdiHhUVy3XXX6bHHHlvsw8ACi0ajeuihh7Rp06bkfY899pi2bdumm2++Wd/4xjf04x//WHfe eeciHiXmm9vnQJL+5m/+Rtdff/0iHRUW2iuvvKLTp0/r6aef1uDgoP7wD/9QGzdu1F133aVPfvKT eX8fLPhKzurVq/Xtb39b1dXVyfsmJyf1zjvv6JprrpEk3XjjjTp8+PBCHxqARXDkyBHddNNNkqQr rrhCw8PDunTp0iIfFRYLDT+XJ5/Pp8cff9w2RPzYsWO64YYbJEk33HAD5wXLgNvnAMtP6sWu2tpa jY6O6tVXX9WNN94oKf/vgwUPOT6fT4Zh2O4bGBhQMBhM3q6vr9d777230IeGRXTs2DF94Qtf0Oc/ /3n993//92IfDhZQX1+f6uvrk7dDoZD6+voW8YiwmE6fPq2/+Iu/0B//8R9zUruMmKapyspK233R aFRer1eStHLlSs4LlgG3z4EkPfXUU/qTP/kTfeUrX9Hg4OAiHBkWkmEY8vv9kqRnnnlGH//4x2f1 fTCv5Wo/+tGP9Mwzz8gwDFmWJcMwdPfdd2vLli3z+WNRwtw+E7feeqvuvvtuXX/99fr1r3+tHTt2 6MCBA4t9qFgkXMlfvlpaWvTFL35Rn/70p9XT06Pt27fr4MGD8ngWvLIaJYbvheXrM5/5jOrq6vTB D35Q3/3ud/XNb35TDzzwwGIfFhbAiy++qB//+Md64okndPPNNyfvz/f7YF7/5bjjjjt0xx135Hxe fX29BgYGkrfPnTvHUmWZyvWZ+PCHP6yBgYFkAEL5W716tW3l5vz587rssssW8YiwWBoaGvTpT39a ktTU1KRVq1bp3LlzWrNmzSIfGRbDihUrNDExocrKSs4LlrGNGzcm//cnPvEJ/e3f/u3iHQwWzMsv v6zvfve7euKJJ1RdXT2r74NFbSGdSGIej0cf+MAH9Ktf/UqS9LOf/YymA8vI448/rueee07SdFeV +vp6As4ysmXLFv30pz+VJL3++utqaGhQVVXVIh8VFsOBAwf0ve99T5L03nvvqb+/Xw0NDYt8VFgs mzZtSn43/PSnP+W8YJn6y7/8S/X09Eia3pB+9dVXL/IRYb5dvHhRjz76qP7pn/5JNTU1kmb3fWBY C7wGfOjQIT3++OM6c+aM6uvrddlll+mJJ57Q6dOn9eCDD8qyLK1fv1733nvvQh4WFtG5c+d0zz33 yLIsxWIx3Xfffero6Fjsw8IC+vu//3sdO3ZMFRUVevDBB9Xe3r7Yh4RFcOnSJX3lK1/RyMiIpqam 9MUvfpET22Xi9ddf1969e/Xb3/5WHo9HDQ0N+ru/+zvt3LlTExMT+p3f+R09/PDDqqioWOxDxTxy +xxs27ZN3/nOdxQIBLRixQp1dnba9nGi/PzLv/yLvvWtb6m1tTVZ2bNv3z7t2rWroO+DBQ85AAAA ADCfFrVcDQAAAACKjZADAAAAoKwQcgAAAACUFUIOAAAAgLJCyAEAAABQVgg5AAAAAMoKIQcAAABA WSHkAAAAACgr/z/OPaUfG5E0rQAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd0lNXahvFr0kMogVCkg4AICigoTUVQQSwo6LGBXVE/ u6IHG1ZsiF1UPIAo6hEF0aOigAUUUVA6SEd6S0hCSG/z/fFkMiWTHkgyuX9rZTFvnT1hlLln7/1s h9PpdCIiIiIiIhIggiq7ASIiIiIiIhVJIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIi IhJQFHJERERERCSghJTn4nHjxrFs2TJycnK45ZZb6NKlCw8++CBOp5NGjRoxbtw4QkNDK6qtIiIi IiIixXKUdZ2cxYsXM2XKFCZOnEhiYiLDhg2jd+/e9O/fn3PPPZdXX32Vpk2bcuWVV1Z0m0VERERE RApV5pDjdDrJyMggIiKC3Nxc+vTpQ506dfjuu+8IDQ1lxYoVTJkyhTfeeKOi2ywiIiIiIlKoMs/J cTgcREREADBjxgz69+9PWlpa/vC0mJgYYmNjK6aVIiIiIiIiJVTuwgM//PADM2fOZMyYMXh2CpWx g0hERERERKRcylV44Ndff+W9995j8uTJ1K5dm6ioKDIzMwkLC2P//v00bty4yOuXLl1anqcXERER EZEaokePHiU+t8whJzk5mZdeeompU6dSp04dAPr06cOcOXMYMmQIc+bM4YwzzqjQxkrgWrp0qd4L oveBAHofiNH7QEDvA3ErbedImUPO7NmzSUxM5N5778XpdOJwOHjxxRd59NFHmT59Os2aNWPYsGFl vb2IiIiIiEiZlDnkXH755Vx++eUF9k+ZMqVcDRIRERERESmPchceEBERERERqUoUckREREREJKAo 5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjki IiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKAo5IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIi AUUhR0REREREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBR yBERERERkYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJE RERERCSgKOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcERER EREJKAo5IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0RERERE AopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCi kCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSI iIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIi IiISUBRyREREREQkoCjkiIiIiFQ1zz8Pxx0H/fvDpk2V3RqRaiekshsgIiIiIh6+/hoeecQeb9oE l18Oy5dXbptEqhn15IiIiIhUJZs3e2+rJ0ek1BRyRERERKqSQYMgMtK9PXRo5bVFpJrScDURERGR quSEE2DhQpg+HZo1g9tvr+wWiVQ7CjkiIiIiVU337vYjImWikCMiIiJV3+HDMGECpKXBzTdDy5aV 3aLy27rV5tt07w6NGlV2a0QCikKOiIiIVG25uTZP5Y8/bHvyZFi1Cho0KNv9NmyAf/6Bnj3Lfo/y +uYbuPRSyMy0gLNwoZWM9pSTA4sX2/yck08+Ou3KzbVhcomJ1r7GjY/O84pUMBUeEBERkaptzx53 wAHYvRuWLCnbvT7+2Oa8nHcedO0KO3cWff6yZfCf/1io+uADOPZY6NwZfvqpbM/vMnasBRyA2Fh4 803v49nZcMEFcNpp1tMzalTJ752dDS+8ANddB599Vrp2XXMNDB9u84B69oSDB0t3vUgVoZAjIiIi VVtMDERHu7eDg6F167Ld65lnrIcELCy99577WE6ODR+Lj7ftr76yD/q33AI9esCNN1oP0Lp1MGwY pKSUrQ0AERHe2773mj8f5sxxb7/yioWhknjgAXj4YfjwQ7jiCvjyy5Jdl5oKn3zi3t6+HebNK9m1 IlWMQo6IiIhUbZGR8L//Qbdu0KEDvP8+dOrkPp6ZCXfcAV26wPXXw7Zttn355d5BAQqGC1ep5tRU 6N/fhow1awYzZ8K777oDUXa2DeVySUqy4HH77bZ4p6/HH4e2baFdO3jiCUhP9z7+8sveQ+WmToVz zrG5RmedBQkJBe8ZUsJZBj/+WPR2YSIivMMkQJMmJbsW4NAhGD0abroJFi0q+XUiR4Dm5IiIiEjV d8YZsGKF/2PPPQdvv22P16yBuXNh717b/vJLG9p20km2/cYbcPHFNuekZ0+4807b/+GHNi8GICPD Pqj79q5ERbn3RURYkAF45x3r9bnoItv+9FPrMXJ5+mn47TcYM8YCVIcO1jM0ciS8+KKd43S6w8iu XeBwQO3akJzsfm5X4CpOt272e3Bxvfbi7NgBxxxjYSUoyALLgAEluxZsPZ/58+3xJ5/YUD/PMCpy FKknR0RERKq3deu8t10BByAryybvu/TrZ3N8tmyBvn2t1+S22woGmkOHrPfGU3Cw+7Fvz8z337sf b9xYsI0//mg9RccfD1Om2L569Qp/TT/95A44YO1bu7bw8z29/Tacfz60b29D1266qWTXjRwJ69db 4MrJKV3Ft+xsd8AB+/389lvJrxepYAo5IiIiUr1dcIH3tmd56eBg6zXxFBkJH30Er70GS5fCxImw ebMVJADrRfEnKanwNnTu7H58+umFn5ebC48+ao/vvBP69LHHdet6hyhfUVHWA1ScjAx7XbNn22ua NMmqyZXErl1FbxclJMT9+wPrCerateTXi1QwhRwRERGp3q691qqI3XmnzW1ZvNj2nXcefP45nHKK nZeVBY89ZhXLPv7Y+x6bNtmwtp9+ghkzCgajwgQH2zCt22937zvrLOuxKcy+fdC0qfXM/Pab9Swd OGA9IUE+H81iYuDss+Hbb22om6dt26zqm2sY288/2xyaJ55wn5OYWPC1goUt396rq692Pw4Lg3/9 y8p1P/xwyXplvvnGhgKedhpMm2bDAUUqiebkiIiISNnt2GG9DDExR+f5srKsNPKMGVbOecYMOPFE uOwy+3H54IOC1z72GIwb5/++gwbZB//Ro+HPP61n4tZbrRfEcxiWr5wcm/fzwQdwww3u5x440ObC NGhggev++70n4+/bB1ddZdXamja1fXFx3sUNwEo4BwfDmWd673/1VSsr7XTCuedawLj1Vhtm58v3 7+bnn20NnIQEuOQSWxcnJMR6mDp3tuF2555r4Wj8eLtm/Hj7PZx2WuG/izZtSl7JTeQIU8gRERGR 0nM67Zv/Tz6xD+Fvvgn/939H/nnfew/++197vGED3Hyz9xo6nuLjrQeidWsbOjV7dsFzbrwRevWy MtETJljAAZtj8tVXdk337sW364svLMR89pl7WJvDYT0wrVtb9TZfO3da9beMDGjVytan8WfuXKv2 duml8PffFmZcRRLA7vHll3D4sPd1DgcMGWJzjjxdd527etsXX1g57BkzIDzcHrv861/ux9nZVkWu qJAjUoUo5IiIiEjpzZvnXlMlJwfuvtvKN7tKMh8p+/cXve2yezf07u2uVHbeebbPU1CQlYkODbVt p7PgvZ991npopk4teNxTQoL1pnhyOmHWLAsS/irDOZ0weLA9Dg4uunram2/asLhBgwq+DrBFPD2L IURH21C9c87xPm/t2oJzbb75xnqaJkzw3t+unRVocGnf3v7cutV6flq1Kry9IpWsXHNyNm7cyMCB A/k4b6znww8/zJAhQ7j22mu59tprWbBgQYU0UkRERKqYjAzv7ezsgtXISurwYfvw7a+3w9eVV1qP g8u11/o/b+pU94d5p9N6ZDzXnnE4bK0aV8DZutWKEXgWHXA6rQdl6lSrjNa7t5WJfuABG5J29dUW BC6/HFau9N+OpUttXow/nkPTfAOOq10uCxbYa/cXcKBgtbfERBty1qiRDXVbssT2P/ec/7Dm2TPk MmWKDbtr29ZC0E03WQW2du2sd2rMGP9tEakCytyTk5aWxtixY+njqgqS54EHHuBM33GjIiIiElgG DbK1a3791bZHj4Y6dUp/n+XL7V5xcdYzMH++faguzKpV3gHLs6fBU1RU4fc4/ngb4uXZE3HOOTY/ xh+n0+axgM3/6d4drrjCyjQ3bGiLkHqWe/a0bFnBYWTFiY62APbKK95lo2fMsHkv27aV7D65ufZ7 /eUXCzybNxdeOc5fkYDmzW2oXGqq/SxbZtXaXMaOtd6ivn3hrbegVq2SvkKRI67MPTnh4eFMmjSJ xo0bV2R7REREpDoID4cffrAP/3/9BS+8ULb7jBljH8TBihg8/3zR57t6JFwKq/p1663W++LPgAHe AWfatMIDjq81a+DJJy1ENWpkVcg8F970Z9Omkt3b5dAh6zXZurXgscLCVHESE+1+jz5qwQxsuF5Q kL2Ou+7yf92nn1rxhEaNrMqarw0b4P33bUhf9+5w3HHudYBEKlGZQ05QUBBhYWEF9n/00Udcd911 jBo1isTCumdFRESk+gsLsyBR0nLLLgcP2iT7U04puIZLcUPezjjDe3vHDnexAE+RkVYOul077/0h IfDGG977li4tWbs9uYaXZWWV/triuIaTpaUVPHbwYNnuGRxsASQ7233f3Fz7iY2Fe+6x5/V8Pbm5 FrZcPWfz5hV+/1mzrFdu0yYb0vbuu1YgIj6+bO0VKacKXSfn4osvZtSoUXzwwQd07NiRN998syJv LyIiIoHgllvsA/DSpTaEKiLC9jduDA8+WPS1w4bZeS65uTax3yUz0z33xuGw6mue7r3Xgo6nfv3K 9jrKo0mTsl3nO5+mTZuSXZeTY0UObryx4Po4YL1RwcEWXF3rCuXk+A9a/viGo//7Pwuyp55a9mAm Ug4Op7OoUiHFe+utt6hfvz4jRozw2r9lyxaefPJJpk2bVui1S8vyzYmIiIhUaydccgkRO3bkb8de cgkHzz+f9LZtyalXr9jrjx8+nKiNG/O3c0NC2PT22wSlpXHsI48QnJJCwoABbH3+eQgK4pj336f2 ihWkdu5McufOROzYwaG+fclo147aixfT4d57CcrKwulw4Cjfx6IScwKZMTGElzAAOAGHz3bascdS y9+QtjK2x/P+u+64gwMjRnDi0KGEHThg5zgcJPbrR/SCBV7nJp9wAs6wMOosX+73XtvGjOHgxRdX SDulZutRil7jCi0hfffdd/Pggw/SsmVLFi9ezHHHHVfsNaVprASupUuX6r0geh8IoPdBQNu71xbs 3LPHa3ej/v1p9NJLtkDmyJHw0ktFvw9cPT95grKz6XjHHTZ3JK+Xov7PP9Nj40YrrXzqqQDUe/ZZ W0ATaPn661YSOS4uvxfiaAUcsBBQ0oDjOt9322/AcTiKLnXtEhIC9evb8L+dO3H4DPlrkZtLi9hY yAs4YL+f+gsW2Pyc2Nj8/bVPOgkmTrQS1MnJON5806uiXJuTTqJNGf+b1v8PxKW0nSNlDjlr167l hRdeYM+ePYSEhDBnzhyuueYa7rvvPiIjI4mKiuK5554r6+1FREQk0Nx/v3ehgJAQmyPy0EPu8tHj x9uCky1bFn4f3+FmYEHFdy7w8uUWct5/Hx57zEKUp82by/Y6qjKn00JgeroVR/A3NA3s9x4b6z3U z9N771lhCX9iY23OU1qaVWB7/HF7rn//245HRFjltbQ0WzvJc4HRo83ptAC2Zo1V8bvoosprixxV ZQ45J5xwgt+haAMHDixXg0RERKSaWbXKAkavXt5r2Pjy6cHJLzLguz7O+vVFh5xnnoELLyzYY+G7 ds9779kaNjfdVLLejUDhWjOnsIBTEjk5VkSgsKDUsaMtBtu6tXfp6CefhKeesseNG9tjh8PKaP/n P/Z3ftNNEBNT9raVxpNPwtNP2+MJE6xAwtChR+e5pVJVaOEBERERqWGeeQa6dbMFJ/v3L7gopcvG jQVDTmGeeIL6c+e6t5csgRNOsGFSd99tH6x9F8v0JyXF1vGpSQGnohUWlC65BDp1soDz7bcWXJ59 1tbLcTlwwNbRyc6Gs8+2oYKjR1tPneu+hw9bsYmrr7a1iyrat996b8+eXfHPIVVShc7JERERkRok K8v9rT3AH3/A//5nvSe+rrjCe3hYaKi7IldIiAUX18KemZm0HD/evS7LJZfA7t32+M037YN0SYKL wwHvvFP61yWFa9QIxo2D666zv4svvoAFC9x/H3Xrep//0kvWU+c552fDBhtKePrp9r747jvbP306 LFqUP4eqQnTq5F0ivFOniru3VGkKOSIiIlI2QUEWUFxrxoCVIPbHd/5LVhZ06GBDorKz3QEnT0h8 vPUMjB5tBQs8lbRnxuks+SKfUrx69WztoRNPtHk4zzxT8JyICCsh7Vq0dP9+O9ezIEJICDRrZo/n z3dfm50NCxdWbMh58017f7rm5Nx9d8XdW6o0DVcTERGRsgkOtnkOrkIAQ4fCkCH+z7300oL7XL0z fjjAigV07lyyoWly5F18MXz1FUyebD00/hw8CNHRBfc7nTa0rVUrmDoVjj3WAk39+u5zHA7o3r1i 2xwdbXOHVq2yohbBwRV7f6my1JMjIiIiZXfTTfbh9/BhW5jS4VvsOM+kSTbU6e23CxYaKMqmTRXS TCmnjh1tfk1xi4Pm5BSsYucSEQEDB8LJJ9uwtAED3MUnmjeH556zuV0iFUA9OSIiIlI+DRtC27aF Bxyw3p5HH/UuTFCasCOVa8OG4gOOS3Y2dO1asNJefLz1AvXr5y5I4BIcDNdeW3HtlRpPIUdERESO jpwcm69RnOBgsurVO/LtkYrhb92iCy+0QPvhh9Czp/exgwcLzt0qwQLyIqWhkCMiIiIVZ9EiK/fc ogW88op7/19/2Zydxo3d+1yTz33l5BBUWClqOTqKWu/Il2ePjEtUlK2Lc8stVgLck8NhVdjuvNPC zeDBNk9HpAJpTo6IiIi4ZWSU7gOup9xcm58TF2fbo0ZBnz42mfz88yE21vYHBcFHH8EZZ9gEdFcp aQ/Bvgt7ytGVkQG1a7urpJVGixa26OZff/k/7nRaUYk6deCHHwr29IhUAPXkiIiIiFU6O+kkmxze o0fhk8eLkprqDjguO3bY8CRXwAELQ1OmQLt2fgOOVBFlCTgAu3YVHnA8HT4MY8eW7TlEiqGQIyIi IvDII7BypT1etszWNimt2rXhggvc202aQP/+cMwxVpzA0w8/QGZmmZsr1cxxx9kQNl+//3702yI1 gkKOiIiIQEKC93Z8fOnvMWeO9QT162eV1JYssaATFFSxCzxK9dKmDUybZvO1TjnF+1hcnA1nvPJK O/booyUrTiFSDIUcERERgdtucy+6GRYGt95a8JxZs2ytG1ePTbNmtljnggXw73/bBPKZM+GXX2D2 bFv4EWzfd9+571NUqWkJPNu2Qa9etkbSuHEFK6stXw7Tp8PSpbZWzoQJldJMCSwqPCAiIiJWGGDp UhuqdsopViHNU3IyjBjhXitl9mz7c+9eG5Lma/ly+OknWw/l3Xe9jzmd8MADtgK91BwTJ8J778HI kfb+2bXL/3nLl7sf5+bCBx/YnLFhw6BTp6PTVqn21JMjIiIiNj/mm29g4UIrFuArKanki0G63HZb wYADtq6KAk7N5HRa0Bk82P/6OgAtW7ofjhsH119vw9h69rRFSUVKQCFHREREYPhwKz4waZINRfv5 Z+/jTZvCmWe6t4ODi7/n1q3+9/tbV0UCQ0neF2DV9a67zhYN9Qw7DgdccUX+ZoPvv3cfS062IC5S Ago5IiIiNUVSkq1dc9VV8O23ts/ptIAzc6b7PKcTfvzR+9rHH7e5NwDdutn1J55ohQVcfOfaBOlj Ro2Tk1Oy83JzYfJkCy3Z2fbeqVcP3nrL7nHRRTB4MNn16nlf55rn5emll2x45aBB8M8/5X8NEhA0 J0dERKSmGD7cHW4+/9yGpmVkwH//W/DcLl3cjw8e9F7PZOVK+Ne/3OuoBAfbfItTToHTT3fvj4zU OjhSMk4njB5tQad3b1tzCQgND7cAExsL114Ll13mfd0331jRC4C//4bLL4c//zzKjZeqSCFHRESk pnD1xIB9W75woZXv9fX4415DhvzyXCgyJ8c+WM6aZcGmRQsYM8YKFYiU1E8/2fpJHoIzMuDVV2Hg QP/XrF/vva05O5JH/cgiIiI1RY8eBbf794chQ9z7HnoInnrK+7yYGO99gwYVvPfEidZLFBtrHzzf fNNKTYuU1MaN/ve/8Ubh1wwaBOHh7u0LL6zYNkm1pZAjIiJSU3z2mQ35OftsK8s7YIDNm/nyS+uJ WbPGgk+PHlaqd/x498KMjz8OW7bYOUOHFv9cixcr5Ejp+KvqBzYkbd8+e7xokS0cOnKklZXu2tV6 KO+7z96vU6ceteZK1abhaiIiIjVF48bw2mvWKzNnDjRvboEnKMjm06xdax8gXZPHH3wQPvoI6tSx YgPjxkGtWtZLUxyn0/3BVKQ8XIuH/vOPDVvLm6/DokUWunv1sh+w950I6skRERGpWYYNg9dfh08+ gfPOsyICLuvXF6yOtXKlzd2ZMMEqswGcddbRa6/UaLlBQVa8olkzePhhd8ABKzQQH2+Pf/vN5oKF hVkvj8JOjaeQIyIiUlM4nfDrr+7trCx4/30rH334sH0bHhVV+PXTp9u8iSVLCh5zOIq+VqS0QkNx 5Oba+9bptPdfaKj7ePv2UL++Pb76ahu+lp1taz1Nn145bZYqQyFHRESkpnA44OSTvbdff93KQffu DXXrwu+/2zkhIVbO11NCApxzDrz8csF7O52QknJk2y+Bp3ZtGDwY+vXz3te2LbRujcP3/Ndfh/PP t+p/c+e612KKjfU+z3dbahyFHBERkZrkq69sMdCzzvIe0vP33zBtmi3wuWyZ9fIkJsLdd3tfv3On 97fpIuWRkQGZmVYEIzTUgneDBjb/ZvNm73PPOw9uvdWq+H36qQUhl9tucz9u0sSGZUqNppAjIiJS kzRvbvNx5s4tOLzszjutN2f4cCs20LKl9eo4PL5Pr1ULmjY9um2WwJWVZevjPPWUPXY6/VdZq1cP vv7a3XPja/x4O/6f/1hIb9HiyLZbqjyFHBERkZooONjK7Tp8BgQlJ8N//2t/7toFN9/s3eOTmlp4 qV+RI8XhsPdsUS680N6vzZqV7t7798OqVdajVBZPPw3HH29r9mzfXrZ7SIVTyBEREampLr20+G+8 fautiVSGq6+2P2Nj4eDBirvvzJnQurWVSO/dG5KSSnf9Z5/BE0/Ahg0wbx6MGFFxbZNyUcgREREJ ZFlZcO+9Nuzs5pu9S/C+847NsSlKrVre2yFaYk+Onqx69ax8+euvw0MP2VpPDRva/J3Bg0sfSnyN GmXzggCWL4fJk0t3/aZN3tsbN5avPVJhFHJEREQC2Qsv2AfEFSvsA9zo0e5jy5YVfW1MDPTs6d6O joaffy5YdU3kCAk+fNiKYaxbBy++6D6QnW0L2j79dPmewHc9ndzc0l0/eLB7sVKAiy4qX3ukwijk iIiIBLK1awvfPvPMwq+rXdv+nD/fvS8x0UpIHzpUYc0TydejR4EAHZSbCwMH2nAwf/buLd9zvvii u1rgiSfCTTeV7voePWDBAnjgAXjjDXj33fK1RyqM+pxFREQC2XnneS+MOHiw+/E119g34vPm2VCd 9evdx3Jy/M99cA3tEaloGzZA375WbS07270/MxP+9z+b3O/5Hg0JsfdweVx5JZx2GuzbB126QERE 6e/Ru7f9SJWikCMiIhKo1qyxD47XXAPh4dCrl83L8XTDDVZ84L//9d6flnb02ikCVtFv7lz/xz74 wP6sXx/uv9/Kn59+Opx6avmft2VL+5GAopAjIiISaDIzbc2bKVPc1dEuu8w74MybZz9duhRfmhds fZLSzlcQqWgJCdChA1xxRWW3RKo4hRwREZFA88gjtiiip1mzbJJ1QoIVIxg/3j3puk2bou8XEaFh alJ1tGpV2S2QakAhR0REJNAsWVJwX7t2EBdn1dK2bfM+5rvtKzOzYBUqkaOtYUMrI92njxW/eOgh 2Lq1YC+lCAo5IiIigef00+HXX93bxx4LX3xhP8UFGl+tWsGOHRXaPJEyWbTIhqqBzTP7+mt7PHeu Dbm84YbKa5tUOSohLSIiEmieeQbGjoVLL4U334QtW6BzZ1vnpqTCw+HVV+GSS45cO0VK6vbb3QEH vEubA4wbV/i1H35oVQZvu83KoEuNoJ4cERGRQBMcDI8+WnC/a1hPcnLx98jIgDFjrPfnjTdUdEAq RUqHDkRdcIG9p3/6Cb791spL16sHhw+7T8zOhltusfljDz8MTZva/jlz4Lrr3Oft3u3uAZKAppAj IiJSUwQFwbPPwj33lOz85GRo1Mg+FD7+uJWjLklAEqkgkdu2wWuv2carr7rDdv364HDYXDGHwxYF dRXbmDcPVq2yRT5956ctXlzwSVz3kICi4WoiIiI1yd13w/vvl3zRwwcesGC0dKkCjhx1QVlZ7g3P 3sSEBFsMNCQEhgyBlBT3sfXrrccGbHFRT1FR4LpnZqb1boaF2UKjf/99ZF6EVAqFHBERkUCTmmpD e9as8X981ixITy/ZvX780SZ8i1Q1WVk2TO3rry2ouBxzDEydCj16wMSJcMop7mOePUNvvw0zZtg9 NmyAkSN5r2+LAAAgAElEQVSPZuvlCNNwNRERkUCSlGTV1Vavtu2XX7YV4j2pHLRURyEhVnwgLAxW rnTvdzph9Gj45ReIjLT3/2OP2bFly2z+jqetW+3PAwe89/tuS7WmnhwREZHqYvt26N7d5hqcd57/ 4WOffeYOOGBzaXyNGVO6SmsiVUF2NqxbB02aFDz27rswcyZ89513QQKwuWiej4cOtcfDh0Pt2u5j t9xS8W2WSqOQIyIiUl3ccw8sX24f9r7/Hl58seA5nsN2wEpB79sHf/7pnrdw6qmweTP8/jsMHnzk 2y1SkTzXgHKJjYW//rLHgwZ5FxK44gr4+GN45BEbfnnuubb/xBOtp+ftt22tnQcfPPJtl6NGw9VE RESqi/37i94GuPJK+0A3d64FnFtuscVA09KgXTtYuNDmLDRoYMHH9cFQpLqIiYFduwruHzUK+vWD s86C2bPhyy+hfXu4914b6uZPhw7e6+/88osNhTvjDDjppCPTfjkq1JMjIiJSXXhOjA4Ph2uvdW+n pVnZ3JQU6+VZuBDuugs++MCOgS0KOmiQldG94gqrtBYXd3Rfg0h53XknnHkmNG7svX/tWgs6YD2U 775r1QELCzi+PvwQ+ve3/y569oSff67QZsvRpZ4cERGR6uLGG+2b6dWr7RvrLl1s/549tr1lC9St C9Om2erue/cWvMfq1dCnj4oPSPXVvj3Mnw85OVYKPTvbfeyTT2z4WVlMmuT+7yIry74gGDCg3M2V yqGeHBERkeqkXz+44w53wAF45RULOGDV1UaP9h9wXBRwpDq76y64/Xb455+C6+AEBVkv5vLl0LGj rYtz220le88fc4z3tr8CB1JtKOSIiIhUd56LJIIVHwjSP/ESoPbuhXfesRDzyy/exxISbD7NOefA xo22ZtTEidbDU5xXX7VhamFhVpzAVYZaqiUNVxMREanu7rnHyufu2AG1atnaOLt3w7PP2jfZhw+7 e3rCwmyld5Hqzjfce4qP994uqmfTpXlzm68mAUFf84iISI23NyODRYcOkeQ5tr+K25CaypVr13LJ mjX8ER0Na9bAH39YmDnnHLjuOvsm+/zz3QEHYMgQm7fjEhlp6+6IBKroaBg2rLJbIUeZQo6IiNRY uzMyeGDzZo794w9OW76cE/78k22uSmSV7OP9+3lwyxZmHzxY4Fh6Tg6nL1/O9NhYZsXFcfbKlewN C4NevQrOK9i40Xs7KcnKS194IZx9tk3ezso6gq9EpIJFRJT83OBg651p1869SOi6dVZ8o21beOaZ I9NGqXQKOSIiUiNtT0+n+19/8fKuXaTnTUrelZHBa/7W3yin5YcPM2zNGoatWcMK39XY/Xhl506u XreO8Tt3csHq1cyMjfU6vjQ5mTiPYJKam8tfhd13yBDv7Xbt4IQT4Ouv4dJLix66dsEF8MMP0KZN sW0WOeIcDrjoIkhPL3jM1TtZq1bBa4KD4fjj7ZyTToKhQ63Xc9s2ePxx+OabI950OfoUckREpEb6 7MABDvjpwQj2XCm9AiRkZXHOypV8GRfHl3FxDFy1isRiek5m+axd85XPdqqfYXXRwcE4/VWQuvZa +OILq8oGtnZInTpw8skFA05wsPf2t9/CwIH2YVCksoWFFQwxLklJ1sMzY4a77LPDAePGwaOPwoYN tm/lSu/hmwBbtx65NkulUcgREZEaKcbPPJT2kZGMatmy3Pd+dvt2uv75JxetXs0fSUnEe4SSuKws tqan82NCAueuXMnQ1atZn5LidX2HyMgit0+pW5eGPgscDli5kroLF/LRvn0FGzRsGCxb5r1vxQpb /NBTTo59QIyKcu9TuWmpKjIy4NNPCz+enm7FNr7+2t7vW7bAfffBoUPe57Vo4X4cFWWV1Mpi1iwr 1/7VV2W7Xo4oVVcTEZEa6domTZiXkMD0AwdoHBrKy+3acWmjRkT49maU0vQDB3jsn38AWJ2SwqHs bBqHhub3Gh0TFkYIcOHq1aTnVYdampzMll69CMsr+/xKu3Yczslh+eHDnFW/PqNbtfJ6jvqhoYxv 147rXd9OAzlAck4ON27YQP/oaDakpdEwNJRutWvbCZGRkJzs3Vh/hRYWLCi6apVIVfbbb1Zo4M03 bX0cgLvvhh9/tLlnkZHw/vs2L2ffPrjsMitFXVqTJ8PNN7u3338frr++Ql6CVAyFHBERqZFCgoL4 b+fOfHj88YSWYk2ZKXv3MipvuMsr7dpxQ9OmXsfX+fTKbEpL4+eTTuK57dsBeLR1a7amp+cHHLC5 QAcyM2kREcHujAw+2r+fs6Kj+ahTJ1YlJ7MqOZlutWuzOS2NJmFhNAgNpXFYmN/2ZTmdnLNyJRvy Cig817YtD7duDe+9B1dead+Gu4waBRMmwJIl7n0KOFLdZWfDnXfCv/4FDRvCeedZz+WqVdCjB3To 4B7SVlazZhXcVsipUhRyREQk4P126BDfx8fTqVYthvusYu4ZcHKdTv4XF0dqbi4XxcRQ22dI2I70 dG7ZsIGcvO2RGzZwTv36tPSo9nRugwaM3b49/5xsp5OXdu7k+WOPzT/P6XRSJziYwzl21nEREdQK CiIuM5NeS5eyO2+uzDPbt7M373H9kBASsrOpFRTEzBNOYEsRVeA2eBx7ats2RrdqRdDQoRAXx+Jf f2XOoUN0a9aMi/v1g86dbdV4VViTqq5ZM9izp2Tn5uRASoqFHLD3eefOFdeW9u2L3pZKp5AjIiIB 7eeEBAauXJkfOjanpfF4IdXChv/9N9PzKpnVDQ5mxSmn0NZjPkxcVlb+fcCGiB3MyvIKOX3q1eM/ HTtyy4YNZAOxWVlM3bePP5KS+PvUU5m6bx+3bNxIttNJ6/BwTq5dm9+SkohZtIgTa9XKDzhAfsAB SMgbWpaam8v9W7bQx3OtmyKEBQURlFdM4buMDC6MjCQ3MhJyc3n9q6+4+5JL1Hsj1UNsLNx4o83L SU0teDwyElwB/7LLoHXrI9eWsWOtPb//DqedBk8/feSeS8pEhQdERKRayMrN5YHNm+m7bBn3bd5M Zgk/mM+Ki/MKJp/7lGN2OZCZmR9wAJJycrji77+9zukSFcWpderkbzuAVT7D0wC2pafjO9tlfWoq +zMzuS0v4ABsz8hgTUoKsXm9KGv8fXDzI9vpJKyIKnCuI2EOBxOPOy5//2exsXj+1h4KD2dtBRRa EDkqsrJgyhT/Acd1/KKLYPbsogsUVITateHjj60y27Rp3sU6pEpQyBERkWph7PbtvLxrF78nJfHa rl08WcKyxm19Fg48tpCFBGsFBeFbcmC35/wVbGjbtR7D3ZzAqM2bC9yrWXh4gX3HRUZSLziYLJ9q ZclFhDXPtkbnDZ0LAbpFRRUa1lztur5JE86OjiYlxx3xfEtXp0VEsLJdu0LvI1LleRYKyc6G//3P qgb++qt7PZ2cHPj8c5g6tWClNQlYCjkiIlItrPSpDLbCt1JYIe5q3pxbmzalRXg4A+vX512Png0X p9PJwexs7vMsLQsMc43n97DPZ22ZRD8Vyk6tU4fGoaE4gAiHgyExMczt1o3IkBBGehQq6FmnDvc2 b56/7fuP8iOtW7Otd2+29+7Nzt69WXjyyZxUpw4z4uI46PO8ER49O8dGRDB1/36+S0hg5MaNfHbg AIlZWXxz8GCBtib7lKcGC0kiVV5UFHTrVnD/p59C//421yw5GYYPh8svhxtugD59oAQL8kr1pzk5 IiJSLZxdvz5feXxIP7t+/RJdFxIUxLtFlIjNzM3lotWrmZOQQCgwqkUL0nJzOa5WLe5s3jx/gU1H Xoj4MynJ6/ps4LK1a/m0c2eCHQ6cTicXrV6dXzI6w+nkyTZtaB0Rwdz4eKbmrWMT6nDwZOvWTPCY SJ0LdI2KomFoKIMbNOAmn8ptidnZ/FXIB7QB9eszokkTagcHM9pnscNFhw5xWr16BYbQAawfNoy0 efOIzAtvuegbUKkmPvoI/vyz4BpQLsuXW+/NZ5+5961bB/Pnw5AhR6OFUokUckREpFq4q0ULwoOC +O3QIXrXrcttzZpVyH0/PXCAOQkJAGQBL+/aRe2gIIY2asT4nTt54p9/CA0KYkKHDtQLCWFuYmKB e8yIjeX57dt5rE0bDufkeBUPcAIbU1PpXqcOE3bvJjMvNGU5nfxn3z5+zHtul90ZGXSqVYt+0dFe ++fFxzNk9epCX8f38fFsSkvjx27d6FOvnleFtd5169I8PJxLGzZkZlwcAA1CQhgSE8Owbt1o2KwZ 5/75J+GZmdQ/fJjmBw9y/+efE5mZyb7oaJokJlL4DCCRI6B27YLrOvkaNcrmxBR3H8+CBOCuuCYB TSFHRESqjVuaNeOWCgo3Lhl+5sQk5+by0f797nNycrhh/Xra+xna5bL48GFSc3K4Zt06HLiHfIU7 HPlza6J9SlLXDwmxymce83QOZmczPTaWGbGx/LtVKx5p1YoJe/YwfseOIoeRObHKcW3/+IMIh4OO kZFkO53kOJ38lJjIkIYNaRMeToTDQbbTSXx2Nh/s38/vSUmc0Lgxs/r1s3bk9Vj93rkzD06fzrwe PRj7/vtF/g5FKlxaGkyZQvY99xBS2PCy4gLO4MEwYgTUrWtV2VJT4aGHbMiaBDz1SIuISI20NiWF XkuX8tS2bYQXUanMJRfYWMTaNKk5OYzdvp3/HTzoFUYynE7OXbWKn+PjeaZtW7rkVWHqGhXF2LZt /c77AStP/fyOHZz01188tHUrcX7m/gAFiiXkAqlOJxvS0tiSns62jAz+s3cv/1q9mpd37ybd6fQa trYxLY0RjRvbhsfv4du+fen/+utE+6keJ3LE5eTAP//gDA31f7xbN6/3q5cWLWDNGvj2WwgNhUsu gcREK0Rw7bXw2mvwxRdHru1SJagnR0REaqTL1q5lXRElmx1YL0y6s2D/SduICBqFhLDEYzjNT4mJ hYalxJwczlq1iiDgvY4dubJxY2oFBfFTQgK/+8zx8bXFVSGqEM3DwtjhUwzBn7+KGPrjO4fH06zT T+eemTMJzckp9ByRI+KZZ/AbcTp1svVp3nkHRo+2sPPQQ7BpEzRtCo89Bg0aFLxu82bo2dNdYe3f /4YXXzySr0AqkXpyREQk4DidTibt2cPoLVv41c8cGoB/fMJDVJD3P4lOyA840cHe/SUXNGjAk23b eu0LBoY1alRku3KBmzdsoOfSpZy2fDnnrFrF1mJCTHG9TCUJOACHCukJAsgo9Ags6tKFK8eMYV90 NClhYWjZUKl069bBjh1w//02BG33bpg1y6qqvf02LFjg/7ovvvAuIT1lytFpr1QKhRwREQk4D23d ysiNGxm3cycDVqzgFz9B5zKPQFInOJjZXbtyZyHzfYIdDq+w8daePcyMjeWimBjA/jF9tX17RjZr Rv969Ypt39+pqcX24Lhk+OlJKous4k8p1BdnnsmM/v159Oab9cFBKl9wsIWZtDRbE+eCC2x4GkBG Bjz4oP/rfKoVUsHz+6Rq0XA1EREJOLPyKoiBzW35+uDB/Gpl7+3Zw0f799M8LIwX27YlNTeXyxs3 pnNUlN8wBDYkbJXP0LbJ+/ZxfGQk5zVoQExICJfnzWvZVcKelerm7rvuou/ateQ6HATlBa+00FCW dOzIma4PmCIVISTEFvYsTE4OvPGG9d7s3Fny+15zDSxaBB9/DC1bwrRp5W+rVFkKOSIiUm38kphI Sk4OZ9WvT3hQEDNjY1mbksLA+vXp49GD0j4ykk0eRQIahoQw/O+/WZ+aynKPuSn7s7L46aSTAJif kMDT27b5fV7fgOOyPi2N9XnPsyYlhV9PPpksP9Xa/AmCajX0yxkUxG9dunD96NHcPHs2WcHBPHzT TZy9fDl7GjXiqp9/ruwmSqDwF3DCwuCss+D77937/AWcsLDC59kEBcHEifYjAU8hR0REqoXbN27k nbyFM/vWrcsFMTE8+s8/ADyzfTtzu3ZlQN4CoZM7duTGDRvYlJrKxQ0b8umBA6zwUyXMM/BM2bev XEO6VqSkEL1wISWdnh9K0XNhqqpp557LtHPPBaBhQgIvnHACMYcOMWzhQiKyyvMbFMkTFga+PaI9 e8J113mHHF/DhsFVV0HXrke2fVItaGitiIhUeQezsvIDDsCipCQm792bv53tdDIjNjZ/u2l4ON91 7crm3r0Z166d34ADUC84mFd37uSvpCQ2FFFpraRKGnAcVM+A4ysuL1QerFeP6f37V25jJHD4G/KZ nAxXXglvvQXh4d7HjjkG2re34WuXXw7HHQe33XZ02ipVlkKOiIhUeeEOByE+VcaahoV5bbfOW3DT U3J2No/98w+NPNbaCAJC8+61PSOD+7ds4dRly1hS2IKDR0DFlBKoWm7+9785e/x4fu3SpbKbIoEm KAhGjbLHxxxjxQU8nXKKlYf2NHEiLFxo6+L06GFlpUs4lFQCg4ariYhIlVc7JIQJHTpwx6ZNZDud XN24MePatWPEunX8nZLC4AYNuK9FiwLXnb96Nb/mlYx1AO0iItiSnk5WBVUsE7fskBB+6tGDPzp3 Zt1119HKo2dNpIAmTWxYWjGFA5K6d6fumWfCrbfaT5MmBU/65hv/Fz/5JPz4oz1etsyqq91xR/na LdWGenJERKRauKVZM67L+4Dz0YEDnLliBefUr8+evn1pHxlJt7/+4rxVq9iZt+7MHRs35gccsN6T zenpAdmLUpWkRkYy9IknqlVRBakEcXHQp0+xpyX17Quvvmrr4aSmQt48vBJxBRyXtWtL2UipztST IyIi1cLyw4eZvG9f/vamtDQe/ecf1qak8MmBAwCsS01lxLp1fNulC297zOGRo2t/w4b6FlWKFhIC n39e7GmpnTqV/J49esDSpYUfHzSo5PeSak//DxIRkSotI28cfWFDzJb5zKVZlZzMVo/y0b4cQK/a tfO/5XMAwRXQTnGLj47mQN66RGC9aJMGD+aRG2/k986dK69hUnVkZEBxw0br1iW5Wzc48UT/x2+8 EQYMgO7d4eWXobD3Vv/+8MUXMHRouZos1Yt6ckREpErKzs3lqnXrmBEbS5PQUJ5s04amYWHs9am8 dHb9+l7zbA7l5NBr2TJ616nDH36KCTiBxXmlox152yWtiiYlkx4eznkvvMD4d98lMiODu++8kz/z PoC+OHw4059+mn/98kslt1KqvKQkGs6aBY88YoUFxo51V17r0wcmT/Y+f8MGG6Lm24s7cqSVl5Ya RSFHREQqRY7TyeS9e9mTkcG/GjXixNq1vY5P3bcvvyz0/qws/m/TJq/j3aKiOCYsjMENGnBVkybc vnEjq/JKRWc4nRzKKT66aH7OkbOsY0fOevXVAvtzg4OZfP75Cjk1zfjx9uMx5LQkWr38sj1o1w4W LICZM6FuXbj33oInd+xoQadFC/CYj8f27eVouFRXGq4mIiKV4tYNG7h140ae2r6d3suWsc5nLZt4 f6uee1iZksKchASGrFnD5wcOcFbemi0uGytg3Rs5MnY3bEhcnTqV3Qw5mvr2hU8/hbL+vW/ZYhXS XnoJxowp/D61a8PFF7u3Q0M1F6eGUsgREZFK8ZlHieGU3Fxmx8d7Hb+ycWOaeKxvU5TXd+8GyD/f gYagVWWr27XjnrvuIq2Ef78SAC65BIYPh5KsR9WtG/hZ94oZM6w3qJgvQJg0yebo3HsvzJ9vBQmk xinXcLWNGzdyxx13cP311zNixAj27dvHgw8+iNPppFGjRowbN45Q/Q9MRET8aBsRkT+8zLUNsC83 l/E7dhATGspfPXrwc2IidYODeWnnTn5LSir0fm/s2pVftljD0Kq+TwYO5NeuXQnOzWXslCmM+OGH ym6SHEmlGaa2cqX//T//bD9//AGnnQYnn2xFBXyFhsL995epmRI4ytyTk5aWxtixY+njUeP89ddf 55prruGjjz6iVatWzJw5s0IaKSIigWd65870qlOHFuHhPNa6NZc0asTujAyuTU3lwa1buXHDBkZv 3UqXqChu27SpyIADaF2WamhnkyZsa9qUW++7j3n6tl1KauZMCzEDBsBjj0Hv3lZh7auvKrtlUoWU OeSEh4czadIkGjdunL9vyZIlDBgwAIABAwawaNGi8rdQREQC0vFRUfzRowc7+/ThmbZtAZgbH0+8 R1nZTw8c4O5Nm9jnU1FNAktKrVpc+tRTZIaoHlLAczhsjZyoqBKd7gTrtSnMiy/C4sWwfDlcfjls 21YRrZQAUOaQExQURFhYmNe+tLS0/OFpMTExxHqMtxYRESlOi/Bwr+0Qh4Nfi+nBkcBwOCqq+HVT pPpzOm1OjU+hEaKjvefOREfDqFFsnDgRFi6EZ56x3pqOHb2v85yfk5kJ//xz5Nou1coRKzzg1P+o RESklAY2aMDIsDAahobSMCSEzBL8W1In2P9SnmGAZoVWHyFZWSzo1q2ymyGVoVMnK/P811/w008w dSqsXQvjx5PsCj6PPQZLl8KSJXDeeRAZaRXbPENPs2Zw0kmV8hKk6qnQfuGoqCgyMzMJCwtj//79 XkPZCrN06dKKbIJUY3ovCOh9IHBreDi3Am9lZDC1iPMcQC3gcCHr4WiAW/WSHRrKtY88wpobbiDG owKXE/u7lsB1OCKCja51sOrWhRNPhL177Qc//y4880z+w+DERJp8/DGO7GxiL7uMzK1bj1azpYqr 0JDTp08f5syZw5AhQ5gzZw5nnHFGsdf00ERDwf4HpveC6H0g4H4fjE5J4cvly0nMzsYBnFGvHr94 LPDnBFIKvYtUR/tiYjjx/fd595VXaLdnD522bydYI0MCS1AQHH88/P13/q46vXoV+v/+Ev27cPbZ ABxTYY2Uqqi0X4KWOeSsXbuWF154gT179hASEsKcOXMYP348Dz30ENOnT6dZs2YMGzasrLcXEZEa 6Ou4OL7MyOCygwcZHBPDqlNOYUFiIu0jI5m2f79XyJHAtC8mhqHPPktIdjapgwcTXEhPnVQTQUGQ 61H7cMoUGDECHn7YhqadfDKce67ta9oUrrrKyk2feiqUYESQSGHKHHJOOOEEpk2bVmD/lClTytUg ERGpHB/v38/Y7duJDArijfbtOT06ukLvv/zwYUZv3Up6bi6Ptm7NuQ0akJqTw4f79pHtdOIE7t68 GYApq1fzwfHHMzc+nllxcbSLjCzxwqASGLJDQrj/9tt5bcIEgnNVILzKuvNOuPpqOP30got0jh8P 8fHw3HO23bEjhIXB+vXw0ku2788/oU8fcIXZV16x4gSNG8Nvvx291yEB54gVHhARkepjfUoK161b x/rUVJYnJ3PRmjWkVeA36Gk5OQxetYp5CQn8eugQQ9esYXNqKgNXruT/Nm3irs2becSnKtLLO3fy 8YEDpObmsjolhS3p6RXWHqke3rrkEtr89798ctZZABysU6eSWyQFnHIKxMUVDDgAgwbBs89aWHnv PTh4EIYPh27dwPVF+cKF7oAD7gp7Bw7AO+8c+fZLwFLIERERtqWn4xlpErKzOZiVVWH335eZyQGP +6Xn5rIgMZFFHuWhk31CVUSQ9z9Rif4+REnA29W4MSPGjKHXhAmc/J//EF+7dmU3SVwGDLDhZfXq +T/+7bf2Z9++sHWrhSGw4WsvvGCPu3e3tXP8qVWrYtsrNYpCjoiI0LNuXZp5rH3Ws04dmvmsWVMe LcLDOd7jA0u94GBmx8cXOG9QdDRNHA7Ojo4mxOHw+kcqVXMzarQlnTuzs0kT/nPhhV77d8fEMOCV VzjvhRcUgCpaVBT4K9EeGQnnnw/9+kFsrM2l8ef55+3P9HQ7z9PBg/bnmWfCBx9YYBo8GBo0sP3d u8P991fM65AaSUsLi4gIDUJD+b17d97bs4fI4GDuat6coMK+XS2D0KAgfu7WjRd27GBlcjLzDx3i C9e3unkcwNddu/Lc4sU8nZiIb02tDFXZEuDJ66+n5YEDDFixgpygIHq9/TZ7GjUC4NKnnuKnUaNU crqinHYaTJoErVp5709Lg9mz7ef992HWLP/Xp6VZmOnXz6uaGgD790NqqvXWXHON/QBkZFiPT9Om VrRApIwUckREBIBWERGMPfbYI3b/Y8LDea1DB85cvtzv8b5169L699/Zn5VVIOCIuKSHhzNizBgA Wu3blx9wAOZ3787uhg1p4ROgpYz+/htuvLHoc3bsgPnz/R8bNszm4vgGHICICCtC4Cs8HJo3L3VT RXwpIouIyFHlOwxuaEwMr7Rrx29JSexTwJFS2HGMz8ooTifbPUKPlNOuXfDDD8Wft39/wX0vvQTT p/s/3+GwHqAQfdcuR45CjoiIHBXz4uPp+uef/HX4MMfXqkVUUBAXxsQwrVMn6uvDjlQEh4PbRo1S UD7aJk+Gnj3d27feCg884H7csKH3+e3awZVXHr32SY2kf1VERKRcViUn8/H+/TQJC+OO5s0J9xlH v/TwYS5evZrdmZn5+0KAhd2706tuXZYdPsz/4uKIcDhIz5t34/lYpDTWHHsszw8fziOffAJAZnAw oTk5mqdzJB08COvWwZIlULu2FRNwadDAykSffrrNtQkKgkcfrfg2fPMNfPIJtGwJY8ZYO6RGU8gR EZEy25iaSt9ly0jJW6xx0aFDzDjxRK9z+i1bRqpPYMkG+ixbxpNt2vDKzp0cyquc1iAkhJHBwfxf t27cuWULmbm5XNWoETdu3Khv56VkHA4eHTmSuaeeSovYWOZ368bOK66o7FZVL5ddZmvb7NlTsvPP Px8aNYILLvB/vGNHm5ezaBEceyx06VJxbQVr68UXW2lqgE2b4IsvKvY5pNpRyBERkTL7MSEhP+AA fHXwIE6nE0deZbbD2dkFAo6LE3hq2zY817KPz87mp9xcXvvzz/xqamtTUuhcqxZrU1OP1MuQALTg pJMAiMjIqOSWVEPLlpU84AQFwfffw4gRcN99tjioP40aWRA5En791R1woPBCCFKjaE6OiIiUWfvI yB2xiaAAACAASURBVALbDo/S03VCQoocJuQEIn1KVf+Zm+tVLnp3ZqYCjpTZNXPnaqhaafmuaVOU 3Fz7+eQTOPVUdynoo6l7d+/tHj2OfhukylHIERGRMhvYoAEvt2vHcZGRnFGvHrNOOKHAOd2LGBv/ ZJs2fNetG4MbNCBSa2LIEfBl3748fNNN9Hz7bfa4FpqUojVu7K585nAUrIJWrx6ccYb/az/6CFat OrLt8zVokK3nM2CAhay8+VhSs+lfFBERKZf7W7ZkQ69e/HLyyRwfFQXAv7dsIWbhQk5YsoQxrVvT p27dAt+mj2jcmH/S0/l4/37ePe64IsOQSFnFxsTwwtVX82enTszu3buym1M9XH89LF4Mb71l82jO Pdf7+LBh8OSTFoD8qYxqiTfdBD/9BB9+aEPjpMbTnBwREalQX8bG8tLOnYDNsbln82a29enDoJUr mZeQkH/e57GxZOYNS/vm4EHiPKqviRwJIx98kLZ793L28uU4oeoOYwsOhrxiHEfdnXe6q59t3gyv vALt28M558CKFdaD89ZbEBUFc+bAq6/C1q2wYYNdc8890Llz5bRdxINCjoiIVKhdPhO9t2dksCs9 nU86deLuzZuZFRdHem5ufsAB2KuAI0fJOa+8QsPERLqvX8+LkyZx0pYt/k8MC4PKel+GhUFaWuU8 t6tC2pw54FmV7qqr3HN1nE7IzoaBA+0HYPt2m5vTtu3Rba9IITRcTUREirUlLY2pe/eyOCmp2HP7 RUcX2PdbUhINw8K4t0UL0j2rIOWpHRxcIe0UKYm46Gjm9u5Nj4kT6T1hAn916ABADpDrcNiaLkcz 4AwebMHGpTL/e7jjDqustnCh9/5ffrE/v/vO1r4JD4e77nIfb926YgPOggXw73/TcNYsC1UipaSe HBERKdKKw4c5ffny/FLR/evVY063boQFBbEkKYkNqamcUa8e6bm5bEpL49Q6dWgcGsqBrCzAhgR1 iIzE6XTSMjycEIeDbI8PLfWDg5nXrRvjdu7ks9JUdRIpp9zgYBZ37sxpb71F77Vr+eXkkwnNzGTa 889zGUfxm+ClS71DVXJywXNq1YJ+/axcc3Fq1bLQsW5dwWN16sDhw+7tkBBbt2b5ctveuhVefx1O O837ulNPtbAxfDgkJtq+t96yNXLOO6/4NpXG/Pk2PC4nh9YAWVnw4osV+xwS8BRyRESkSFP27fNa C2f+oUM8u307rSMiuHnDBpxAMJCLlYRuGBrK5I4dGbdjB0k5OdzXvDmT9+5l4p49OIBQh4Nsj/u3 jYyke506DIiOZk58fP7CoCJHS2ZYGL+cfDIAWWFhXDlmDG8OG8aYadM4Z+lSgtu3twUmfVXU3JmS hPvTTrNFLz3Vrw8e89zyhYRYaHn+eQstDRvCu+/aEDjfHqp+/fyHqosugvfeg88/tx6aF1+0sHHo kPd5Bw8W3/bS+uYb79/rl18q5EipKeSIiEiRGviplLQuNZWv4uJw9cd4fsyLy8pifmIiC/PWrvgi Npa3PRYW9OzFcQCjWrZk3M6dPLR16xFovUgZBAXxW9euDH7pJa77/numTprk/7xp06BpUwsOH34I H3/s/7zwcCjvoqTp6d49MFFRcO+9sHcvTJzoPaQrKQmGDLFwUKsW3HCDe45PRga0a2fXt2kD77xj PT4XXwwpKXDssVY8AGDkSPvxdOutFpjArj///PK9Ln/yhg8Wui1SApqTIyIiRXqgZUs6RER47bsg JoboIsrE1vJY82Z/EXMbgh0OPty3j4m7d5e/oSJHwPL27XntzDPJPuss7wOhodC/v/0MGmQhoTBl CTi+60a1bOm9nZICTzxhc2UyMiA+Hk480X183jx47TV7HB7ufW2nTrByJXz1FTRrBj17Qt++EBlp oa2oNateew3yer2IjYU//ij9ayvOyJEwahR06EDi6afbGjgipaSQIyIiRaodEsLG3r2Z1LEjdzZv zmedO3NFo0Y0DA0lxM86GV2johjl8YEsqohJ1NlOJ3MSEvinvN9yixwJTier2rfnvrvu4pyxY3G+ /747MOTkQPfu7oUnBw+2wFARmjaFzz6z3haA226zHhd/C3D+/Tfs3m1D13yHzsXH25+PPmploF33 fv557/OeecZCUVqaDYkbNarwtk2b5p6/k5JiPTsVLSgIxo+HjRvZ8tprcMwxFf8cEvA0XE1ERErk pqZN8x8/vHUrM+Pi8rfbRUTQqVYt7mzRgoH16xPkEX4mqJdGqiuP9/GCjAyS9+yhjiuQ5+bCvn1w 3XU2X8Y10b9PHwsepXkOz6FmxxwDq1bZPJqhQ62XplYtO/b66zYh3xVeXOLjLWC5CgK47nv55fa4 ZUtYu9bCUNOm4NMzi8dwUr/bLuvXu6usuaSmlux1ihxl6skREZFSW5eS4rV9XK1afN21K+fUr8+i Q4dY4lFqOqyooS8i1YQDOPO449jUvLn3gexsmxcDULcuXHll6W7sGXC6d7cg0fD/2bvv8Diqq4HD v9mmXfUuW7JVLXfLxnIFU0MoAQIkYFoooTrEtCQEPkIoCSUJJdQACT2ETigOxaGY2NiAca8qtiVZ Vm8rrXa1fb4/RlpptWo2siTL530eP+zM3Jm9k2ilPXPvPSdR29brOwOcjz/WppV1D3AA8vO1rGcd /ei4btcRUpNJSyDQPcABuPji4LTVl10W2mbFCpg1SxvJ6eqOO/q8PSGGi/zlEUIIsd9OT0gI2j4t IQGfqnLm1q0cvWkT8zds4BdFRQD8JTubuD7W7wgxUk0wm4lt//KvAhsTEzn3rruCG02ZAnl5ndtX XdV3vZiu9XC6270bYmK0wOmee7SRmH/8Qzv23HPa/t68807ovoF+7k4+GdasgYcegi++0Eanunvq qeCgae5cbdpaR5ICIUYY+asjhBBiv12ZmkqUwcDq5mYWREdzYUoKq6xWPuzylPnpykp+mZrKwpgY 9i5YwLKGBq4qLMTu96MnOCObEEPJrCg4B1Bg8rjYWJ6trg7atyU7myU33cR1VivTpkyBK67oHG0B bbrZpk2wYYM26vLTnwZf9K234LHH4PPPQ1NQd4zg/N//aWtSOtqbTJCUFHydRYtCC3bqdNo0OoDI SG3kZaDmzdP+9aZ7kd+JE/fv+kIMMRnJEUIIcUDOS07msdxcLkxJAXqelvbL9toikQYDF6SkcFJc HCABjhheAwlwAF7sFuAAqDodz/z4x+x78EG4+WaIjw89MTpay7p21FGdyQM69i9apC3yP/bY4AAn JQUef1yrQ9N93cv//qclB1i0SAtkFiyAt98OnlZ2wQXw2mtaYc9582D5ci1b2mD5wx9g5kzt9dSp ockLhBhhZCRHCCHEoJgfHU2CXk9Dly9uK5ub+balhfnR0bxWU8N7B6NwoBAHSR+TwzixPWDvU0qK VtjyV7/Sth99VAuKWlu1wKWrWbO0mjN6vZbOuas5c7RRnlWrtLU2iqLVyHn5ZW0U6e67tYxoXZMN dPjmGy1d9KJFMG1a/33uTccIld0eHLgJMULJSI4QQohB82BHmtou9jqdANy8ezfdn5/H9JFeWoih FtZDSvSeHB0Tg36AbXnvPW3tysaN8MQTWpASHg7JycHtli/X/uvzadPQliyBE07QRkx+8YvOdoqi TXV79FFtaprDAXfd1TlNratXXtECpiVLtOQE3ae3HQgJcMQhQoIcIYQQg+asxERMXb786YH5UVEA KN2+FF6YnMy+hQuZHRk5lF0Uolf/yM3l5vHjGddLcgBL+5TMYoeDra2t/V+wvFwLRjq8+SasXatN OVu2TCuqmZ0NS5cGn6eq8Pe/a/9dsiQolTUQmmHNbu+54Ogzz3Rmb3O54Pnn+++zEKOEBDlCCDEK Vb1QxdcZX/PtxG9pXN5Dytk+NH/TzNeZX7PSspKia4tQB7h+AWCb3Y67S3sfUOl2A/BgTg7G9i9r kXo9ETodiqIQI5nXxAhxaVERD5SXU+vx9Hi8rX20pNrj4de7d/d/wZ5GezrWrs2bpyUn2L0bHn5Y W8PTld+vpW2+++7Qa5x0Ekya1Ll95ZXByQ86dE9W0H1biFFMghwhhBhlHIUOCq8sxLXXRVtxG9vP 2Y7X1tfqgmA7L9qJq8yF3+mn8qlK6t6uG/C50T0ELKXt09XOS07mT9nZALT6fPyjuprri4vZaLMN +PpCHEwd4bl7AIH9DrudozdsYElhIS29pXYeN07LlNbhssu01MvdGY3w3/9qNWjaRz4DampC28fE aGttXnlFGxH6+997fv+//lVLFqDTaVPffve7fu9LiNFCHp8JIcQo4yx3Qpfp+b5WH54GD4aogf3K d1e7g7dr3D22+6ShgUq3m1Pj4xkbFgZodUWMioKny5fE3C5PmHe3tQVdY1l9PVaf5FoTh54Kt5sK t5uvWlqwer08PGECVxQWUuxwcGZiIg/k5KBTFLjvPq12jtsdPPrSndGo1cLpGvTr9XD55T23j42F iy7qu5MZGVqyAL+/cwRJiMOE/MQLIcQhzGf34Sxzovo6g4roedGYszurmkcfGY05vYcq570Ye9XY wGtjkpHEHyeGtPm/PXs4detWrigsZPb69exzOlFVlUsKCgIBjh6YFh7OnSUlrLRaeaW6Gm+3J+R1 fRU3FGIEGEgygu9sNq4sLOSTxkZ2O508vG8f/6iq6myQldV3gNOhPeV6wBVXwIkn7mePeyABjjgM yUiOEEL0QVVViq8tpuqFKsJSw5j6+lSi50UPd7cAsH5lZdsZ2/BavUTOjmTm5zMxxhoxRBuYvWY2 VS9UoQvTkXp1KopugJmggNxHcok9NhZ3lZuEMxIwjw8NkJ6sqAi8rna7eae+npPi4ninvj6w3wds dzjY7nDwSWOj1MYRh6SHcnI4Pi6O12pquGfv3h7bLIiO5rtu0y53dRu1HJAzz4S//U17bTT2Pooj hOiXhPZCCNGH2jdqqXy6EtWl4ixxsvOincPdpYBdN+7Ca9VGQlo3tFLxeGfgYUoxkXFrBuNvGo8+ Yv/TNCednUTyBckY441B+6tfqmbjMRuJaQwekfGrKuF9pIOWAEccqk6IiyPBaOS85GROiIkJOT4/ KornJk3i7MTOEU89cEZCwv6/2WOPwZNPakVGv/wS5s8/8I4LcZiTkRwhhOjDQNenDAe/M7guhr+t hzoZB6hoaRGVT1aiGBRyn8ol9cpUrCutFPy8AFT4bRPc8ScFa4QW7Ny2Zw+zIiO5LyuL35WUoKLV wGmW9TbiEBZrMLDCauWGXbvwqionxMSwcuZMYoxG7D4f4Xo9M9tToP8pO5uJ4eEUOxyclpDA0bGx getUuVzcWVpKs9fLtWlpHNvlWBC9Hq69dihuTYhRT4IcIYToQ9LZSey9dy+eei2l7Ngrx/ZzxtDJ vCOTnRftRPWqmFJNpC5JHZTrWldZqXyyEgDVq1L8i2KSz0+mdVNrIP3UjG1wxHcqK47Ttp2qyoPl 5XyYl8e1aWmoqkqj18sfy8pw+/14/H7e6jKVTYiRbIzRSIrJhFFRuK64OJDH44vmZjylpayYNSuk GKiiKFwxtuffD6ds2cIWux2ADxoa2DxnDhN7SvkshBg0EuQIIUQfzBlm8tfn0/CfBkypJpLOGjl1 JpIXJxN5RCTOEidRc6JCppYBqH4tKulrTY7X5kUfqQ8U6/S1Bo++qF4Vv9NPzDExKEYF1aNdMybW BHQZ2drhhDwCdW9iDAauGjsWBXiovDzkfRU6U/YKMZL8ODGRt+vqaOwhMcaq5mZerq7m570ENN3Z vN5AgAPg9PtZb7NJkCPEQSZrcoQQoh/mdDNp16YdlADHWeak6csmPNaeiw/2Jzw3nPiT4jHGG3Hs drDviX1Uv1JN7Zu1lP6xlJXhK1lpWcm+J/aFnOtt9rJh0Qa+iv6Kb7K+wb5D+yIWd0Ic0Qs6kyvE HBND40eNREyNIPPuTG3BAXDRY17S25cBja2EC3/toOY1raZHi8fDlLVrOWrjRo7cuJGiHhZhdw1w 0nqpMC/EUIvW6zktIaHHAKdDb8VCexJlMDC5S0BjUhRmtU9xE0IcPDKSI4QQw6T+g3q2L96O6lIx pZmYvXo25ozgTGbueje272xYsi2ETwrH7/FT+0Ytfqef5MXJGKK1X+NNnzex+aTNQfVxutp13S5a vm1hzKVjsGRbKLuvDNt3NuxbtMDGVeZi1w27mPnpTHRhOmaumEnjR43s/u1umlc207yymZp/1mDf aQ9kEUgs8fP8JdAcAzHNoPdD8S+Lcde4ufCYOgq7BDZb7fY+1+gkGQwYgDL3yFnzJA5P48PCSDIa yTab2dNeyDZcp8Ph1z5c8QYD5yRpDzz2OZ08VlGBAtw4blygXhSA0+djeVMTFp2Oj2fM4HclJTR7 vSxNS2NKRMSQ35cQhxsJcoQQYpiU3lWK6tLGM9wVbiqeqCDngZzA8bY9bWw4cgOeGg+KQWHyPydT 888aGj9qBKDi0QpmfzMbfYSeouuLeg1wOtS+Ukvtq7UYE414akOfRHubO59c6816jAlGnLudgX1N nzWFnKP3Q3yX3d4mL0W/2k3eT+CrpcFt+0pCsNnhkKlrYkTY7nBw7KZNvDhpEiuam3H4fNyVmcnG 1lY+bGjgyJgYssxmWr1ejt60idL2QOiN2lruy8piSkQEU8LDOW7TJr5tTyt9SUoK/5o6dThvS4jD jgQ5QggxTBRjt4XLpuDtymcq8dRowYjqVSm9q5S2ws7REfs2O81fNxN3fBzOXU4GxE+PAQ46GHfj uKBdxmRj8MIZHf0GUgB1yXDuO1CfBG+ep+3LLIGKNPD0MitNAhwxknhUlb9VVrLWZsOjqtR6POx1 Oilqa+Plmhrer6vjunHjAgEOQJnLxUUFBYFRnW+71M15uaaGv+TkkCLTMoUYMrImRwghhknOQzno Y7QFLuHTwkOCDJ0l+Fe0PlKPEhYcCLVuamXvg3tR3aFhQkReBLl/zyUiL3hqTPfgyjLRQv66fFIu TAnsU1UVv8tP+v+lo4vQYYg1MPbqgS20jmnR/vuLp+HNc+Gtc+CFy+GEz5FoRhwyOgIcgM+amoLW lX3c1MTZ27ZhUkITeqjAv+vqgvYZFAWLTr5yCTGUZCRHCCGGSeyiWBaWL8S510nz6mZqXq4h+fxk wtK0ef3jbhxHw38aaF3fiiHBQO4TubjKXRRdU4Tf6Sd8Sjh7bt6jXaxbqrIxl49h8nOTtfc5JpY9 v92Da6+LpHOSsO+wU/tqbaBt+ORwoo6ICmyrfpXt52yn/l0t5XPY+DAiZkRgTjdjTDLiqescCTLn mIOmtMWeGAufWQPbSe1Zo/93DCw/dVD+ZxPioPtBTAyrmpv7bONSVcaHhTHGZKLK5WJfl/VkKSYT P01K4uF9+zAqCk9NnEi0oe+vXJ83NfFpYyMzIiO5KCWlz7ZCiP5JkCOEEEPItslGye9KUL0qGbdn EHt0LKW/Lw0EFOUPlzNn4xxMySaMsUby1+bjqnRhTDSiN+thASSfm4zP4WNVxKrOC6sQNiEMnV5H 2rVpjLteGxUq+kURlU9XohgVYo+Lpf79esKnhRM5K5LWTa0Yk4xYV1hZFbuKqDlRWHIshE8JD/QH wFXuwlXuCqwF6soQF/xnpGVtS4/3XTk4JXyEGBJXpKZySkICN+/RHiLkR0ZybGwsj+zbFzRjM0Kv Z21+Pnafjx9t2cLK5maSjUaezM1lTnQ0d2dmYtTpCOtnFOfDhgbO2Lo18Jyi3Onk1oyMg3NzQhwm JMgRQogh4LF6KLikgIYPGwLrWlrWtJC/KT8ooHBXumn6oomU87UnuYpOwTzOjKPQQdVzVRhiDKTd kIY+XB+yRib5J8nk/DkH+047xTcU0/BxA85ibZRF9ag0faplCLB9Z2PcTeOY/Mpk1uWtC1zD+rkV 6+fW/ZrI7Cp1BW37W/zozDr8Tu2i5hwzrr0ufviFyvvnQE2C1s7kALeUCREj1OMVFayYNYtTExLY 1dZGpE5HXmQkv01P5/hNm9jpcGDW6bgtPZ3zt29nt9PJTxITeW/6dKINhkCh0Mh+Rm86vFdfHzST 89/19RLkCPE9SZAjhBD7wWf34ShyYM4w91h8szd7bt5Dw7KG4Gu1+nDtdWFIMOBt6MxsFjYuLKid q8LFhiM34G3U2pQ/XE7KhSnoLDr89s4op+XbFgqXFFL7ei2+5t4zmQHYt9q1dTw9JRIYQHKBDuHT w2n+ssu0HoVAgKOL1BE+KRznbieJtfDKJQpvnKkS1QqnfQi33wPfLBz4ewkxVL5uaeGoDRtYnJzM /Xv3YvV6iTUY+DQvjw35+exwOEg1mbiysJAPG7URznU2GxlmMxcewFSzHHNw6vgJFsug3IcQhzMJ coQQYoCcZU42HrsRV5kLfYyevI/yiDkyBne9m5ZvWrBkWYiY1nP9i7aS0GKYxiQjkXmRTP/3dAqv KMRr9TLuV+OIXRQb1K55dXMgwAHwNnqpeKICJTx40XPz/5pp/l/f6wg6xP0wjojpEUQviKblm56n mPVHH6MPDnAgaF2Qv9UfNMXN4FC56LXO4/fdpiUleOM8aEw8oC4IcdCsb21lfWtrYNvq9fLbPXuI MxjQKQp3ZmSwzW4POqf79kD9evx4SpxOPm1qYnpEBI9NmPC9+i6EkCBHCCEGbO8De3GVadOzfM0+ Sm4vYfILk9mwcAPuKjfoYPLzkxlz6ZiQc00pwalj9XF6ki9KxphgJPaYWOYXzwe0NS3VL1UTsygG S46F2rdrqX6xusf+qI4DS1Wmj9FT868azFlmpr03jY1HbsS5Z4ApqLvob7SoPwqw+G2Yuw4uf+F7 XUqIIfFVc3Mg49oqq5UfJSTwQrX2+VSAE+PiDui6Rp2OZyZNGqxuCiGQIEcIcRiq/mc1Nf+swZRq IueBHExJA6xd0S2mUP0qVc9WaQEOgB/K7isLCXLq/l0XlM0MwNfko+KRCtqK2sj7ME/r10vVFPy8 AFQtXXTW/Vnsum7XAd2jPlaP3+5H9YQGQr5mH/YtdnYs3oEp04S71N3DFTTRC6KJnB2Jq9xFw8cN 4O216QEbUwUGF/gMoOoH//pCDIZYvR5rl4K2NR4Pr1VXc0ZCAqkmE2clJnLCAQY5QojBJ0nbhRCH laYvmii4pICmT5uoeamGHRfsGPC5438zPrBeRh+lJ+uPWegiutWyCQ/9lm77zhayr0Pj8s7pXBVP VAQCKV+rj/KHygfct+58Vl+PAU53fQU4AKbxJsw5ZlKXpJJ9f/YB96cvPh18egp8cgos+RvM2HJQ 3kaIA6YHVsyaRUK3RAJO4D8NDVw/bhynJCQMS9+EED2TkRwhxGHFtj444OgrAOnOkmVh7o65OHY6 MGeZ8dR7qHuzDsWooHpUDPFaLZvuohdG93pNnbkzSOqejrl75rLutXCGQv1b9dS/pWV/MyQcnD8Z ke3LlUxeOO8t7d9r58PfrzkobydEj4yAp5djt6WnMysqis9nzeJ3e/YEkg2A9pGsdbuZGtHzejwh xPCQIEcIcViJOSomKPVyzNEx+3W+IcpA9DwtaNly0hZaN3UuTM59LFe7fjcJpycQNScK27puAZUB oo+KZs24Negj9aQuTaVpRVPIlDBLrgXLJAuNH4bWqRlKXTPAHWyL3wC9FzwmeGMx2Pbv/yYh9psH OCE2li+t1pAEg/+ur+fL5mayzGZemDyZi3bu5NMmLSV7XkQE86J7f5AhhBgeEuQIIQ4rMUfGMP29 6dT8q4awtDAy78w84Gs5S4MX67sqg0devC1etv90O01fNBE+NZyMO7S6FykXpuC1edl0zCas/7UG 2u++brc2L6YbfaReC5CGeBRnOOlULSkBQHKNlolNJliLg22vy0X5woXkffcdDd7OoH67wwHAquZm Gr1e/jNjBq/X1uLy+zkvOZlwvSwmE2KkkSBHCHFIcpY5Kf9rOYqiMO7X4zCPM/d/UrvEMxJJPOP7 5yxOPj+ZyqcrAdBF6NBF6th6xlaMSUay7sui4tEKmj7TnvY6tjmo9dZiybagM+nwNHnwt/VQkKaH hGWtG1tDd45yHcmxq1Pg4V8jAY4YErkWC/+qqcGr9v5EYaPNhkmn45IxoVkUhRAjhwQ5QohDjtfm ZePRG3GVayMn9e/XM3fb3B4X/R9MuU/mEjUvCtc+F+GTw7UkBu1Bin27nYgZwXP02wraaCtoo/Gj RqKPkuktA7EnG5xSF1EMgSyzmfOSkrissLDPdsdLBjUhDgkS5AghDjmOHY5AgAPgLHHSVtxG5MzI Ie2HolMY+/OxAGy/YHvQKIztOxvpt6RrNW56GJ1pWd2CYlZQXephNQ1tf2XvAXObBDri4FKAJq+X /7avs+mgA64aO5ZjY2P5qLGRLLOZ29LTh6WPQoj9I0GOEOKQY840o4vQ4bdr07300XrCxocN2vVb t7bi2OkgekE05vT+p8HVv19P3et1wTt1UHRtUSDA0Ufp8dmCox3VqWq/hYduPf8hZ0wN/OW38OZi aIyHHdNA8YMq09fEIFIBq9fLW3XBn2MF+PX48eSGh3NBSsqw9E0IcWAkyBFCHHJMKSZmLJtBye9L UBSFrPuyMMYbB+XatW/WsuNCbdqZPlrPESuPCIwQeaweCi4rwLbORuyxsUx6dhJ6i566d+tCL+QD T01nQlqfzddzCmgJcPo1Y5v2z2WA2hRIrIevF8If7xzunonRxtNtLY4P2NDaSm54+PB0SAhxwCTI EUIckuKOjyPuq4HNjbeutLLz4p14Gjyk/TKNnD/n9Nq2/KHywOiLr8VH5d8ryX0sl6rnq6h8ppLW 9VoSgNpXawlLCyP6uGhq/lnTfyeGocbNaBPmhfEV2usTvgSjB+68G1RJbCUGyfyoKKxeL4VtWvGm MEVhVuTQToMVQgwOGfAXQox62xdvx7XXhd/up/wv5TR80hB03NPoYdevdvHdjO+wrQ2uZaOPd28i 4AAAIABJREFU0FPw8wKKri4KBDgdyh8qZ/tp2wkpqtHOkmshMj+SiNkRmFJNg3pPAo5eDY9dB1c9 hQSQok9K/00A2NjayqUpKRgU7YzpERFkmgeeuVEIMXLISI4QYlRTfSqeuuA65u5qd9D2llO3hAQ3 HSqeqcDf0ksU08vuDopRwVHg0NYODfRbltgv03eC2QX1/waPEb6bCzVjh7tXYqTpHgOfnZCAW1X5 sDG4wK5bVbm9tDTw0V7f2srL1dVclZra67UL7HZ+sn07u9raOCsxkVemTMGkk2fIQgw3+RQKIUY1 Ra8w5pLOehb6eD1Rc6IC2z67r9cAB+g9wOn1DTtfOnY4AskRZKTh4MkqgeufgF//Ff5+DaSVg9HV /3ni8PVuQwN7XS5OiInB0i0g6f6Jd/j7/h1wVVEROx0OPKrKW3V1PFlRMci9FUIcCAlyhBCjXtJ5 SZjStOlivkYf6/LWUf3PakCbjmaZMHj5iRWLDNkMNX2XADLaBkevAs/gJdsTo9RWu50vmptp8/vp uqwrTOn8DOeYzVyYnNzndWrc7j63hRDDQ4IcIcSoVr+snq0/2oq7ossXDxWKlxYHNvM+ySPhzASi F0aTem0qGXdnHHCwojpUlDAJdIbTvnEQ1whX/gOmbRnu3ohDwViTiUidjii9nocnTGBDfj7/mTGD 9XPmkGTqez3d1WM750dG6HRcKKmmhRgRZE2OEGJUq3iyosepYqqnc6clx8KM92YEHR972Vi2nbWN 1o2t3U/tV/jUcOwb7ft9nvj+/MBlL2pBTnwzPH/ZMHdIjBgK8Nvx43m5RsuGWNVlxKXS7Q5MU7uj pITyhQs5Iioq9CI9+E16OjMjIylua+PEuDgmSrppIUYECXKEEKOaIbbnX3Oxx8eG7Gv8tJHKv1Vi iDWQdU8WMUfFHFCQIwHO8NEBOSWd2zKmdvj5aWIiP46P5436ej7qklhABX6SlMSfcrQU8n8tL+ez piai9Hre6FIEtMHrpdbjIUM/8NzkP4yP54eDdgdCiMEgQY4QYlTL+XMOrZtbaStoC9pv/Z8V1aei 6LWvwfYddrb8aEugOGfLuhbyv8nHXeOm7q0ein2KQ8LxK+Czk4a7F2IovVNfT6XbzcbWVoyKEijw OSU8nBkREYF2N40fz03jx1PvdvOl1UqNpzML42179vDKlCkoioTJQhyqZE2OEGLUaNvThn27HVVV ce5z0rqtlbBxYczfOZ/JL08Oauu3+/G7tQkqfq+f8kfLAwEOgGObg+KlxeQ8nEPmHzOH8C7EYLrt fvjFkzChuP+2YvT4uqUFp9+PR1UJ1+m4PyuLVUccgaWH0ZlEk4llM4Knq75aW8vq5mYAXH4/95aV cU1hIV80NQHwP6uVpUVFPLB3L55+sq8JIYaHjOQIIUaF0ntKKf19KQARsyKwb7GDH2JPiCXv4zwS f5xI+ORwHAUOAMZePRa9RY/f42fLyVuwrrCGXLP6xWqqX6xGH6Un6cIkrJ9Z8dR6QtqJkUsBFr8N Z70Pf74F1s4DSxvU9Z0wS4wiDr+fR/ftY350NMfHxQUdq3O7MSoK7h4CFW/7CNDlBQW8WlsLwHNV VTw9cSK/KC4OHN9ut/PilCkH+S6EEPtLghwhxCHPY/VQekdpYNu+qXNNjPULK3X/riPl/BRmfzOb mldrcJY4iT81nrJ7y2j6vKnHAKcrn81H3asyZe1QZvLA7+/RXn9+HNxz57B2Rwyxao+HM7duZdPc uWRbtJTxS4uKeLKyEgUwd6uVc0ZCAsfEauv2/ts+egPgA16vrQ0EOAAfdysoKoQYGWS6mhDi0KfS d7HN9oe03hYvZX8oo/yBcjafsJmS20v6DXDE6JO/HqZvhj/fDMYumcWzd0NC/fD1SxxcNr+fnG+/ 5Zxt21httfJkZSWg/epo6zaS8+bUqeja1+NM77KOB2BOt6xrUySbmhAjkozkCCEOecY4Ixl3ZFD2 hzIAwqeH49juABViFsWQ+JNEAGpfq8VdLYX6DnexNrjrD5DQCH+7Fr6dD+P2wbErwauHFcfBAzdL QdFD0RSLBZeqEqXXo1cUNrSGZkd8p76ead0Cl67Sw8Iwd1m78+qUKSwtLqbc5eKC5GRuGj+eOKOR 12trSQ8L428TJx6UexFCfD8S5AghRoWsu7NIuSgFn8NHZF4kzlInFY9XUPtOLRsWbGDSs5N6TSct Dj8J7TOMJuzW/nUw+OCHn0PRRHh78fD0TRy4nW2dWRQnh4ezYfZs3q+v5569e/F1aZdhNnN8bCwr rNpI7oLoaOo9HuINBv4+aVLQNceGhfHO9OlB+25JT+eW9PSDdh9CiO9P/uILIUaN8Imd00Zc+1zs e2QfAO5yN9vO3MaC0gU0ftxI/Xv1GBIMGJOMIamlhQA4/zVY9mNwmYe7J6I3eRERbLFr6+8UIM5g oNHbmSKxwOGg0efjruxsFJ2Ou0pLAZgREcG5SUlcnJLCCqsVi07H0bGhdbOEEIc2CXKEEKOSs9QZ tO2udIMfpr87HZ/Dh86iY+sZWyXIET1KsMLj18Ft90K9ZGIbcX6fkcFD5eWBbZXQ5AEAMe3Tzu7M zOS0+HjqPR6Ojo0lon3/SfHxQ9JfIcTQk8QDQohRKfaEWAwJnc9xEs5MQBem/crTh+tRFIWo/Kje TheHKT/QFK29zt0Fb50Hz10+rF067BnQRmpMisIJMTGUzp/PH7KyGGMyBbXrKWBJMBoDr+dER3NK QkIgwBFCjG4ykiOEGBVavmuh7J4yFL1C5t2ZRM6IZPY3s6l9tRZDvIHUq1Oxb7dTtKQIT4OHtF+m kfH7DCoer8Db5O33+uLwoAPiWoL3ZZdAeCs4IoelS4c1HfD7zEwuSE4mt0sWs5K2NlJNJipcLnxA vMHA+pYWwhUFR3t652i9nsQuQY4Q4vAiQY4Q4pDnrnOz+Yeb8TVrS4ubVzcz6YVJ2NbaiDoiisQz texqW8/YirNEm8ZWvLSYiLwIlDBl2PotDh1HrYZPTx7uXhx+/MCdpaXcW1bGBIuF+dHRPDphAmdu 28ZWe2c9rFqPh1qPB4PS+Xlu8fm4u7SUBydMGIaeCyGGmwQ5QohDgs/ho+mzJgwxBmKPDV4k3FbU FghwADy1Hradvi1QOyf9tnRiT4gNWaez96G9KDoJckT/ljwD1WNh6wy0uVNi0FkUhSyzmR1toevk 3KrKDoeDHQ4HOmB7lwCnq65FOgE29ZBCWghxeJA1OUKIEc9n97Fx0Ua2nbmNTcdtovjG4qDj4ZPD g9bfAEHFQffet5ctJ25BFx78K6/x/UYtIYEQ/YhvgsduAL2v/7biwLSpKslhYcyPiiJKr8fUS7sd Dgc/iIvr8Vj3LzW9tRNCjH4S5AghRrzGTxpp3dj5RLbi0Qp8js5vm8YEI7NWzCLulL6/0Pjtfvmt J76XlOrh7sHo9qXVym/Gj6fl6KM5v5f1NCfFxfHOtGnclp7OnKjg5CFZZjP/mDiRi1NSeGzCBG6V WjZCHLbkz70QYsTTRwZnQ1LCFBRj8JwhnVlH1OwBZEvzD2bPxOHmNw+B2aG9TiuHY1cMb39Go44p Z1N6yIJ2R0YGd2ZmEmUwcG92NndnZgbW4eiBh3NyuDI1lZenTOG6ceNQFJlbKMThStbkCCFGvLiT 4hhzxRiqn6tGMSlMfm4yOqMOVVXxNnppWdvCtrO3obpUbb1E+1S1uJPjaN3aiqfSM6z9F6PHEZvg jfOhIQHSKsDkgadq4M3zh7tno8OCqCjOStQShRxtMDDBbGaXU1tLd2R0NHdkZgYFLtcWFQWCIh/g 6rYmRwhx+BrUIGft2rXccMMN5ObmoqoqkyZN4vbbbx/MtxBCHIYURWHys5PJeTAHXZgOvUWPu9bN 5pM2Y99sR2fWaQEOgApRc6JIXZIKemha3jS8nRejTrRN+9fhiufhrPfgjrth16Th69ehSkfnAGuk wYCxvainWVFYN2cO/6qpwaQo/CwlBX23kZlaj6fP7b78t7GRF6urGWMycWdmJjEGee4rxGgy6J/o efPm8eijjw72ZYUQAmNs5xz9snvKsG/WMiz5ncFz0KLmRDHm52NYGbGy5wt1/VYF2jwXWVAuDpDJ A2Nr4G9L4fLnYd/44e7RyDPGaOSurCxu2b2bZl/nhy0zLIxSlyuw/VlTE9vtdvIitaJEMQYD16al 9Xrda1JTeWTfPgBSjEbOTEgYUH/W22yctnVrYBRom93Of2fO3O/7EkKMXIO+JkeVoWIhxBDwtgQX 8NSZtV9n4dPCybgjA9Wnojp7/n0UNTeK3KdziTk6RgIcMWiMXnh6CVz7JORtGpr3VBjejNaJBsOA v0hck5rKpWPGBO3rGuCAdi8dIyp+VeW3u3czZe1azty6lVp3aCbEv06YwLvTpvH0xImsnzOHcWbz gPqyprk5KN30/6zWAd6FEOJQMehBzu7du7n22mu56KKLWLNmzWBfXgghAEhbmhZISKAYFaa8MYUj a49k7ta5hI0NQ2fUEb0wOvik9m+Dtm9tNHzQQPZfsiXAEYMqwgHnvg0P3Aw/XH7w308lKFv6oOge NCX0MY3LB2yeM4dHJ0xgeV4ei9vX03RnaU8i8KfsbH6RmsqU8PCQNgZF4a8TJqAHCux23vV4eKC8 nAKHgw8aGri6sLDHa2dZLCQYDPsV7B0RGRnUPj9qAElLhBCHlEGdrpaRkcHSpUs59dRTKS8v55JL LuHTTz/FIPNchRD7ydvqpXVDK2HjwrBkW0KOR8+JZu62udjW2QifFk7E5IiQNlPfnMqGeRtwV7lR wpTOdTtA40eNxJ8UjxKhoNplBFoMLpNXKyD66cnD3ZNQZkXBp6r0tnql+6ehwevtsR2A0+9nemQk 09unl8UaDLxZXx/SzuX3U+xwkBsezt8mTuSjhgZO27o1qM3e+fN5va6O9G++QQXGdVt/U9hDkdB/ VldzWUEBfiDeYGDN7NlM6iGA6m5RbCyvTJnC81VVpJhMPJiT0+85QohDi6IexPll5557Lo888ghp vcynXb9+/cF6ayHEIczf5MdxuQO1XAU9mO82Yzyl55oZHdQ2FYygGIK/GKl2Ff8eP6pJpe1nbYP/ 2FuI3kTA5Y9BSfZwdyTYbJ2ODf7ByaV+sdHIDWYz67xe7nI6aVJVXH20z9Tp+LPZTJpOx5UOBwXt /TjdYOBWs5ljWluDlst1SZYYeK+uzrfb2dXlXnpqI4QYPfLz8wfcdlCHWJYtW0ZdXR2XX345dXV1 NDQ0kJKS0uc5+9NZMXqtX79efhZE4Oeg7P4ySspLtJ0+8D/lJ+fYHKIXRKMzBM+yVVWVwisKqX6h GnRgiDWQdG4SuU/kdrY9RvtPSWEJZX8oG8I7Eoc1O1z2Itx5FyOqKl2D0UiCz9frCM1Ui4Ud3UZN jIpChE6HtUvSgJvS0ni4PZvqyatX0zCAZ6alfj8P6/V8k5/Pep+PjxoaiNTrOTk+Hoffj7pqVVD7 P2Rm0uj1MtFi4erUVHTdRndSNmxgV0tLYHtCWhr5mZn99kMcOuT7geiwv4Mjg/pr94QTTmDt2rVc dNFFLF26lLvvvlumqgkhBqRtTxver7y4a9whhT7dFW42Hb2JLSdtwe/x43f7ce5z4vf6afigQQtw APzgbfRS9UwVBZcVUPfvOnxtnV/Kxt8yHsUkxQHF0DlmFTxzjVY4NDAk0fvsr16lGI3cOG7cgNv3 9ZfXrNPR1McUtN+kp/OzlBTyIiLIDAvjiMhIHpkwAWe30Z9/t09Lc/n9fU5p666mPc1zuF7POcnJ nJKQgKIoROj13NUlQJmn13NLejoPT5jAkrS0kAAH4LHcXMaYTIBWR2d//jcSQoxugxqBRERE8PTT Tw/mJYUQh4GGjxrY9hOtmOfaP6wl76M8ouZEYVtnC2pnXWGl6tkq9t6/F1e5C8tEC0mLk3q8Zu2/ aqn9Vy1Rc6IY96tx1PyzBkehA9Ut89XE0Jq4C165BOzh4DJBuB1++TeYuhOMHvj0h9Daz7r3U+Lj OTEujtdqagJBQl96Cjl0wKyICDba7b3O2kwzGjkzMZGfjx0btP8XhYU4u43UVLhcvFJdzR2lpUHT yjpkmc0sTkpip8PB8sbGQKHOK7tdu6s7MjM5NykJm88HRUWBmjm9mR0Vxb6FC2n2eok39j6ltdHj 4briYgocDs5ISODObkVFhRCjjwyzCCGG3d4/7Q0kBfA2eql6oYojvj4C+3Y762evD6ppU/NKDa5y bdZ/W1Ebe+/Z2+e1bets7Lxw50HruxADFeHQ/gHcezuMqdFe/+Q9uPEhaOgWrx8VFcVmh4M5UVFc kpLCyV3quhyI5ydO5Kbdu0OCkZPi4lCAI2NiuCY1NRAs7Glr48rCQsqcTup6CKy8wMUFBb2+3y9T U/l1ejoAxe2BTo7Fwqn91LKZEqElEVk/wCBEryh9BjgA1xQV8XZdHQAbWlsZbzZzRR/BlhDi0CdB jhBi2OkswU9r9RY9OoOOqJlRTHhkArtu3AV+SFqchLf5AOb6CDHCdAQ4AOPK4e3F8Pp58MwSbZ8e eGv6dMaGhQHw2L593yvAMQJHx8bS5AvOmT7ZYuGDGTMI62HE5MIdO/jWZgvZP1AdfQfIDQ8ndwBZ zw6WbXZ7n9tCiNFnBC2FFEIcrnL+koNpjDavPnxqOOm3pgeOjbtuHEdWHsn83fOZ9sY00m9JDwmK eiSPcMQh5vw34IJ/aa876soAlDmdfNBDWuau+hrHiNXrOScpCYtez1HRnbWjEg0GPps5s8cAB6C4 h5TNfQnX6YjV61GAn6WkcH5y8n6dfzCdHBcXtH1St20hxOgjXwOEEMMucmYkC0oXsP6z9eSfnB+S Qc2UYgq8jjs+jrk75uLY7qD+/Xqq/lHV4zUz78qk4T8N2L458CfRQgy1q5+FmjHwxQ98fNPSwgcN DbxYXd3veX2t0rH6fLxWV8enTU3Ud0kQcEdmJml9pFs+OzGR59rfu2PNjQ64IyODTxob+abLKI8O +PqII5gRGYlbVXsNnIbLQxMmkGE2U+BwcHpCQr9T5oQQhz4JcoQQI4IuTIdujC4kwOnOVeWi+Npi 7Dvt+Jp9vbYr/X0pGXdmSJAjDjlz1sGXx0Hph7W8mFk3aNet75YB7bOmJq7rIxvZ0xMnMisyknKX i7MTEzEoCglGI1kWC3dmZfHzggLeqK0lTFF4dtIk8qK07AlhI3BBv15RuGn8+OHuhhBiCEmQI4QY Udz1bnRhOgxRPf96KrisgKb/NvV/IRWM8X0vRhZiJGqJgv+7H/xNdfBQ8LEfxsZi0es5Mjqar5qb +U9j44Cv2z0DWprJxNbWVjLNZqJ6KPdg0OlY2kcQ9MLkybwwefKA318IIYaSBDlCiBHDeb+TNe+s QTEo5D6ZS+rVqUHHi28s7j3A0RGUhS1yViS2tTKKI0a++FPjMY010bymmbaCNs57S9vv08GJYTF8 5moG4MZx4/jrhAmB824BriwoCEwp66BHW9PT2p5kwKgopIWFcev48SxvauLrlhbyIiJ4t76ep6qq SDYa+XTmTPIiI/H6/RhG2FSz72s03pMQon8S5AghRgTrSiued7SVBapXpfiXxSRfkBwY0bH+z0rF oxU9nquYFMLGh+Hc7ezcF67Q/HXzwe+4EN+XASY/Nxm/18/WU7fS9JkWyI/5aRIv7o7nvcdtGO1+ TrnUBDcHn/rs5Mncm52NAlyycyfLm5rwARMtFiaHh2PR6bg9I4NMiwWAa9LSoL1tdXta6FqPh7tK S8k0m3ls3z6iDAb+OXkypycmDtX/AgdFtcvF6Vu3sr61lTlRUfxnxgxSTKb+TxRCjAoS5AghvrdS aykvb36ZmLAYrplzDWZD74uZe+OzB6+vUb1qUOFOrzU0dfSYq8ZQ81INqlvF0xi89Nq2RkZxxKHB sd1B0xdNGJONZN2fhaqoeJu8OCucFF9SyLT2j8Ge3+4h4UcJREyLYIfdzuMVFYTrdPw2PZ3/Wa0s b+oc5dzQ2sqfs7M5MT6+x/f0dUtHXe1y8W57Bjer18uFO3diXbQI3QhcXzNQ/1dSwvrWVgDW2Wzc XlLCPyZNGuZeCSGGigQ5QgyDipYKylvKmZ48nUhT5HB353upaa1hwbMLqLFrhT8+2vURy3+2PHDc 5rJxxQdX8PW+r1k4biHP/fg5osJCy7vHnRCHLk+Hf4s25yx1SSrGhM41NXEnxhGRF4F9i1bfYszl Y3BsdwQCIV9T70kIhBjJvFYvm3+wWVs0YwJcvbf11Huocbs5ZuNGGtoTCbxXX0+Z0xnSNkKvZ5XV ygcNDWSbzVyTmhoIWm5NT+e/TU3UezzEGgycnpDA112ypdl8Plx+f1Aq6+5q3G7uKi2l2evl2tRU FsXGHtD9HywN3QqYdt8WQoxuEuQIMcSWFS7j3LfOxeVzkROXw1eXf8WYyDHD3a0D9r+y/wUCHID/ 7v4vzc5mYswxANz+xe28tUNbZPDWjrdIjUrlkVMeCbmOLkxH+NPhZDVnoY/QE3t08BcmfYSe8b8Z T8VjFRjHGsl5MIetZ2w9iHcmxMETNj6MhNMS8NR7qHu7PYOaSp8BTuTsSKLmR7HGZg0EOAB7eghw rktLww8cv2kTHeF/ocPBI7m5AMyIjKRw3jwKHA4mWiwYFIUXa2oCtXEuHzOmzwAH4JQtW9jUPlLy Xn09m+fMGdaCn90tSU3l48ZGvKqKUVG4euzY4e6SEGIIyUo8IYbY7774HS6f9k1md9Nunlz75DD3 6PvJjM0M2k4MTwwaqSmxlgQd39O0p9drKSaFhFMSQgIcgKYvmyi4tADbOhuNyxrZefFOsu/LRjEN YDqNJFkTI40RMv+YSfxpPU8n6y7pgiQybsug/t16cvwmTF2mkcV2y4y2MDqax3Jz+aihga7jm+83 NAS1izcaOTImhkSTiVijkW9nz+bFyZN5b/p0nu1nWpfN6w0EOABtfj/f2UKniLr9fv5YWsrFO3fy Zm3tgO51sPwoIYF1+fk8O2kS6/LzOUVq4whxWJGRHCGGmE4Jfrag1/X9tHSkm5c2j8dPfZwH1zxI dFg0z5z+TNA9njP1HJYVLQvaPhAt37QE5b9tWd1C7DGxxBwTg/Uza98nyywVMcJ4G7ysSVqDzqLD NNaEu8qNEqaQcmEK1f+shi5L0CJmRaAYFbafsx2A8KnhvLV8Cn+p3YdFr+eB7GxWNTfzSk0N48LC eLx9tCa3PdlAh+7b3cUZjVw6ZmCjylEGA5MsFgrbR36MisLMyNCptzfs2sXTlZUAvFJTg0Wn44wh TGgwMzKyx34JIUY/CXKEGGIP/PABzn7jbOweO1OTprJ03tLh7tL3tnTe0qD7eHHTizz09UPEhMXw 5I+e5D8X/Idv9n3DwvEL+VHujw7oPaLnRwcV+ohaoI0WxRw5gCBHiBGmo5Ctv82Pu81NyqUpROVH 4drnYtob09BH6jGlmtCF6TAmGVkdtzpwrmOHg4VrFb76yezAvllRUSGFPS8dM4aitjbeqasjx2IZ 9EX3n+TlceuePTT7fCxNS2NaRERImxVNwSnfV1itQxrkCCEOXxLkCDHEfpjzQ8puLKPSVsnEhImE GcKGu0uDakPVBi5//3LU9mjkR6/+iH037eO0iad9r+vGHR/HlFenUP1cNbZNNpo+aWL9gvVMfGYi tnU27NvsmMaYpDaOGDH0KXp89T4YQE4M6xdWal5qX9umh5mfziRyujYC4ff40Vl0+Ns6C0EZ4vr/ 860oCvdlZ3NfdjYOn4+/7N1LldvNz1JSOHoQkgRkWiy8Pm1an22OiIoKjPYAHCGjKkKIISJBjhDD ICE8gYTw0Tk/vKihKBDgAFTaKrG5bUSHRfd7rsfvYUXJCqLDoslPzQ85HjE1gtYtrXjrtbk8tm9t bJi3AdWtYog3MPGZiXhqPey5fQ+t37WGnC/EUPLVDDzjn9fWZX6aD3ZcsAPVrZJ4ViIT/z6RyS9P puCyAvwOP2nXpxF3fFyf11P9Kj6HD0Ok9mf+op07ea89RfSL1dV8O3s2s6JCsxwOtqcnTiRCp6Oo rY0zEhK4eIDT4YQQ4vuSIEcIMagWpS8izhxHk1ObpnJMxjEDCnBcXhdLvl7C5qbNANx61K3cf+L9 geOqqrL1tK14aoMX2HSkkPY2etl7/14m/X0Szj2h2aaEGGn0sXriTozDEGug+tnqoGOeGu3nvPqF aqLyo0j7ZRpJP0lC9ajowvrOGdT0ZRPbf7odb6OXxLMTmfrGVJY3NgaOu1WVL63WIQlyYgwGnp08 +aC/jxBCdCfZ1YQQg2pc9DhWX76a3yz8DX847g98eOGHAzpv+e7lgQAH4E+r/4TdbQ9sV79UjWtf t/y63RKrNa9sxrrKirchtHCoECPN9H9PZ/pb0/HUBQfuiiH4B7vj517RKf0GOACFVxTibdQ+A/Xv 1lPzzxpmdFsvM72H9TNCCDGayEiOEGLQTUmawgMnPbBf54Tpg9cmGXQGDDrtV1RbaRtFVxcFn2CG iY9PZPevduOzadOC3NVutv90+4F3XIghohgVvM1aIBI2NvhnP2JmBK3rtemWSphC/OkDSzPdoeO6 XbffnjaN64qLqXS7uXzMGE6M379rCiHEoUZGcoQQw2Jl2UruWHEHj699nOrWak7KOYmTU08GQK/o eeLUJ3B6nTy45kH+9NWfsBqDM6hNf2M6qVemknRBUtD+julrAIp5ADV0hBgGqkel5HathlTWvVnE /iAWnUVH7PGxzFw+kwmPT0AfrUd1qexYvIPWna00fNRAzWs1eFv6Hqkc/+vxgdemNBPJ5yUz3mzm vRkzWJufz5K0tIN6b0IIMRLISI4QIsjKspVsqdnCMRnHkJeSd1De48VNL/Lz938e2L7989tZfcVq 7p19L/9Y/A/CjeFEh0Wz4LkFbKjaAEDGNRk89cRTWDwWIo+IJP7UeLwtXi2o6ZJauisOuj8GAAAg AElEQVTV2cNOIUaIjmlpxngjsz6bFXSs5esWfC3tI5SVbradvi2w1ix8Sjizv5mNIbrnP+EZ/5dB zNExuCvcxJ4QiynJdBDvQgghRiYJcoQQAc9vfJ4rPrgCAJPexGcXf8bRGUeHtLO5bLy0+SVUVeXS WZcOKLFAV89tfC5ou8XdwuPfPs7VqVczPkZ7Cr2jbkcgwAEoiymj7Y42phmnkbokFZ1Rx6bjN9Gy uiXQpnuaXSFGLB3kPJjT62HVExygd02m4djpoPG/jSSfk9zr+bGLvn+KaCGEOJTJdDUhDhNNbU3U tNb02ebZDc8GXrt9bl7a/FJIG7fPzXEvHcd1H1/H9Z9cz3EvHofb5w5qs6psFYvfWsyVH1xJRUtF YH9hfSEnvHQCW2q2hFzXYgyuxu70hGZIizg/gvRb0jHEGPA0eoICHNAKK+qj9X3eoxAjgc6sCxQE 7Un6LekYYrXnkLpoHTpz8J9rY5zxoPZPCCEOdTKSI8Rh4PFvH+fG5TfiV/1ck38NT5/+dOBYRUsF 7+x8hwRLAskRwU+Gu2+vr1zPi5teDBph2Vi9kWVFyzhj4hmY9CZ2N+7m5FdOps2rFQD8et/XbL9W SwZw5utnUthQGNK/yYmTuW7edbyz+h0+bfuUUyacQmRYaNHABEsCn+z6BLfPzUmZJ2EaY6Ktpg29 2hnYdEzxEWIk8zv87Lx4Jwk/TkBnDH3eGJUfxbzCedh32ImYEkHz6mZ2XrJTq5OzNI24H/RdJ0cI IQ53iqqqwzZpff369eTnhxb8E4cf+Vk4eKxOKwl/ScCvdk7jWvXzVSxKX0SVrYrZf59NdatWo+Oc KedQYi1hS80WLEYLLa4Wjk4/mvfOf4+ihiKOeeEYPH5Pj++Tl5LHiktX8PzG57n505uDjn135Xf8 8qNfsrZybdD+tKg0vH4vJp2Jclt5YL9JZ2LV5at4et3TvLDpBQDOnXouekXP69tfB2DO2DncqruV hKsGVlRVMSlE5EXgrnLjrnD3f4IQQ2BhzULCksP6b4hW4HMgdXJGC/m7IEB+DkSn/f1ZkJEcIUax rTVbOf+d84MCHIA2jzbK8vGujwMBDsC/C/6N+3Y3F797Ma9tew2AVXtXcdeXd+FwO3oNcAC21Gzh 18t/zctbXg7ar6Bw0isnBYqDdlVhqwjZB+D2uznr9bPY8ostXJN/DW9uf5OixiL+U/SfQJt1Veu4 puUa3uRNdAOYeau6VVrXtfbbToih5NjhQFEUCq8oxLHTQfxp8Ux4aAKKPjQzoKJTUMIkY6AQQgyE BDlCjGI/ffOnFDcWB+07LvM4os3RvLDxBQrrg6eOxVviWfDcgpA1M3WOupC2Pfmm4puQgEpF7THA 6U9VaxW3fnYrW2q28F3ldz22aYhu4OmTnuaaT69Br+pZl72OOWVzQGasiUOEKdlE0ZIiGpY1AFDx aAXmdDPjfzW+nzOFEEL0RYIcIUaZnXU72dW4i/nj5rO7aXfQsQunX8gZk87gqOeOwqcGRwJh+jCi TFGsq1wXtN+oM3LFEVfw4JoH+3zfBEsCs1JmUVBfEHLMYrAE1ujsj9e2vYbD4+izzVtHvsWy/GXo VT1hsWG8XvQ6xudlUbYYgQyQ8+ccyu4pw+/2k3VPFhFTI2grDv5s7P71bmwbbEx5eQqKTkZuhBDi QBweE3uFOEy8se0NZjw1gx+//mOmPTktZFRl9tjZ3L/q/pAAB8Dlc1FiLQnad/bks1l39TpOzD6R G+ffiELvX7ianc0snraYnLjgtLgzkmew4tIVpEam7vf99BTgLExbGLLPGebEbrbT6GzklHGn0BDZ sN/vJcTBFjEjgvG/Gs/C8oXkr80n9SrtM5F4ZmJI29p/1VL7eu1Qd1EIIUYNCXKEGEX+tPpPgQCm vq2emLCYwDEdOn6Q/YOQ6Wu90Sk6LAYLhfWFqKrK3LS5qD1V3GznVb1c8M4FIaNHW2u3cteXd1Fy Ywl7rt/D3NS5RJmiDuDuNHkpeX2uwfHr/Ly94O3Adl99FmIoOUucNK9p5tuJ3/LdtO/4Nvdb7Dvt ZP4hk0nPTUIxBj9E8DQGr4Hz2X0U/bKIjcdupOy+MoYxb5AQQox4Ml1NiBGu0lbJDZ/cQKWtkktn XsrV+Vf32jbcGB60fWzGsaBoNXKun389s8bMIsIYMaCpY37Vz6vbXuXVba8SExbD9fOvJ8oYhc1j 6/Ucl8/V4/5Pdn9C6kOpfHHpF3x04UeMeWhMv+8PoFf0IaNOz2x4pt/zXl/0OuUJ5UyqnMTFqy4e 0HsJcbD5rD723LYHd6WW3c9d5ab0rlKmvTGNsZePpW1PG3vv3QuAKc1E0k+Tgs7fdeMuqp6tAqB5 ZTPGBCOp1+z/CKkQQhwOJMgRYoRb/NZiVpevBmBN+Rqy47I5MfvEHts+cvIjHP/S8dg9dgCWFS3j ncXvcPaUs/Grfl7a9BKL0hfxQdEH+FU/8eZ4Gp2N/fah2dXMH1f+8XuNwDS0NXDT8ptIj0nvcbpc d0eNO4pKWyUlzSX9tu3J6imrWT15NTPLZpK3N++AriHEYOs+WuNv65xSmn1PNnHHx+GqdBF/cjym ZFNQW9v64AcMVc9X4a5xM/bqsYSNGVgaaiGEOFzIdDUhRhCfP/TL/+aazUHbL29+OaRNh7lpczli zBGBbRWVdwvepc3TxlUfXMVl71/Ge4XvBdbqxFn2r6Cgzd37KM5AVNmqaHX2n8ZZj54d9TsOOMAJ UOCWn93CMyc+w5vz38StD66PI1PZxFBLuTAFXUTnn96GZQ1sPHYjriptFDTuB3GMuXhMSIADEHtc bNC2ba2N0jtL2XjkRrw278HtuBBCHGIkyBFiBFi+azmJf0nEfK+ZGz6+IejYgrQFQduvbHmFDVUb Attev5dmZ3Nge1z0uKD2dfY64v4cx/Obng953+7rZw62nfU7QwqC9sSHb7/TTmfHZpM/NrRImNPk 5PVFr/PUqU9x97l3Bx3rK5GCEAfD3vv3hsyhaF7ZTOEV/adoz/5LNln3ZhF/enzQfmeJk9YNUgNK CCG6kiBHiGGmqioXvHMBDW0NeP1eHlv7GB8VfxQ4PjdtbnB7VLbWbAXgsz2fkfCXBGL/HMtP3vgJ Xr8Xrxr8RPeT3Z/0ulbmYOspiNjbsvegvNce6x7WV63vs82ayWvYm9D5/j5FCuqIodVW3Ia/1d/j /v7oDDoybstg6itT0UfqA/sVg0JYukxXE0KIriTIEWKYef1eml3NQfvqHfWB1+OjQ4sCvrzlZaY+ OZWzXj+LFlcL/D979x0eVZU+cPw7NZn0XkggCUlIIEAIRXpTQVRAXQSxogiuWEBdVH6oqIi66lpw QRQVsYLYpSpI7x3pEAghlZBG2iQzmZnfH7NMGGZCEkihvJ999nm4555z7rlKzLxzznkP8MuhX/jX H/9ixfEVDTtgrAkB3DXuNda7HJeDPXv/s6xot4JNsZuYdO8ktkU7P2hUiAbjJLYOuN0xjXR11N5q En5OwK2NG7oYHfFfx6OL0tXjAIUQ4soniQeEaGIalYaxHcfyyQ5r1rBIn0huib0Fi8XCx9s/ZmvG VjqEdGB39m40Sg3NPJuxMmWl074+3Ppho4zZZDHZkhtcaXJ8cnh92Ou2670t9nLn5jvxKvNi+Obh soRNNApthBa3WDcUKgWBwwIJHRNqu1d5ppKyw2XoonVo/J0fbOs3wI/r9l/XWMMVQogrjgQ5QlwG Zt06i1tibyFfn09uWS5JnyRRXlluN6OjQIHRbCT1TGq9PVeB4rKcbWlMFdoKvu3zLVggNjuWpBNJ NTcSojoKqM2PlMKswP9mf4ynjXh190KhsAbXZYfL2Nl9J5UFlSjdlXRY2QGv67wadsxCCHEVkuVq QlwGFAoFQ+OGkhSSxHPLnyO9KN0uwIGGWfp1rQc4dhTwzKhnKNZeWgY5cY2r7Y+UCo796xgn/32S XT12oT9m3ZNzeMxhKgus++rMpeZaJSQQQgjhSIIcIS4jCw8vrFXg0SGkA490fISRCSNr3bcsw6qZ zqDj8TGPczhUPliKhlVxoioZiKnYRMFf1myC5SfL7eoZTtmnPRdCCFE7EuQIcZnIKc3h3xv+XWO9 xKBEPrrlI34+9DPz989HgQKlkx9ljdJ+Lb/M2tRM76InLSiNZ0Y9w5u3v8ne8L1NPSRxldKG25+D Y8w3AuA70P7sKp/r7c/GEUIIUTsS5AhRSx9u+ZDB3w3m/1b8HxWV9Z+S+eSZkw6b+e9sfadDvfTi dKZvmW5bzmbBghnHlLRqpWy5u1hlrmX82eFPxo8ez8FmB5t6OOIq45bgRrtf2+HRycP2Wzjl/1JI mZJC7PRYAu8ORBumJWBYAHGfxTXtYIUQ4goln4KEqIXPd37OhGXWQzoXH11MmbGM6TdPr9dntA5o TZRPFCmFKQC4qFw4XnjcoV6ePo/v939fY3/6yprP3RA1UMKE0ROYM3MOGpMGnzIf1CY1Kouq5rbi 2qQCzDjdm+N9vTcBQwIIeTAEjY+GoOFBlOyoOsQz8+NMoqZGkfBdQqMNVwghrlYS5AhRC5vSN9ld b0zfeMH6/7fi/5i3bx4RPhHMvW0uUb5RTuuZLWb2ZO/BXetOmGcYt8XdxrLkZRzJP0KFqYKdWTur fYZkRmscRrWRJx9+kkK3Qtu37u/NfU+ysAkAVF4qTEXnHHxzgfNlW89pjWuEq+1aE2i/pPT8ayGE EBdPghwhaqF7eHc+3/W57bpHeI9q63639zvb3prUM6nc98t9bBi9AYC9p/aSVZJF9/DuuGncuG3+ bSw+uhiAWL9YjuYfrfWY3DRuV+xZNVeaQo/CqgsLnPQ/KUGOAMB3kC8BgwM4Mu4I5lLHZaNn6WJ0 oAKT3kTmx5mYik0E3x9M8P3BnPruFC7hLsR/Gd+IIxdCiKubBDlC1MLDHR+mzFjG/H3zOZp/lIVH FtI+uD0Pd3zYoe6x/GN218cLrEvOPtzyIU8tewoLFuL845jWf5otwAHqFOAAuKpdJchpCgr47MbP uG3HbbaiXI9cLEoLgUWBTTgw0RRKtpfQ9vu2FK4uJHtOtrXQyVk5+mQ9u3rswjXKlTNrzwDW5Wmd 93Qmfm48CqVkPxRCiPokiQeEqKVHOj3CgdwDnC47TUphCo8seoR9Ofsc6g1uNRgXlYvteljrYQC8 svoV2/Kyw3mHWZW66oLPC3ILwl/nX+39PH1etfckXXTDMivMdn9+ZfgrjHl0DJm+mU04KtEUjHnW rGitPm5F9H+iCXsiDL/Bfk7rVqRV2AIcAEOWgYMPHCRjRgYWkyw9FUKI+iQzOULUUkF5AYXlVcuW zBYzJwpP0DaorV29pNAk5t85n+mbpxPmFcZ7N72HxWLBbLFfytIhpANhnmFkFGc4fV5OWc5Fj1X2 6jSspOQkvu35Lfub7+ek/0kyAq3/DlcnrOae9fc08ehEYzKdMbHOZx2+N/rS+uvWqHQqjAVGDtx9 gKLNRZhKTVD5v8pKUHmqMJ2p2rhTsKyAgmUF6I/rif0gtmleQgghrkIS5AhRS8HuwfRq0Yv1J9cD 0MyzGd3DuzvUSzuTxpjfx9hmWgwmA+Fe4ZypqPoGt2tYVx5o/wBrT6zlm73fNM4LiHqzoe0GNrTd 4FDuVebVBKMRDc2rlxclO0swl5lRaBRYjPZfIpjOmMj9KZeTbU8S9UoUGl8NicsSAShYVUDyhGTM ejMRL0egi9JxZNwRylPL7RIW5C/Jhw8a9bWEEOKqJkGOELWkUChYdu8yZm2fxenS05woPMHwH4Zz V8Jd/LPzP231lh9fbreU7KeDP9HMs5ldXwNaDkCtVOOmcUOr0mIw2Z9qrlVqMZqNMiNzBQkoCuDm 3Tc39TBEAyhaX2T7s8VoQeWjwlTomEatIt3x/Czf/r50+buLXVmXv7uQ9XkWh8cctpW5tXGrxxEL IYSQIEeIOnDXujOxx0SGzBvCoiOLAFh1YhWhnqEMjRsKQIR3hF2bUI9QonyiSC9Kt5VF+0Xz/ub3 mb1zttPnGMwGp+Xi8uRa4conH3+Cyizn51wLnAU4CrWC4LuDa91HyOgQylPLyf0tF12sjlazWtXn EIUQ4ponQY4QNTCYDPxz0T9Zfmw57YPb8+XtX7Ijc4ddnR2ZO2xBzg0tb2Ba/2l8tP0j/Fz96Bre lROFJ2jp2xKDycCINiMYlTiKB397sAneRjSEcpdynn3gWQbuGUi5ppyQ/BBQQnJIMkknkuhxpPqU 4+IKo6Zqj83/NJ/cnMDbAvG6zrpc0WKyUHqwFLWPGtdwV8c+sM4MR02NImqq8zO0hBBCXBoJcoSo wdsb3mbu7rkAZBRnMGHZBPpG9mX+vvmANZNZn4g+dm1e6PMCL/R5gWf/fJb/bPqPrdzX1ZdY/1iW HF1ywcxp4spzPOQ4H4d8bL2wwNkEdz/2+JF/bP4HTy57ssnGJuqHJlSDa3NXircV26WIdm/rbgtw zAYze2/dS8GKAlBC7H9jCXsszK6f/BX5pL6aikKtoOVbLW1thRBC1B8JcoSoQUpBit318YLjzBs2 Dze19TDOuxLu4oaWN7A2dS2vrX0NtVLN69e/TsfQjmxM32jXtqC8gHGLxzXm8EVTOC+D929dfuOJ ZU9Iau8rmRKMWUaMWUaHW5Wnq6Z2cn/NtQY4AGZIfiaZZo82s52DU5FRwb6h+zDrrdkW/775b7qd 6IbaU34dCyFEfZJzcoSowZ1t7kSpqPpRqTRX0vLDlszZPYc/jv1Bp2adyCrO4tbvbmXF8RUsS17G wK8HUlxRTLewbk04cnG5UJqVGKn6cGxWmDFjvkAL0ZTcO7o7Flbzr0sTpCHgjoCqgvNzhVjsy/TJ eluAA1CZX4khU/bgCSFEfZMgR4ga3Bx7M890e8Z2vSOraj9OYXkh45eOJzk/mRJDia08T5/H2tS1 vH7D6406VnF5cq1wpUhXxMfXf8wDjz/A0OeHMvClgayLW9fUQxNOxEyPqV1FJSRtTMK1edW+G7WP /YyM7w2+KFRVM3ju7d3Rhmht17pYHa6RzvftCCGEuHgS5AhRCxvSHM9EOavUUEpCUAJB7kF25YPn DebNdW86HBYqrj3FHsWMeHYE3/f5nrTANEpdSzGpTOxvvr+phyacUOlqmSXPDEceOYIxv2qWLm9R nl2Vigz7tNIaXw0d1nWg2ePNCH8qnA6rO6B0kV/FQghR3+S/rELUwvnn3JylVqp57frX8NP5sebB NQxoOcDu/tS1U9mXs68xhigucxal45lHLXNaNsFIRE0yZmTUum7hykK2tt6KSW9NK+0aZT8rc/41 gFuMG61mtCLm/Rhcmrlc2mCFEEI4JUGOELUwfdB0uoV3Q6fWMaTVEL687UumXT+NY08eo1u4dd9N fEA8T3V7qolHKq4keyL2NPUQxHmCHwzGVOx4Ds6FGHOMHH/hOABh48MIHRuKNkyL7wBf2/k3hlwD +X/koz+ur/cxCyGEcCTpXISohTCvMDY9vMmuLF+fzz0/3cPWjK10COlAvH88ni6e3BxzM0uTlzbR SMWVZEmnJSgtSjqmdCTfLZ/Wma2Jy4qTQ0UbkXsHdyJejEDppiTj/QxOzT0FgNJdibm09skhMmdk Yi4x02pWKyJeiMCrmxeuLV1xCXWh7GgZu3rtwphjRKFVkPBjAgFDAmruVAghxEWTIEeIOvp85+ds Tt/MkfwjrE1dC8CqE6tYdWIVAO2D2zN90HSeX/485abyphyquAIs6ryIRZ0X2a5VJhWJKYm89ONL +JT7NOHIrg2lu0s5cOcBVN4qTGeqZnDMpWaipkWR8mLKBVpXsRgtZH2ahTZUS8Z/M6gssKaVbvlO SyrSKjDmWPftWAwWUl9LlSBHCCEamAQ5QtTB9M3TeeqPCy9J+/vU30xaMUkCHHFRTCoTO2N2srjT Yu7dcG9TD+eacW6Ac1bAsADy/8jnzLozAKh91YQ8HIIuWkd5ajmVZyo59dUpuxmfgr8KbAEOQObM TAJHBNr1q3SVleJCCNHQJMgRog7+OPZHjXVUChX6Sll3Ly5N0JmgmiuJeqVrrUN/SA8WiHgpArc4 NyKnRqI/rsczyRPPJE8ADo0+RPYX2dY2rXToj1h/3hUuCry6eVG0ocjWp9pfTfOJzclfkk/pvlI0 ARqi341u/JcTQohrjAQ5QtRBu6B2DvttOoR04FTJKbJKsgAwWeq2aVkIZ3xLfe2uLVhQoKimtlB5 qTAVXdrPnlKtpFdBLyxmC2ofNQdGHuD0gtMA+N/mT8wHMRRtKbIFOAD6I3oiX4tEoVSgi9OR/m66 bT+PSwsX4j6LQxuopdOuThgyDGiCNLVPUS2EEOKiyZy5EHUwtf9UWge0tivLKcmh1FDaRCMSVyOX ChcsWNgetR2wBjirElaR5p/WxCO7fJlKnAQ458WEah81XCC+KDtYhtpbjcZXQ9mhMluAA5D3Wx5b W23l4MiDDu38B/sTMTmClP9LoWhTkW35WvwX8Xh2sM7+KNVKXCNcJcARQohGIjM5QtSBi9qFH4b/ wGOLH+NA7gFyy3LJLMls6mGJq0yFSwUvjXyJCpcKQgpCMKgN5Hvm8+msT5t6aJcvJ4nQXCJdqEip OoyzsrASz86eFG8vdtqFJkCD/oQeXaQOs8GxQ4vR8ayjsCfD8OzgicVicUgPrU/W43u9r0MbIYQQ DU+CHCHqYPWJ1dz63a2UGctwUckhfqLhVLhYP5xn+1qXRvU+0JvoU9Fk+GbwTZ9vMClNjNwwUg4U vQCf/j7kZOZgqbAGJ7pWOkoPVT/rasg2sOfGPVx36DqnAc25mj/bnPCnwm2HeSoUCgKGBpD7Sy4A Kk8VvjdIgCOEEE1Fghwh6uD1da9TZiwDoMJU4XDfQ+tBiaGksYclrnJuejde+PEFDGoDzzz4DDne OQBsarWJb/77Dd5l3k08woahCdIQ92kcae+ncWb1mVq3U7orCb4vmNgZsQSPDCZ9ejpqLzUt32zJ 3tv2Urqn+kCn/Fg5hmwDumgdan81lXnWTGkqbxUWkwVziRn3tu60mNQCjZ/Grm2beW3I+CgD42kj QfcEoYvWXdyLCyGEuGQS5AhxnuySbL7c/SVuGjfGdByDTlP1QUWr0l6wrQQ4oiGU6cp4+463uWv9 XbYAB6BEV8Krw17lva/fa8LRNZxm45oRMDQA/TG90yBH20xL0L1BpL+TXlWogo4bO+LR3gMAvwF+ +A3ws91O+D6BQ6MPUX6inMqCSsx6+2VprpGuaIO1KDVKElckkjotFYDIlyJxiXCxBkAtdSi1jlta lS5Kmj/dvD5eXQghxCWSIEeIcxToC+j2WTdSz1g/2MzYNoNAt0DCvcKZPXg2b1z/Bjsyd3Cq9FQT j1Rca1a2W8nKNivBgt2G+t2RuylwL3DIxnY1OPnWSbx7ehNwewDHnjlmd6/5c82JfsuaijlzVibm kv8FKybIW5yHS5gLR8cfRX9MT8DQAILvD0YbqsUtzo2OGzoCYMg1UHawDGOBkezPs1G5qYiaFoVS Yw1gPDt40vbHtnbP1fjYz94IIYS4PEl2NSHOsTFtoy3AATiSd4QNaRv4fv/3BL4TyLLkZRyfcJw3 rn+jCUcprlkqHDKGWVQWxvxzDMnByVi48D6SmqgD1ZfVV1+Wcgt/3/Q3pQdLCRgWYCv37uVN1LQo 8pbmkfyvZLSB9jOsZ9ad4eBDB8n5LofiLcWkvJDC5hab2d5+OxVZVctMtQFafHr7EDg0kHa/taPN vDZ1WmJmMVkoPVhKRbbj0lUhhBBNS4IcIc7R3Lt5tWeRGMwGJv01iXl75zEgegBKhfz4iCZkAV25 9QN5vlc+X/T/4pLP0ak8XQmVta+v0CpwiXRxCLzqlQXyfs8jYUECbRe2JeGnBBJXJJK/JJ+9t+wl /b10ylPK7X6b5S/Np3iTYwa1soNlnHzjZL0My1xhZs/APWxrs43NzTeTNTerXvoVQghRP+RTmhDn aB/cnmGth6FSqFApnJ9nsTVjK52bdebbf3yLt8vVueFbXAEUYFKaaHOyDaNWjeKFn15osEdFvRXl tNy7jzeGTAPnTyAp3ZSgBoWufqKfskNlbGy2kdRXU3Fr44bSRUnuwlz7SudlfNYEOl9WZtLXz2G9 OQtyKFxZCICl0kLyk8n10q8QQoj6cRktTBCi6W1M28iPB3+0XWuVWgxmg12dXi16YTKb+GL3F5yp qH3GJyHqm0Fr4ECLA5zyOYVPmQ/uenf8SvxwNbqyvP1yIvIiuGPrHRf/AAV4XudJRWqF9Sux8wKJ wrWFYHBs5jvAl+KtxRiynNysy+NdFfj09qFgeQEAxlNGDt57kM47OmMqunCwUp5eXnXxv7GrfdWE Twi/pDGdZTHZR3YWswWLxYJC0ZDTWkIIIWpLghwhznGi8ITd9fkBTpx/HFPXTmXq2qkk58s3t+Ly kOeVx/RbpwPgUeFBiUtVlj8zZoZtHVan/tw7uKMJ0VC0pojiLcUUb3F+eCYW0ARrMJ4y2o/ntzyn 1RVaBRZD7fcNRUyKoGSvfcZC/XE9lcWV5P5qP5PjeZ0nxVut43RLcKNsf5ntnjZUS9zsODySPHAJ rZ/zrYJGBJE5K9P6TAW0fKulBDhCCHEZkeVq4opnsVjI1+djsVzapmuA/pH9CXQLtF0HuAXY3T+c d5jk/GQJcMRl69wAB2BP5J4691G6u5TCZYUO6ZXPF/Z4GEnrkwibEIY6oObvzBL/TMSru1eN9RQB Clq+05KIlyIo2W3/PrqWOsx6s8NhnSovFf5D/Gn7a1uaPdrM7p42SIv/Lf71FuAAqNxUJK1LImlT EtcduY7wJ+pnhkgIIUT9kCBHXNGO5R8j5r8x+L/tT/uP25NVfGmbf0M9Q9kyZgtT+03lPwP+Q1JI ku1edXt0hLictcpq5VBmxIhCU7dZB7WfGqWHErWvGu9+3sR/HU/s+7HoonVUFqG0mU8AACAASURB VFRSmWufsUDlY//z4tnFE5++PkS+GnnB5/gM8MFjmQdqTzXbk7ZjyLafTQ24IwBtkJbgB4JtZQq1 gsIVheQtzCP56WSCHwgm4PYAUIBLuAtxn8bV6V1rS6lV4t3NG7cYtwbpXwghxMWT5Wriijbpr0kc LzgOwL6cfUxdM5VZg2ddUp9RvlG81Pclxv4+luXHl9vKn7zuSebtmydn5IgrhtagpfOxzoB12drR 0KO4GlxpkdfCYSZEoVE4lKEAj04euDRzIea9GFt65bLDZST/K5ms2Vn4XO/Dqa/O+ZlQQutvW+N/ qz/5S/MpWF6AJlBD82eth2R69/LGo4OHwwwNgNJDiWdHT05vOs2RJ4843Pfu4034U9YZk/i58QSN DKJoaxGpr1SlfS9PKceYbaTtL20xG8xOD+0UQghx9ZMgR1zRiiqK7K8NRdXUrLud2Tvtrk+Xneb1 G17nuT+fI788HwWKSz6XRIiGZNAaGPfIODzLPDGqjJS7lPPFTPtU09pwLR4dPMhflO/QPuqNKCIm RdiVWSwW/h70N+UnrBv7z2w8L/mGGfwH+6P2UBM0IoigEUF2t1U6FR3WdSDnuxyO/NM+kDGXmEl7 Kw1VF8dZU9+bfElclmi7VigU+N/sj0eiB2nvpGEutS6t0wRpcAmzLkuTAEcIIa5d8htAXNGe7vY0 WpX1IEB3jTtPdHmizn1kFGWwOX0zuWX2G5n7RfSzu16wfwFjfh9Dfrn1w6AFC346v4sbuBCNqNit mHIXa1BS6lJqd2/fdfvI/TPXoU3k1EgiJkVQuL6Q7Z23s7XtVnIW5FBZWGkLcAAwgS626gDN8H+F o/a48Pdnag81oWNCcQl3vkfGkm9x+O2kDdY6revSzIX2S9rjO8AXv1v8SPwzEZW7LC0VQohrnczk iCvaoJhB/P3o3+zN2Uun0E5E+To/z6M69/98P9/s/QYArUrL7yN/Z2D0QMwWM28NeAt/N3/25exj Q9oGTp5xPEQw0C2QNgFtWJ+2vl7eR4hLVdMM4/RbpvPmd2/iX+LPnhZ7WGhZyIuGF+3quES4EPlS JKZSE/uG7KOy0Lrf5uC9B+lyoAseHT0o2WldbqbyUNFuYTvKT5aj9lLj1bXmxAIACqWCdkvbkfxU MvqjeipOVtjuqRJVxL8dz5FHjlCZV4lbWzdavtGy2r58+vjg86dPrZ4rhBDi2iBBjrjixQXEERdQ 943Ffx3/yxbgABhMBsYuHEu+Pp8KUwUv9n6Rl/u9DEDHTzo6DXIO5x0mtTCVFfev4Mavb7z4lxCi ntS0hPJos6OM/NdIXMpdKNWV0jy3OQaVAa2paqakIrWCLa22UJ5RjqWsqj9LpYXylHLa/9Gek2+c pLKokrBxYSi0CtReajw6eNRprB5tPeiwogMWi4XU11IpWF6Ae3t3iu4pIqhnEEH/CMJUbkLlKjMz Qggh6kaWq4lrVqmx1KEsrSiNUmMpleZKXlnzCjsydwDw1o1voVU6Xy5TbirnrQ1vSfY10ahGdxh9 0W0rFZWU6qx//9MC0nj5rpfJd7ffk6M/qrcLcMB63oxnZ0+0AVpi3osh/rN4incWsyVmCzu77WRn j51UlthnWTur9GApp38+bX9I5/8oFAoip0SStC6JVjNboXCt2jNUXYBjLDBy+NHD/H3r35yaJ8lA hBBC2JMgR1yzBkYPpENIB9u1syAlT2891DCjOMPhYNBzLT++nBCPkPofpBDV+Hbvt/XW1+ZWm/mq z1c11vPp74PSxf7XxvHnjsP/jtMp2VlCznc5Du1O/3Ka7e23s3/YfrYlbCPllRRO/3Ta4Wyr3IW5 ZMzMwJxhxlxp5sSrJ9h7217S3k9zqHvw3oNkfZJF/pJ8Dt57kIKVBXV8a+f0J/ScmHaC9BnpmCsu fE6QEEKIy1e9L1d788032bNnDwqFgsmTJ9OuXbv6foQQ9cJV7cqmhzex5OgSTpeeZmjcUJ5Y+gQ/ H/wZgDj/OL7a8xU/7P+BgvKaP0BlFGc09JCFsKkwVdhde2g9KDE4pmWujqvKlXJT1azK4k6L8ajw IKY8hpFxI8n+ItuhTc68HHK+y6HZ481oNeN/5++c/1WZk6/O0t5Jw1JpDVJMRSZSX7WmfA55KIT4 OfEApLyUQuq0/6WC9oSjdx8la7b13Ku83/NQapWEPR5m67No8zmZFC1QtKUI3+t9a/3+zlRkVbCz 606MOUYA8pfl035R+0vqUwghRNOo15mcbdu2kZqayvz585k2bRqvv/56fXYvRL1zVbsS4BbAxvSN /Gfjf5g9eDY/Dv+RmbfM5HTpab7d+y2f7fqMlSkr7dq1D2qPj4tsdBaXjxJDCa5q11rXv7vd3awa tYqv7/iahMAEKtWV/Nj/RxI/SyR+TjxhT4U5/ob432RK5sxM28xJzPQY28GiXj29CL43mPOpPJwv Ocuem22bLcmcnVl1oxjy/7RfPndmg32qaq8e5yQ4UIBX99olPLiQwlWFtgAHIH9xPqZS0yX3K4QQ ovHV60zOpk2buPFG6+br6OhoioqKKC0txd3dvT4fI0S92Z+zn4FfD7R9K74jawfTB03nyz1f2lJF AxSUF+Ch9aDUUIpSoeTvnL/RKDVNNWwhnCqvLK/V+U2eWk9e7fcqzb2tB3QObzOcQ7mHCPEIIdjD GqTEvh9Ly9dbkvlJJoVrCsn7Lc+uj8oi696bkPtC8L3Rl8r8SnStdCjVjt+dRb8Xzd+D/saQ4bjk c1ffXbT+pjXaYK1dgOEW70bFiarZqvODmDbftiHlpRQq0ioIuicI336XNosD4BppHyRqgjQo3WRV txBCXInqNcjJzc2lbdu2tmtfX19yc3MlyBGXrY1pG+2W/axNXUvvL3pTbCh2qHt2KZDJYv1m12g2 OtQR4nLg5+pnF6SfK8Q9hEc6PWILcABc1C4khiQ61FW5qWj+dHOaP92cw/88bFs+5t7eHb8BVWdE uYS44BLi/MwbsGZR657aHWOBkZP/Pkn6B+lgAixQvKWYQw8eIv6reA4MP0D5yXJUN6lou6AtqdNS KdlZgk9/H8KeCLPrU+2tJvbD2Lr8Y6mRdw9vot+LJv29dNQ+alp92gqFQlFzQyGEEJedBk0hff5G USEuN4khiSgVSswW65IZN42b0wBHiCuFBQuf3/Y5Q+OGsjNzJ72+6GUXyGeXZjN17VR6R/Tmxpa1 T3se90kcgcMCMRWb8L3Jt84HbipUCmtWtv/EoNQpOTmtKiV7xckKPDt40vVoVwC2b96OylVFy2nV n43TUM4GdUIIIa5s9RrkBAUFkZtbdXJ2Tk4OgYGBF2yzY8eO+hyCuII1xd8FFSrubHEnC1IXAM7T SgtxpTl27Bi7SnehQMHMrjNZlLaIhWkLMVG1v2TkgpFEuEcwqd0kWnrWMpjwt/7/5GHHM6PqwhRv Ahfgf7GXpb+FHTt2YDFaKJ9cTuWqStYErkH3Hx2qBEnNfi2TzwgC5O+BuDj1GuT07NmTGTNmMGLE CPbv309wcDBubm4XbNOpU6f6HIK4Qu3YsaPJ/i5EFURBatW1j6sPheWFTusqUNA6oDXdwrsxZ/cc u3s3Rt3IipQVDTlUIWrUL6IfySSzdP9S9EY92zK3EewRTM8WPVl7cq2tXl5FHnkVeUzeO5mjTx5l w8kNjF82njJjGS/0foH72t/XcIPsBCVtS8hblIdrS1eC77buA8qYlcHRVUcBsJy2oHhXQac98jvi WtWUvxfE5UP+Hoiz6hrs1muQk5SUREJCAiNHjkSlUjFlypT67F6IBnFD1A28veFt22btEPcQhyCn X0Q/TpedRqlQ0im0E52adeLLPV/a9ueoFCpy9bkOfQvRmDqGdmRb5jZWp662K08vSqfUUEqkdySl xlJOl5223TuWf4wSQwlD5g2xpUp/8NcH6RTaidaBrRtsrB6JHngketiVVeZXXvBaCCGEqK1635Pz zDPP1HeXQjSoAdED+HXkr/x66FeifaPRG/W8vr4q/bmXixf3tb+PMQvHALA3Zy9z98y168NkMfF3 9t+NOWwhHOzM2lntvYLyAlsQc+4+tEExgyiqKLI7C8pkMXG84HiDBjnOBN0dRNr7aVTmWYObsCfD amghhBBCONegiQeEuNxUVFbgonbMAjU0bihD44YC1ixqmzM281fKXzTzbMaye5cxe+fsGvs2I6ej iyuDxWLhmW7PEOgeyISuE3BRu9AtvBub0zcD4K5xr9PBovVF11JH592d2f35buL7xePTV86iEkII cXEkyBHXhHx9PoO/G8ym9E20DmjNknuXEOkT6bSuh9aDFQ+sQG/Uk1mcSZB7EHqjvnEHLEQ9UqBA q9Lasqz1jezLuze9a1fnz/v+5I7v7+CvlL8oNZYy8qeRuGncGBI3pFHH6hruimawBp9OEuAIIYS4 eHLKmbgmTFs7jU3pmwA4mHuQiX9OvGD9An0BPeb0IOa/MYS/H86B0wcaY5hC1Av1ed9fDWs9jOX3 L2dU4igmdp/Ir3f96tDG08XTYS/aoiOLGnScQgghREORmRxxWSoxlJBXlke4Vzgq5aWnkM3X51/w +lyF5YU8tewpdmfvBqCoosgWIJ1LhcouJa8QlwuFUgFm0Kq0PNHlCdusTe+I3hds18q/FTuyqrLX xAXENeg4hRBCiIYiMznisrPi+AqavduMyOmR9PqiV417A04UnmDWtlksPrK42jpjO47FVe0KWDOh PdblMaf1dmTuoPXM1nz191fV9qVSqEgMTpQAR1yWFCgwmo0AGEwGliQvcahTYihh0opJ3PvzvXY/ NzNumcGw1sOID4hn/HXjmdB1QqONWwghhKhPMpMjLjvjl46n2FAMwOb0zXy8/WMm9nC+vCw5P5nr Pr3OlhnqpT4vMbX/VId6PVv0ZPc/d7M5fTPtgtvRMbSjQ505u+Yw5vcxtlTSZ52biQpgQtcJTO49 mbgZceTp8y76PYWob1qVlse7PM77m9+3lZUZyxzq3f/L/fx6yLpk7bu939EhpAOfDfmMTs068eOI HxttvEIIIURDkZkccdkpryy/4PW5ftj/g13q2092fFJt3biAOEZ1GOU0wLFYLIxfOt4hwInyieLI E0d468a3uCn6Jib1nMSLfV6k55yeDgGOSiEns4umZTAZuKfdPTT3ag5YZ3Ve7P2i7f6y5GW0ntma 3w//btdud/Zubv72ZioqKxp1vEIIIURDkZkccdl5ue/LPPz7w5gsJiK8I3g46eFq6wZ7BNtfuwdX U9PeyTMn2Z29m7ZBbWnp2xLAdrDnuYoripm5bSYPJz3Mcz2fA2DNiTUczjtsV69vRF/WpK6p1bOF aCgapYZg92B2P7qbTWmbaOHdgnbB7QBrMo1hC4Y5ndkBOF12mtyyXMK85GwaIYQQVz6ZyRGXnVEd RrH/sf38ed+f7Hl0D6GeodXXTRzFA4kPoFFqiPKJYu7tc2vsf0v6FhI+SuC2+beR8FECK1NWolAo eOvGt1CgsKubq8/l/c3v03NOT1ILU6vtc03qGrxcvGr9jkI0BKPZyBvr3sBP58etrW61BTgAp0pP OQQ4akXV91yJwYmEeIQ02liFEEKIhiQzOeKyFBcQV6vMTiqlii9v/5K5t81FoVDUWB/ggy0f2JIZ lFeW8+6md7k+6nrGdx1PRWUFz614zqHNmYozrDu5jgifCFvWtfMVVRQR5x9HRnFGkxykKARAkaHI aXmUTxRRPlGkFKYAEOMXw/d3fs+Xu7/ETePGxB4T6yWToRBCCHE5kCBHXBVqG+CA9TR3Z9clhhJe X/e68/5R0Mq/FQABbgHV9n3+MjYhGpNKoeLxLo/blS0+spj/++v/SCtKs52D4+vqy+jE0byz8R3a B7Xn2Z7PolbKrwMhhBBXD/mtJq45w9sMZ8nRJWSVZBHpE8kbN7wBQG5ZLmcqztjVbRdkXe4zoesE rgu7DoD4gHin/erUOvSV+gYcuRAXNrHHRI7mHeXpZU9z8sxJov2i2Z65nQqTfUKBgvICJq+aDMB8 5lNQXsDbA95uiiELIYQQDUKCHHFNmbd3Hvf9ch9mixl3jTs/Dv+RGL8YAJp7Nadzs85sz9wOQIhH CI93eZwuYV3sMrIFugeiRImZqrTSOx/ZyZTVU+SEeNHoFChICk1iQMsB7MraxVsb3rLdyy7NrlUf q0+sbqDRCSGEEE1DEg+Ia8r7m9+3nXlTaizli91f2O6plCpW3L+Caf2n8XCHhymqKOLRxY/S5dMu zNs7z1avhXcLXrv+NdRKNUqFEq1SS/fPu9Pav3Wjv48QFiw82+NZHu38KH8e//OCdVUKFVqVlgEt B9iV++n8GnKIQgghRKOTIEdcU7xdve2vXbwd7r/Q5wXUKrUtE5XZYubDrR/a6lgsFmZtm0WluRKz xYzBbKDCVME7m95Bp9Y1/EsIcZ6t6VvxcfVBq9Q63HNVu/Ji7xeZ0mcKWf/KovyFcn4e8bPd39VV J1aRUpDSmEMWQgghGpQEOeKaMn3QdCK8IwDo0byH7eyb82mUGrtrX1df25+XHF1CenG603Z1SYAg xMUI8wzDU+tpV3Yw9yA+rj58849vHA6lLa8sZ2zHsXRq1ok/jv1BUUUROWU5dvvHDCYDxwuON8r4 hRBCiMYge3LENaVNYBtSJqRQYijB08XTaZ2c0hx+PvSz7dpD68EHgz6wXb+65tVq+9eqtNUetihE fcgoznAo25q5lRJDCcMThhPtF02n2Z1s97QqLZP+msS8fdYll60DWrN+9HraBrVlX84+wLr/LCk0 qXFeQAghhGgEMpMjrjkKhaLaAAfgj+Q/yCzOtF2XGkqJ9IkEwGgysiNrh/N+UdhS9FZHKT9yogHk 6/N5csmTFOgL6BjakSl9pqBRavDQejDzlpm2AAessz6rT6xm5QMrmdRzEk93e5oNozfIvhwhhBBX FZnJEeI855/67qfzQ6uy7nVQKBSoFCpb8oKzvLRe1R7CeK5zM7IJUZ/m7pnLxvSNxPrGsjh5MQDD YocxKnEUE5ZNsJth9NP5EegeyJs3vtlUwxVCCCEalHytLMR5BkQPYFLPSbhp3Aj3CueH4T/Y7qmV aj4Y9AEK7PfenB/guKpdG2WsQpzrSN4RW4ADMH//fEb9Oopv7vgGD42HrXzc4nEczTvaFEMUQggh GoUEOUI48eaNb1I6uZS0p9PoH9Xf7t5jXR7j5NMn6dKsS7XtyyvLG3qI4hrXPbw7c2+bi4vK5YL1 5u2bh4+rDxN7TLSVHco9xONLHm/oIQohhBBNRoIccU0qMZRw63e3on1NS8dPOpJamFqn9uFe4XQP 795AoxOiZi19WzKqwyhaeLeosW6+Pp88fZ5d2emy0wDkluXy/b7vWZe6rkHGKYQQQjQFCXLENemt 9W+x5OgSjGYju7J3MX7Z+Dr3Mb7reIdla0I0FleVK2+ue9MheFEpVIR5htmu4wPiGRA9gFGJo3DT uNnKx3UeR3ZJNh0/6cjIn0bSZ24fpq2d1mjjF0IIIRqSJB4Q16RTpafsr0tOVVOzemlFaQS5Bzn0 BdYPoF3CurApfRMeWg/OlJ/BguWixyuuHS4qFypMFTXW++rvrzCajQ7lJouJ53s+T4RPBEUVRQxp NYSMogx0Gh27/rmLNSfW0DqwNb1a9GL65umkFaXZ2r676V1e7PNivb6PEEII0RRkJkdckx5IfMCW MQ1gbMexdWr/3qb36P9lf06VnnI6m1NuKqdzs864a9wpLC+UAEfUWnUBjqvKPpmFswDnrOMFx+kQ 3IGiiiIe/PVB2nzUhoSPEnhnwzuM7TSWXi16AeDt6m3XztvF21l3QgghxBVHZnLENalXi15sH7ud talraRvUlr6RfevUfsbWGbY/W7AwImEEvx/6nXJTVcKBD7d8iMliqrcxi2tXkFsQOWU5ta6fWZxJ 9H+jqTRX2pV/tuszJnSbQNugtgDc1/4+Fh1ZxE8Hf8LH1Yc5t82p13ELIYQQTUWCHHHNahfcjnbB 7S6qrb+bPymFKbbrHuE90Cq1fLP3G1uZBDiivlwowAn3CqddUDuWJi+1lS05usQhwHFGrVTz44gf KTGU4KZxQ6mQyX0hhBBXB/mNJsRF+GzIZ0R4R6BAwe3xtzOuyzhZkiYaxIUCj57Ne3J8/HEW3bOI dkFVAXuJscRp/TFJY2yzOOfy0HpIgCOEEOKqIjM5QlyExJBETjx1gkpzJWql9ceoZ/OefLv321q1 D3QLtKXwFeJCzBaz0/K72tzF1//4Go1KA4C71t3uvlKhtLV9tNOjPNn1SdoEtmnYwQohhBCXCQly hLgEZwMcgHFdxlFeWc70LdNJPVP9uTtuGjcSgxNZnbq6VkuKhHBmdMfRtgAH4JGOj7AlfQsWLLio XPjlrl8oM5YR6xdL+5D2TThSIYQQovFJkCNEPXq6+9MUG4p5efXL1dYpM5axImVFI45KXE00Sg3P 9XyOgdED7cofSnqIGL8Y9ubspU9EH6fL0oQQQohrhSzCFuIifbXnK9rNakfPOT3ZmbXTVv5sj2e5 Pf52XNWutA2UD5ri4i24cwFtAuyXmBnNRm6Oudlp/d4RvXmsy2MS4AghhLjmyUyOEBdhT/YeHvrt Idueh1u/u5WMZzJQKpToNDp+uesXW93B3w1m8dHFTTVUcQUb/dtop0kEHl38KGXGMu5rdx+v9n+1 CUYmhBBCXN5kJkeIi3A0/6jdhvDskmzOlJ9xWveXu36hT0Sfi3rOA+0fuKh24upQXZa0fTn7OF5w nKlrp9JzTk8+3v5xI49MCCGEuLxJkCNELX28/WP6ze3Hg78+SHxAPP46f9u9ns174qvzddpOo9Kw 6O5FjEgYga+r8zrVSStKw1XtWnNFcdVRoKhVvY1pGxm3eJzdAbVCCCHEtU6CHCFqYeHhhYxbPI41 qWv4cs+XPLf8OTaM3sDE7hOZ2m8qS+9dWm3bNSfWMODrAaQUpDBv2DzubXtvrZ+76sQqyivL6+MV xBVEq9QyoesEu7Kagp5Pd3x6yc81mAyM/HEkLtNcaDOzDQdPH7zkPoUQQoimIHtyhKiFcxMLnL2O C4jjnYHvXLBdvj6fIfOGUGwoBuCO7+9wOPfEx9WHwvLC+h2wuKIZzAY+2/UZE7pOYFvGNiJ9Iuka 1pWJyydiNBvpFNqJA6cPoK/U29q4adwu+bkfbfuI7/d/D8DB3IOMXTiW9aPXX3K/QgghRGOTIEeI Wugb2RfFGgUWLAD0i+xXq3bpRem2AAdAX6mnmWczMoszbWUfDvoQLxcvfF19GfnTSLJKsup17OLy EO8fz9H8o5gsJqf3NUoNRrPRdl1iKGH2jtlk/isTH1cfAEZ1GEWpsZRmns349/p/839//R9gneWZ 2n/qJY/xVMkp++vSU9XUFEIIIS5vslxNiFroF9mPX0f+yr3t7mVyr8nMuW1OrdrF+sUS6xdru47w juC7f3xHmGcYSoUSH1cfNqVvItwrHLVKLQHOVUCr0jqU+br6su6hdXx1x1confxnV6VQ8eXtX6JS qOzK9ZV6cstybdfert4082wGwKRek/hx+I+82u9V1o9ez4DoAZc89nva3YO7xt12Pbbj2EvuUwgh hGgKMpMjRC0NjRvK0LihdWqj0+hY+9Ba3t/0PmaLmQndJuCucedMxRnMFjOF5YXM2j6L2Ttm83zP 5+s8Jq1Si8FsqHM70XAMJsd/H8/3eJ4iQxFnys8w7fppTF452e6+t4s3d7e7mxbeLRi2YJhtBqVb eDeifKKqfdawNsMYxrB6G3u74Hbs/OdOlh9bToxfDDfF3FRvfQshhBCNSYIcIS5BXlkec3bNQa1U M6bjGDxdPB3qhHiE0CWsC5NWTOLXw78yoesESgz2qYFNFhO7sncR6xfL0fyjgPXb/4Lyggs+//Ub XifKJ4o317/Jjqwd9fdiolZUClW1y8/ONWnlJCatnGS71ql1dvtpfHTW5Wg9W/Rk32P7mLt7LlqV loeTHkalVDn015Ba+beilX+rRn2mEEIIUd8kyBHiIpUaSuk5pyeH8w4DMG/fPDY+vBG10v7HKr0o nXt/vtf2Df+zy58lzj/O1u6sUI9Q3h7wNiN+GMGRvCM1BjhqpZrPdn6Gq9qVPaf21OObidoyWUwo qNqrVVvnBjg6tY4PbvrAdr382HK+3vM13q7e9G7Rm6TQJNu9HZk7eGHlC1SaK5nSd8pFn78khBBC XO0kyBHiIu3K3mUXqGzL3Max/GO08G7B0388zbbMbfRq3otQz1C7JUzlleV8MvgTFh1ZxPz988ks zuS6sOt444Y3eOi3hziYW7u0vZXmSodASTS+ugY454rxjWHL2C346fwA+OnAT9zz8z22+4O+GUT6 M+loVBqKK4q58asbKaywZuLbkrGFI08cIdQz9NJeQAghhLgKSZAjxEUK8wyzW66kU+sIdA9k8l+T +WTHJ4Bj6mmA9sHt6Rbejb6RfXln4DtYLBYUCusZKMcKjjXeC4gGpVaqifSKJLkwudo6PVr0sAU4 AC+vftnufk5ZDnn6PEI8Qvh4+8e2AAes2deS85MlyBFCCCGckOxqQlykKN8o5t4+l+ZezWnp25Lv 7/weP50f+07vq7bNuM7jWPPgGlzULrayswEOwLDWzjeR3xF/B/1a9LvgeNzUbnaZsUTjUyqq/pPq r/Pn3UHv8myPZwlyCyLGNwYVVftrIrwjaBPQhu6fdSfonSCG/zDcIfNaoFsgQe5BAMzfP9/unk6t IyEooQHfRgghhLhySZAjxCW4r/19nHz6JMfGH2NI3BAAboquPiPVE12esJ154swrfV9xKLu77d38 NOInVj20itvjb0er0uKh8eDmmJvx0noB4OXixQOJD1BqLL20FxKX5NyDXk+VnmLEDyOY0HUCp549 xdhOYzFRlaQg9Uwqk/6axOaMzZwuO82PB34k1j8WtcI6wa5T61h490Jb4O/J7AAAHgtJREFU4OTr 6mv3rFGJo+xmgYQQQghRRYIcIeqo0lzJjK0zmPzXZHZl7XK4P7HHRD4d8imPdHyEpJAku3t/HPvj gn1r1Vpa+ra0K5u3bx4/H/yZzOJMVqasxGAyUGIsYWnyUooMRdwQdQNHnzhaY6IC0fgqTBWkFaUB 0DqgdY31D+Ud4sDjB1h8z2JOPHWCruFdbfemD5pOC+8WAPRo3oN/3/jvhhm0EEIIcRWQIEeIOhrz +xieXPokb65/k55zerIvx3F52piOY/hkyCe2pUZnrT25tsb+377xbYeyJ5Y+wZ7sPRRVFDnc+yvl L1IKU6pNNaxVOh5OKRpHhHcE7YLaATj8XXAmoyiDWP9Ybom9xaF+QlACJyacoGhSERtGb8Db1btB xiyEEEJcDSTIEaKOfjn0i+3P+ko9y5KXVVu3S7MuF7x2ZlDMIAJ0AXZleqOeNoFt0Kl1TttUmCow m81O78lhoRdPgaLmShfg4+qDu9a6T6o2SwkjfCLsro0mI2+se4MHf32Qnw78hEKhcHoWkxBCCCHs SZAjRB1F+0bbXcf4xVRbd0rfKUzuNZkbom7g5b4v83zP52vs313rzspRK/Fy8bKVPdfzOSJ8Ilh8 z2IGxQyyO6xxdNJonl/xvG1juofG45I/nAsrH1cfMp/JZN6weQS4BTitE+kTSZCb81maE4UnbH/u 3aI3PZv3tF13Du1MxYsVjO04FjeNG3H+cXx1+1d27Scsm8ALK1/gyz1fcucPd7L4yOJLfykhhBDi GiAppIWoo+/v/J4xC8eQUZTBA4kPcHv87dXW1ag0vH7D63V+Rrvgdhwff5xVJ1bRzLMZPZr3AKB/ VH/6R/UHILUwlUpzJSaLibgZcba2JcYSHurwEF/s/uKCz2gb2JaeLXry+c7PqbRU1nmMVxsvrRdF BvvlgC/2fpEnlj7Bzwd/dqgf4R1BUmgS7w58F1e1K38k/4HRZGTCHxMorywHsPu7oVFpWDVqFX+l /IVOraNvZF8AZg+Zzewhs+363pm1k+ySbJYfX25X/lfKX9za6tZ6eV8hhBDiaiZBjhB1FOsfy5oH 1zT4c/zd/LmzzZ3V3j+7tKlAX4BOrUNfqQdApVAxufdknu/5PAv2L2DK6ilO2+87ve+C6a6vVIFu gZwuO+30nrfWmzOGM07vnR/g3BB1A/GB8fxr+b8c6qoUKo6NP2a3D+qhpIeoNFfSPqQ9n+/8HE+t J69d/5pdO41Kw6CYQRcc/9sb3ub5FdYZP0+t/dK0DiEdLthWCCGEEFYS5AhxhfPV+bJg+ALGLx2P vlJP+6D2PLb4MbKKswj1DGVKnylMXTu11v0pUGDBYv8MF1+aeTXjUO4h2+GnteGqdrXNajSWPH1e tfeKjcW17uevlL9smdHO1zuit0Oih9k7ZvPk0icxmowAWLCwIX0Dq0atwk3jVuvnvra2KjAqNhTT Pbw7CoWCoa2G8kDiA7Z7c3fPZcbWGfjp/Pjvzf8lLiDOWXdCCCHENUn25AhxFRjcajA7/7kTlULF n8f/ZPnx5ew7vY/lx5ez4MACxiSNuWB7BQq0Ki3x/vFOz/EpqCiguXfzOn1YV6Bg9uDZqBTOs75d qhCPEDRKjUP5uWfVOLsX6hFa62ccyTtCj/AedmUuKhdev95+CeKpklM8tvgxDCYDlv/9D2BrxlYW 7F9Q6+cBDv+MH+38KBtGb+D5XlX7uTanb2b0b6PZkbWD5ceXM3je4Do9QwghhLjaSZAjxFVi76m9 ZBRnOJQfzj3MdWHXXbCtBQuzbp3Fx4M/pm9EX6d1/kz+k2KD/UzI2YMqz6dAwf3t72dvzt46zfzU RV5ZnsNYa5Nw4ZbYW4j0iaz1c+5pdw97Ht3Dd//4jlm3zmLHIztse6TOKjYUV/ueamXdJsw/HfKp LdAZ3Gowd7e926HOwdMH7WbbkvOTMZgki54QQghxlixXE+IqEege6HSpmbvWneEJw3l8yeMYzUan bRUoePj3h4Hqs8Wd3y/AzJtnknomlX9vsD+YUqVU8dXf1kxhWpW2Vh/ANUoNT7V5inf2vVNjXQCj 2Ui4V3iNY9QoNXbv/dWer2zXoR6hZJVkXfA5rfxb0T64Pe2D21dbJ9o3mqFxQ/n98O9A1ZK/G6Ju YETCiFq9z1lD44Zy+tnTFFUUEeIR4rRO74jeuGvcbWmpr4+6Hq1KzkMSQgghzpIgR4grxLy98/hw 64f4uvrywaAP7NJIAyw/ttzph3w/nR8+rj4svWcpA78d6LCcS6VQ2c1CJOcnO32+s77bBLUhISjB IcipNFdlazOYDPi6+lJQXlDtu/m6+jKxx0TeX/9+tXXO56fzo01gmxrrnR/YnXudVZKFm8aNMmOZ 07YapYYbW95Y4zMUCgU/j/iZhUcWYjQZ6RrWlbLKMmL9Yqs9pPVC3DRuF1waGOMXw9qH1vLFri/w 0/nxbM9n6/wMIYQQ4momQY4QV4CdWTu575f7bAHKkW+PkDw+meKKYmZtn4XeqHf6YVqBghd7vwjA q2tfdbpfZdPoTVz3+YWXsznTL6If7YLakfBRgsO982dPZt4yk1dWv8KR/CNO+yooL+CFlS/U6fm9 m/dmQPQAEvcmsufUnmrrBbgF0DqgNetPrifCJ8Lu7BqdWmdLFODMHa3vILskm8N5h0kITCDQPbDa uiql6oLpxOtbx9COdAzt2GjPE0IIIa4kEuQIcQXYn7PfLkA5VnCMUkMpN31zE5vSNwEQ5hlGUkgS u7J3WZd+dX2Ke9vfS2JIInqjnnUn1zn0O7H7RLqEd+HVfq/y8uqXAXjyuif579b/1jim165/jV3Z uxyWez3S8RFGth3JmIVjKKooYmL3idzd7m40Kg3Dfxhe53dXosSMY3D225HfWHh0oe2fi1qpts0g NfNohrvWnZSCFHLLctmTvYe7Eu4ivzyf9sHtWZe6jsLyQvSV+mr3FQF0D+9O3Iw4ig3F+On8WPnA ShJDEuv8DkIIIYRoXBLkCHEF6NG8h90ejJ7Ne5Kvz7cFOAAZxRl8PPhjIrwjCHQPtNvPodPoaOHd gpNnTtrKpvWfxgt9rLMnU/pOYVzncZgtZoI9gpm/b77dWTNqhdruwNARbUbQq0UvThSesNtz4+Pq w38G/gdPF0+OjT9m9w7B7sF4aD0oMZTYrk+VnnJ4V6VCSZB7EB/d8hHuWnfi/ePp9nk3p3tnzg38 zl0il1mSaVevyFDE/P3zbdddw7qyJWOLrY9Qj1Ce7/U8Ty17yq7dl7u/tCVbyNfn8/bGt/n2H986 jEMIIYQQlxcJcoS4AkT7RbP6wdV8tvMzfF19eb7X82hVWrxdvDlTYT3cUqVQEe0bTevA1k77WHT3 Ih5f8jgF5QVM6DqBMR2taaVTClIoM5bRJrANCoU1O9mmhzcx6tdRnC47zdNdn+bRLo/y26Hf2JKx hR7NezC4lTVlcaRPJAvuXMAra15Bq9Ly7sB38XTxdHj2Twd+4u6f7rYtYfPX+bPn0T3M2DqDbZnb WJmyEqPZiL+LP5vGbiLWP9au/R/3/cGTS59kY9rGapMn1EVxhX2WuKySLP69/t8Mjh3MoqOLAOsy txDPEDgnDpPN/UIIIcSVQYIcIa4QnZt1pnOzznZlv438jSeWPoHeqGdK3ym2AGfxkcXM3DYTtVLN o50fZWD0QNoFt2PtQ2vt2k9bO42XVr0EwLDWw1gwfAFKhZJov2jWj15vV/e2+Nu4Lf42h3FVVw6w J3sPd3x/BymFKXblefo88vX5vHa99eDL1MJUjhUcw5JtsQU4JrOJsQvHsmD/AqJ8o/j+zu/JKs7i Hwv+QVFFEQBx/nGkFKZgsVhQKVUOB4+eTSpw/h6hx7o8xsxtMzmYe9BWll2Szeik0dza6lby9fnc 3fZuyoxl7M7eTXZJNi28W9j2NwkhhBDi8iZBjhBXsL6Rfdk7bq9d2d5Te7nj+ztsH+oXHllI7xa9 WX7/clzULrZ6BfoCpqyaYrv+6eBPrD6xmuuj/r+9+4+qqsz3OP45goJCCEcFzV+o+IMstVgWekjR 0hQixyaUDCimWN1lYlMk5jhaOqZpP1wus2UuMFdl4yTmlCtnxLrFcLNCMco0s0tmXBwJDDMBFfDc P1ie8QilnIBtD+/XX+yH/eN7znrWZn/Yz372+CbXceL0CZVXlatfYD95tfNS5dlKnak7o8StiQ0C jlT/Qs2+gX1dy30D+8pms2nmf8/Ui8Uv6uGbHtbB8oN6ufBlSdIX33+hlLdS9MkDn+iHjB9UVVMl X29ftfdqr7pzdYpaH6WPSz52O8Yg+yClXJ+iee/Nc30XN/W8Sfdff79SI1L1wA0PqPtz3XXi9AlJ 9cPkBnYZqKnhU932UzS7SMU/FqtP5z7q2L5jk7+bfaX7lHckT9/++K1O157WpLBJihkY0+T9AACA y0fIAQxTeKywwZCuvO/ytOXLLZpx3Qy39ounhW5s9rVLeefQO5qWPU1VNVWK7BWp5GHJevifD6vm XI28bI1Pnzy8+3C3KZLPOc9p4qsT9dXxryRJ//j6H0q9IdVtm6M/1T9n49XOy21I3Jm6Mw0CjpfN S1lTslx3qc4bYB+glOtTtP7T9SqvKldmXKaW/s9SVZ6t1Lyoebo2+NoGtXZq30mDuw5uwjfyH7nf 5mriaxPd3hO0On+13kp4S3cMvsOjfQIAgEsj5ACGGdlzpDq066Cz59xfwJm5N1MrP14pR2+HVkxY oaCOQVowZoH+8q/6IWN3DL7Do7s4s/852/WemY//72Pll+S7wtKF7985z8fLR0+OfdKt7YfqH1wB R5Kqa6vVL6if20QFKSNSGj1+p/adFGYPc73fxyabNt65UVF9otQvsJ8+0AeudfsF9lPy1mT99Yu/ Sqp/7ubTBz9t8FLR5vJy4cuNvgh1+9fbCTkAALQgQg5gmCFdh2hH0g6l56Rr77/3utrf//Z9SdKe o3sU4BOgxeMWa/G4xUoclqiqmioNCxn2i9Mp/5yLL+Ibuxs0acAk/XnMn/VD9Q8K7xauMHuYJGnu zrlat3edQvxC1NO/p0pOlUiqf89O3KA4TQ6brO1fb1e/oH6/+A6a7TO269GcR1VRXaG0G9M0/drp kqTnJj6n49XHVXC0QNGh0ZrrmKvA5YGu7cqrypVTlKM/XP+HJn/uyxHiF9Jo+5CuQ1rkeAAAoB4h BzBQdGi0ts/Yru7PdW/09198/4Xr50FdBv2qYy0Zt0T3v32/6px1rvBy/q7KeYnDEuXo43Bre/ur t7Vi1wpJ9c/0dPT+z/MuNedqdKDsgOIGxzUYKuZ0OlVWVaZA30DXbGcDuwzUtru3NagtqGOQ3kp4 y62tu39319A3Seod0LupH/myzR8zX58e+1TvffOeAnwDFOwXrNsH3q60G9Na7JgAAICQAxjLv4O/ fL19G8w4JkkT+k9otuPcO+JeOfo4VHKyRB9+96Hmvz/f9TsfLx/Nvml2g2eBJKnkZInbcnVttdvy nqN7FDc4zq2tqqZKsa/H6oNvP1CQb32AubnvzU2q981pbyrlrRSVV5XroZEPacKA5vsuLhbgE6Cc pBw5nU7X9NwAAKDlEXIAQ/l18NOrU1/VA28/oOraak0Km6TgTsFy9HHovhH3NeuxwuxhCrOHKftA tlv74K6DNX3odDnWO3Sg7IBCA0P18pSXdX2P6xU7KFZd3u+i49XHJUn9g/rrm4pvJNU/VzOm75gG x1m7Z60++PYDSVLF6QrN3D6zwexyl3JTr5t04KEDHnxKzxFwAABoXYQcwGB3XXOX7rrmLp1znvPo eZtLOXnmpD4v/VyhgaHqFdBLd11zl9YWrFXtuVpJ0vjQ8XKsd+hM3RlJ0meln+nON+7U4YcPq0/n PtqdultvfvmmQvxD9Lshv1PaG2k63fG04q+J1y39b2lwvMqzlW7L5yclAAAAuBAhB2gDWiLgfPfj d4paH6Xik8Xy9fbVlmlbFDMwRnkpecopylF413CVV5W7As6F250PXf2C+il9dLrrd7PCZykiIuJn j3nfiPu0tmCtjv50VDbZ9KeoP3lcf+25Wnm34xQIAICJ+AsPwCOrP1mt4pPFkqTTtae18P2FihkY o8hekYrsFSlJrqFlF/p9+O89Dl29O/fWZ//1mT787kOFBoZqePfhTd5H3pE8xW+OV1lVmZKHJyvr jqwWCYEAAMA6/GUH4JGL74I0dlckOjRaa2LWaEiXIeof1F9PjH1CG+/c+KuO27VTV00ZMsWjgCNJ iVsTVVpZqnPOc9pQuEF/++Jvv6oeAABw5eFODgCP/DHyj/r7V3/XwfKDCvAJ0IoJKxpdb+bImZo5 cmYrV/fzjlcdd1+uPv4zawIAgN8qQg4Aj4T4h6jwwUJ9U/GNrr7qanX27Wx1SZdl1o2ztPzD5ZKk Hv49NHXIVIsrAgAAzY2QA8BjPt4+Cu8WbnUZTfL0rU8rOjRax04d06SwSeru3/gLUwEAwG8XIQdA mzMpbJLVJQAAgBbExAMAAAAAjELIAQAAAGAUQg4AAAAAo/BMDgDLbCjcoN0luzWm7xhNv3a61eUA AABDEHIAWGLlRyv1aM6jkqQX97yoqpoqDdMwi6sCAAAmYLgaAEts/9/tv7gMAADgKUIOAEuEd3V/ v841Xa9p0vafl36uiHUR6vl8Tz3x/hPNWRoAAPiNa7bhalu3btWqVavUp08fSZLD4dCDDz7YXLsH YJhltyxT5dlK7fn3HkX1jtL8MfO1r3DfZW8fvzleh44fkiQt/tdijew5UrcPur2lygUAAL8hzfpM TkxMjDIyMppzlwAM5dfBT1lTsjze/siJI7+4DAAA2i6GqwH4TbpwNrYAnwBNCptkYTUAAOBK0qx3 cvLz85Wamqra2lplZGQoPDz80hsBgAfW37FeUb2jdOzUMU0bOk0D7AOsLgkAAFwhPAo5mzdvVnZ2 tmw2m5xOp2w2m2JjY5WWlqaxY8eqsLBQGRkZ2rZtW3PXCwCSJK92XkqNSLW6DAAAcAWyOZ1OZ0vs OCoqSnl5ebLZbD+7TkFBQUscGgAAAIBhIiIiLnvdZhuulpmZqR49eig2NlaHDh2S3W7/xYBzXlOK hbkKCgroC6AfQBL9APXoB5DoB/iPpt4cabaQExcXpzlz5mjTpk2qq6vTU0891Vy7BgAAAIDL1mwh JyQkRK+88kpz7Q4AAAAAPMIU0gAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAAGIWQAwAAAMAohBwA AAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZADAAAAwCiE HAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxByAAAAABiFkAMAAADA KIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAAGIWQAwAA AMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZAD AAAAwCiEHAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxByAAAAABiF kAMAAADAKIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAA GIWQAwAAAMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAA AAAYhZADAAAAwCiEHAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxBy AAAAABiFkAMAAADAKIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACj EHIAAAAAGIWQAwAAAMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAA AKMQcgAAAAAYxeOQk5+fr9GjRys3N9fVdvDgQSUkJGjGjBlatGhRsxQIAAAAAE3hUcgpLi7Whg0b FBER4da+dOlSLViwQK+//rpOnjypvLy8ZikSAAAAAC6XRyEnODhYa9askb+/v6utpqZGJSUlGjp0 qCRp/Pjx2rVrV/NUCQAAAACXyduTjXx8fBq0VVRUqHPnzq5lu92usrIyzysDAAAAAA9cMuRs3rxZ 2dnZstlscjqdstlsSktLk8PhaI36AAAAAKBJLhly4uPjFR8ff8kd2e12VVRUuJZLS0sVHBx8ye0K CgouuQ7aBvoCJPoB6tEPINEPUI9+AE94NFztQk6ns35H3t7q37+/9u7dqxtuuEE5OTlKSkr6xW0v nrgAAAAAAH4tm/N8SmmC3NxcZWZm6vDhw7Lb7erWrZuysrJUVFSkhQsXyul0avjw4Zo7d25L1AwA AAAAP8ujkAMAAAAAVyqPXwYKAAAAAFciQg4AAAAAoxByAAAAABjFkpCTn5+v0aNHKzc319V28OBB JSQkaMaMGVq0aJEVZcEiW7duVXR0tJKTk5WcnKyXXnrJ6pLQypYtW6aEhATdfffd2rdvn9XlwCL5 +fkaNWqUkpOTlZSUpCVLllhdElrRoUOHNGHCBG3cuFGSdOzYMSUlJSkxMVGPPPKIampqLK4QreHi fjBv3jzFxcW5rhEuvHaEuVasWKGEhATFx8dr586dHp0PfvUU0k1VXFysDRs2NJg+eunSpVqwYIGG Dh2q9PR05eXl6eabb27t8mCRmJgYZWRkWF0GLLB7924dOXJEmzZtUlFRkebPn69NmzZZXRYscuON N2rVqlVWl4FWVl1drSVLlmjUqFGutlWrVikpKUkTJ07UypUrtWXLFiUkJFhYJVpaY/1Akh577DGN HTvWoqrQ2j755BMVFRVp06ZNOnHihKZOnarIyEglJibqtttuu+zzQavfyQkODtaaNWvk7+/vaqup qVFJSYmGDh0qSRo/frx27drV2qUBsMBHH32kW2+9VZI0YMAAnTx5UpWVlRZXBasw4Wfb5OPjo8zM TLeXiOfn52vcuHGSpHHjxnFd0AY01g/Q9lz4z66AgABVVVVp9+7dGj9+vKTLPx+0esjx8fGRzWZz a6uoqFDnzp1dy3a7XWVlZa1dGiyUn5+v1NRUpaSk6Msvv7S6HLSi8vJy2e1213JQUJDKy8strAhW Kioq0syZM3XPPfdwUduGtGvXTh06dHBrq66uVvv27SVJXbp04bqgDWisH0jSa6+9pnvvvVfp6ek6 ceKEBZWhNdlsNvn6+kqSsrOzFR0d7dH5oEWHq23evFnZ2dmy2WxyOp2y2WxKS0uTw+FoycPiCtZY n4iNjVVaWprGjh2rwsJCZWRkaNu2bVaXCovwn/y2q2/fvpo1a5YmT56s4uJiJScna+fOnfL2bvWR 1bjCcF5ou6ZMmaLAwEANGTJE69at0+rVq7VgwQKry0IrePfdd7VlyxZlZWVp4sSJrvbLPR+06F+O +Ph4xcfHX3I9u92uiooK13JpaSm3Kg11qT4xYsQIVVRUuAIQzBccHOx25+b7779Xt27dLKwIVgkJ CdHkyZMlSb1791bXrl1VWlqqnj17WlwZrODn56ezZ8+qQ4cOXBe0YZGRka6fb7nlFj355JPWFYNW k5eXp3Xr1ikrK0v+/v4enQ8snUL6fBLz9vZW//79tXfvXklSTk4Okw60IZmZmXrnnXck1c+qYrfb CThtiMPh0I4dOyRJ+/fvV0hIiDp16mRxVbDCtm3btH79eklSWVmZjh8/rpCQEIurglVGjRrlOjfs 2LGD64I2avbs2SouLpZU/0D6oEGDLK4ILe3UqVN65plntHbtWl111VWSPDsf2JytfA84NzdXmZmZ Onz4sOx2u7p166asrCwVFRVp4cKFcjqdGj58uObOnduaZcFCpaWlmjNnjpxOp+rq6jRv3jxdd911 VpeFVvT8888rPz9fXl5eWrhwoQYPHmx1SbBAZWWl0tPT9dNPP6m2tlazZs3iwraN2L9/v55++mkd PXpU3t7eCgkJ0bPPPqvHH39cZ8+e1dVXX61ly5bJy8vL6lLRghrrB0lJSXrppZfUsWNH+fn5aenS pW7PccI8b7zxhl544QWFhoa6RvYsX75c8+fPb9L5oNVDDgAAAAC0JEuHqwEAAABAcyPkAAAAADAK IQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZADAAAAwCj/DyHbXuqPvoYDAAAA AElFTkSuQmCC ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd0lNXahvFr0kMogVCkg4AICigoTUVQQSwo6LGBXVE/ u6IHG1ZsiF1UPIAo6hEF0aOigAUUUVA6SEd6S0hCSG/z/fFkMiWTHkgyuX9rZTFvnT1hlLln7/1s h9PpdCIiIiIiIhIggiq7ASIiIiIiIhVJIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIi IhJQFHJERERERCSghJTn4nHjxrFs2TJycnK45ZZb6NKlCw8++CBOp5NGjRoxbtw4QkNDK6qtIiIi IiIixXKUdZ2cxYsXM2XKFCZOnEhiYiLDhg2jd+/e9O/fn3PPPZdXX32Vpk2bcuWVV1Z0m0VERERE RApV5pDjdDrJyMggIiKC3Nxc+vTpQ506dfjuu+8IDQ1lxYoVTJkyhTfeeKOi2ywiIiIiIlKoMs/J cTgcREREADBjxgz69+9PWlpa/vC0mJgYYmNjK6aVIiIiIiIiJVTuwgM//PADM2fOZMyYMXh2CpWx g0hERERERKRcylV44Ndff+W9995j8uTJ1K5dm6ioKDIzMwkLC2P//v00bty4yOuXLl1anqcXERER EZEaokePHiU+t8whJzk5mZdeeompU6dSp04dAPr06cOcOXMYMmQIc+bM4YwzzqjQxkrgWrp0qd4L oveBAHofiNH7QEDvA3ErbedImUPO7NmzSUxM5N5778XpdOJwOHjxxRd59NFHmT59Os2aNWPYsGFl vb2IiIiIiEiZlDnkXH755Vx++eUF9k+ZMqVcDRIRERERESmPchceEBERERERqUoUckREREREJKAo 5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjki IiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKAo5IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIi AUUhR0REREREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBR yBERERERkYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJE RERERCSgKOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcERER EREJKAo5IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0RERERE AopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCi kCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSI iIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIi IiISUBRyREREREQkoCjkiIiIiFQ1zz8Pxx0H/fvDpk2V3RqRaiekshsgIiIiIh6+/hoeecQeb9oE l18Oy5dXbptEqhn15IiIiIhUJZs3e2+rJ0ek1BRyRERERKqSQYMgMtK9PXRo5bVFpJrScDURERGR quSEE2DhQpg+HZo1g9tvr+wWiVQ7CjkiIiIiVU337vYjImWikCMiIiJV3+HDMGECpKXBzTdDy5aV 3aLy27rV5tt07w6NGlV2a0QCikKOiIiIVG25uTZP5Y8/bHvyZFi1Cho0KNv9NmyAf/6Bnj3Lfo/y +uYbuPRSyMy0gLNwoZWM9pSTA4sX2/yck08+Ou3KzbVhcomJ1r7GjY/O84pUMBUeEBERkaptzx53 wAHYvRuWLCnbvT7+2Oa8nHcedO0KO3cWff6yZfCf/1io+uADOPZY6NwZfvqpbM/vMnasBRyA2Fh4 803v49nZcMEFcNpp1tMzalTJ752dDS+8ANddB599Vrp2XXMNDB9u84B69oSDB0t3vUgVoZAjIiIi VVtMDERHu7eDg6F167Ld65lnrIcELCy99577WE6ODR+Lj7ftr76yD/q33AI9esCNN1oP0Lp1MGwY pKSUrQ0AERHe2773mj8f5sxxb7/yioWhknjgAXj4YfjwQ7jiCvjyy5Jdl5oKn3zi3t6+HebNK9m1 IlWMQo6IiIhUbZGR8L//Qbdu0KEDvP8+dOrkPp6ZCXfcAV26wPXXw7Zttn355d5BAQqGC1ep5tRU 6N/fhow1awYzZ8K777oDUXa2DeVySUqy4HH77bZ4p6/HH4e2baFdO3jiCUhP9z7+8sveQ+WmToVz zrG5RmedBQkJBe8ZUsJZBj/+WPR2YSIivMMkQJMmJbsW4NAhGD0abroJFi0q+XUiR4Dm5IiIiEjV d8YZsGKF/2PPPQdvv22P16yBuXNh717b/vJLG9p20km2/cYbcPHFNuekZ0+4807b/+GHNi8GICPD Pqj79q5ERbn3RURYkAF45x3r9bnoItv+9FPrMXJ5+mn47TcYM8YCVIcO1jM0ciS8+KKd43S6w8iu XeBwQO3akJzsfm5X4CpOt272e3Bxvfbi7NgBxxxjYSUoyALLgAEluxZsPZ/58+3xJ5/YUD/PMCpy FKknR0RERKq3deu8t10BByAryybvu/TrZ3N8tmyBvn2t1+S22woGmkOHrPfGU3Cw+7Fvz8z337sf b9xYsI0//mg9RccfD1Om2L569Qp/TT/95A44YO1bu7bw8z29/Tacfz60b29D1266qWTXjRwJ69db 4MrJKV3Ft+xsd8AB+/389lvJrxepYAo5IiIiUr1dcIH3tmd56eBg6zXxFBkJH30Er70GS5fCxImw ebMVJADrRfEnKanwNnTu7H58+umFn5ebC48+ao/vvBP69LHHdet6hyhfUVHWA1ScjAx7XbNn22ua NMmqyZXErl1FbxclJMT9+wPrCerateTXi1QwhRwRERGp3q691qqI3XmnzW1ZvNj2nXcefP45nHKK nZeVBY89ZhXLPv7Y+x6bNtmwtp9+ghkzCgajwgQH2zCt22937zvrLOuxKcy+fdC0qfXM/Pab9Swd OGA9IUE+H81iYuDss+Hbb22om6dt26zqm2sY288/2xyaJ55wn5OYWPC1goUt396rq692Pw4Lg3/9 y8p1P/xwyXplvvnGhgKedhpMm2bDAUUqiebkiIiISNnt2GG9DDExR+f5srKsNPKMGVbOecYMOPFE uOwy+3H54IOC1z72GIwb5/++gwbZB//Ro+HPP61n4tZbrRfEcxiWr5wcm/fzwQdwww3u5x440ObC NGhggev++70n4+/bB1ddZdXamja1fXFx3sUNwEo4BwfDmWd673/1VSsr7XTCuedawLj1Vhtm58v3 7+bnn20NnIQEuOQSWxcnJMR6mDp3tuF2555r4Wj8eLtm/Hj7PZx2WuG/izZtSl7JTeQIU8gRERGR 0nM67Zv/Tz6xD+Fvvgn/939H/nnfew/++197vGED3Hyz9xo6nuLjrQeidWsbOjV7dsFzbrwRevWy MtETJljAAZtj8tVXdk337sW364svLMR89pl7WJvDYT0wrVtb9TZfO3da9beMDGjVytan8WfuXKv2 duml8PffFmZcRRLA7vHll3D4sPd1DgcMGWJzjjxdd527etsXX1g57BkzIDzcHrv861/ux9nZVkWu qJAjUoUo5IiIiEjpzZvnXlMlJwfuvtvKN7tKMh8p+/cXve2yezf07u2uVHbeebbPU1CQlYkODbVt p7PgvZ991npopk4teNxTQoL1pnhyOmHWLAsS/irDOZ0weLA9Dg4uunram2/asLhBgwq+DrBFPD2L IURH21C9c87xPm/t2oJzbb75xnqaJkzw3t+unRVocGnf3v7cutV6flq1Kry9IpWsXHNyNm7cyMCB A/k4b6znww8/zJAhQ7j22mu59tprWbBgQYU0UkRERKqYjAzv7ezsgtXISurwYfvw7a+3w9eVV1qP g8u11/o/b+pU94d5p9N6ZDzXnnE4bK0aV8DZutWKEXgWHXA6rQdl6lSrjNa7t5WJfuABG5J29dUW BC6/HFau9N+OpUttXow/nkPTfAOOq10uCxbYa/cXcKBgtbfERBty1qiRDXVbssT2P/ec/7Dm2TPk MmWKDbtr29ZC0E03WQW2du2sd2rMGP9tEakCytyTk5aWxtixY+njqgqS54EHHuBM33GjIiIiElgG DbK1a3791bZHj4Y6dUp/n+XL7V5xcdYzMH++faguzKpV3gHLs6fBU1RU4fc4/ngb4uXZE3HOOTY/ xh+n0+axgM3/6d4drrjCyjQ3bGiLkHqWe/a0bFnBYWTFiY62APbKK95lo2fMsHkv27aV7D65ufZ7 /eUXCzybNxdeOc5fkYDmzW2oXGqq/SxbZtXaXMaOtd6ivn3hrbegVq2SvkKRI67MPTnh4eFMmjSJ xo0bV2R7REREpDoID4cffrAP/3/9BS+8ULb7jBljH8TBihg8/3zR57t6JFwKq/p1663W++LPgAHe AWfatMIDjq81a+DJJy1ENWpkVcg8F970Z9Omkt3b5dAh6zXZurXgscLCVHESE+1+jz5qwQxsuF5Q kL2Ou+7yf92nn1rxhEaNrMqarw0b4P33bUhf9+5w3HHudYBEKlGZQ05QUBBhYWEF9n/00Udcd911 jBo1isTCumdFRESk+gsLsyBR0nLLLgcP2iT7U04puIZLcUPezjjDe3vHDnexAE+RkVYOul077/0h IfDGG977li4tWbs9uYaXZWWV/triuIaTpaUVPHbwYNnuGRxsASQ7233f3Fz7iY2Fe+6x5/V8Pbm5 FrZcPWfz5hV+/1mzrFdu0yYb0vbuu1YgIj6+bO0VKacKXSfn4osvZtSoUXzwwQd07NiRN998syJv LyIiIoHgllvsA/DSpTaEKiLC9jduDA8+WPS1w4bZeS65uTax3yUz0z33xuGw6mue7r3Xgo6nfv3K 9jrKo0mTsl3nO5+mTZuSXZeTY0UObryx4Po4YL1RwcEWXF3rCuXk+A9a/viGo//7Pwuyp55a9mAm Ug4Op7OoUiHFe+utt6hfvz4jRozw2r9lyxaefPJJpk2bVui1S8vyzYmIiIhUaydccgkRO3bkb8de cgkHzz+f9LZtyalXr9jrjx8+nKiNG/O3c0NC2PT22wSlpXHsI48QnJJCwoABbH3+eQgK4pj336f2 ihWkdu5McufOROzYwaG+fclo147aixfT4d57CcrKwulw4Cjfx6IScwKZMTGElzAAOAGHz3bascdS y9+QtjK2x/P+u+64gwMjRnDi0KGEHThg5zgcJPbrR/SCBV7nJp9wAs6wMOosX+73XtvGjOHgxRdX SDulZutRil7jCi0hfffdd/Pggw/SsmVLFi9ezHHHHVfsNaVprASupUuX6r0geh8IoPdBQNu71xbs 3LPHa3ej/v1p9NJLtkDmyJHw0ktFvw9cPT95grKz6XjHHTZ3JK+Xov7PP9Nj40YrrXzqqQDUe/ZZ W0ATaPn661YSOS4uvxfiaAUcsBBQ0oDjOt9322/AcTiKLnXtEhIC9evb8L+dO3H4DPlrkZtLi9hY yAs4YL+f+gsW2Pyc2Nj8/bVPOgkmTrQS1MnJON5806uiXJuTTqJNGf+b1v8PxKW0nSNlDjlr167l hRdeYM+ePYSEhDBnzhyuueYa7rvvPiIjI4mKiuK5554r6+1FREQk0Nx/v3ehgJAQmyPy0EPu8tHj x9uCky1bFn4f3+FmYEHFdy7w8uUWct5/Hx57zEKUp82by/Y6qjKn00JgeroVR/A3NA3s9x4b6z3U z9N771lhCX9iY23OU1qaVWB7/HF7rn//245HRFjltbQ0WzvJc4HRo83ptAC2Zo1V8bvoosprixxV ZQ45J5xwgt+haAMHDixXg0RERKSaWbXKAkavXt5r2Pjy6cHJLzLguz7O+vVFh5xnnoELLyzYY+G7 ds9779kaNjfdVLLejUDhWjOnsIBTEjk5VkSgsKDUsaMtBtu6tXfp6CefhKeesseNG9tjh8PKaP/n P/Z3ftNNEBNT9raVxpNPwtNP2+MJE6xAwtChR+e5pVJVaOEBERERqWGeeQa6dbMFJ/v3L7gopcvG jQVDTmGeeIL6c+e6t5csgRNOsGFSd99tH6x9F8v0JyXF1vGpSQGnohUWlC65BDp1soDz7bcWXJ59 1tbLcTlwwNbRyc6Gs8+2oYKjR1tPneu+hw9bsYmrr7a1iyrat996b8+eXfHPIVVShc7JERERkRok K8v9rT3AH3/A//5nvSe+rrjCe3hYaKi7IldIiAUX18KemZm0HD/evS7LJZfA7t32+M037YN0SYKL wwHvvFP61yWFa9QIxo2D666zv4svvoAFC9x/H3Xrep//0kvWU+c552fDBhtKePrp9r747jvbP306 LFqUP4eqQnTq5F0ivFOniru3VGkKOSIiIlI2QUEWUFxrxoCVIPbHd/5LVhZ06GBDorKz3QEnT0h8 vPUMjB5tBQs8lbRnxuks+SKfUrx69WztoRNPtHk4zzxT8JyICCsh7Vq0dP9+O9ezIEJICDRrZo/n z3dfm50NCxdWbMh58017f7rm5Nx9d8XdW6o0DVcTERGRsgkOtnkOrkIAQ4fCkCH+z7300oL7XL0z fjjAigV07lyyoWly5F18MXz1FUyebD00/hw8CNHRBfc7nTa0rVUrmDoVjj3WAk39+u5zHA7o3r1i 2xwdbXOHVq2yohbBwRV7f6my1JMjIiIiZXfTTfbh9/BhW5jS4VvsOM+kSTbU6e23CxYaKMqmTRXS TCmnjh1tfk1xi4Pm5BSsYucSEQEDB8LJJ9uwtAED3MUnmjeH556zuV0iFUA9OSIiIlI+DRtC27aF Bxyw3p5HH/UuTFCasCOVa8OG4gOOS3Y2dO1asNJefLz1AvXr5y5I4BIcDNdeW3HtlRpPIUdERESO jpwcm69RnOBgsurVO/LtkYrhb92iCy+0QPvhh9Czp/exgwcLzt0qwQLyIqWhkCMiIiIVZ9EiK/fc ogW88op7/19/2Zydxo3d+1yTz33l5BBUWClqOTqKWu/Il2ePjEtUlK2Lc8stVgLck8NhVdjuvNPC zeDBNk9HpAJpTo6IiIi4ZWSU7gOup9xcm58TF2fbo0ZBnz42mfz88yE21vYHBcFHH8EZZ9gEdFcp aQ/Bvgt7ytGVkQG1a7urpJVGixa26OZff/k/7nRaUYk6deCHHwr29IhUAPXkiIiIiFU6O+kkmxze o0fhk8eLkprqDjguO3bY8CRXwAELQ1OmQLt2fgOOVBFlCTgAu3YVHnA8HT4MY8eW7TlEiqGQIyIi IvDII7BypT1etszWNimt2rXhggvc202aQP/+cMwxVpzA0w8/QGZmmZsr1cxxx9kQNl+//3702yI1 gkKOiIiIQEKC93Z8fOnvMWeO9QT162eV1JYssaATFFSxCzxK9dKmDUybZvO1TjnF+1hcnA1nvPJK O/booyUrTiFSDIUcERERgdtucy+6GRYGt95a8JxZs2ytG1ePTbNmtljnggXw73/bBPKZM+GXX2D2 bFv4EWzfd9+571NUqWkJPNu2Qa9etkbSuHEFK6stXw7Tp8PSpbZWzoQJldJMCSwqPCAiIiJWGGDp UhuqdsopViHNU3IyjBjhXitl9mz7c+9eG5Lma/ly+OknWw/l3Xe9jzmd8MADtgK91BwTJ8J778HI kfb+2bXL/3nLl7sf5+bCBx/YnLFhw6BTp6PTVqn21JMjIiIiNj/mm29g4UIrFuArKanki0G63HZb wYADtq6KAk7N5HRa0Bk82P/6OgAtW7ofjhsH119vw9h69rRFSUVKQCFHREREYPhwKz4waZINRfv5 Z+/jTZvCmWe6t4ODi7/n1q3+9/tbV0UCQ0neF2DV9a67zhYN9Qw7DgdccUX+ZoPvv3cfS062IC5S Ago5IiIiNUVSkq1dc9VV8O23ts/ptIAzc6b7PKcTfvzR+9rHH7e5NwDdutn1J55ohQVcfOfaBOlj Ro2Tk1Oy83JzYfJkCy3Z2fbeqVcP3nrL7nHRRTB4MNn16nlf55rn5emll2x45aBB8M8/5X8NEhA0 J0dERKSmGD7cHW4+/9yGpmVkwH//W/DcLl3cjw8e9F7PZOVK+Ne/3OuoBAfbfItTToHTT3fvj4zU OjhSMk4njB5tQad3b1tzCQgND7cAExsL114Ll13mfd0331jRC4C//4bLL4c//zzKjZeqSCFHRESk pnD1xIB9W75woZXv9fX4415DhvzyXCgyJ8c+WM6aZcGmRQsYM8YKFYiU1E8/2fpJHoIzMuDVV2Hg QP/XrF/vva05O5JH/cgiIiI1RY8eBbf794chQ9z7HnoInnrK+7yYGO99gwYVvPfEidZLFBtrHzzf fNNKTYuU1MaN/ve/8Ubh1wwaBOHh7u0LL6zYNkm1pZAjIiJSU3z2mQ35OftsK8s7YIDNm/nyS+uJ WbPGgk+PHlaqd/x498KMjz8OW7bYOUOHFv9cixcr5Ejp+KvqBzYkbd8+e7xokS0cOnKklZXu2tV6 KO+7z96vU6ceteZK1abhaiIiIjVF48bw2mvWKzNnDjRvboEnKMjm06xdax8gXZPHH3wQPvoI6tSx YgPjxkGtWtZLUxyn0/3BVKQ8XIuH/vOPDVvLm6/DokUWunv1sh+w950I6skRERGpWYYNg9dfh08+ gfPOsyICLuvXF6yOtXKlzd2ZMMEqswGcddbRa6/UaLlBQVa8olkzePhhd8ABKzQQH2+Pf/vN5oKF hVkvj8JOjaeQIyIiUlM4nfDrr+7trCx4/30rH334sH0bHhVV+PXTp9u8iSVLCh5zOIq+VqS0QkNx 5Oba+9bptPdfaKj7ePv2UL++Pb76ahu+lp1taz1Nn145bZYqQyFHRESkpnA44OSTvbdff93KQffu DXXrwu+/2zkhIVbO11NCApxzDrz8csF7O52QknJk2y+Bp3ZtGDwY+vXz3te2LbRujcP3/Ndfh/PP t+p/c+e612KKjfU+z3dbahyFHBERkZrkq69sMdCzzvIe0vP33zBtmi3wuWyZ9fIkJsLdd3tfv3On 97fpIuWRkQGZmVYEIzTUgneDBjb/ZvNm73PPOw9uvdWq+H36qQUhl9tucz9u0sSGZUqNppAjIiJS kzRvbvNx5s4tOLzszjutN2f4cCs20LKl9eo4PL5Pr1ULmjY9um2WwJWVZevjPPWUPXY6/VdZq1cP vv7a3XPja/x4O/6f/1hIb9HiyLZbqjyFHBERkZooONjK7Tp8BgQlJ8N//2t/7toFN9/s3eOTmlp4 qV+RI8XhsPdsUS680N6vzZqV7t7798OqVdajVBZPPw3HH29r9mzfXrZ7SIVTyBEREampLr20+G+8 fautiVSGq6+2P2Nj4eDBirvvzJnQurWVSO/dG5KSSnf9Z5/BE0/Ahg0wbx6MGFFxbZNyUcgREREJ ZFlZcO+9Nuzs5pu9S/C+847NsSlKrVre2yFaYk+Onqx69ax8+euvw0MP2VpPDRva/J3Bg0sfSnyN GmXzggCWL4fJk0t3/aZN3tsbN5avPVJhFHJEREQC2Qsv2AfEFSvsA9zo0e5jy5YVfW1MDPTs6d6O joaffy5YdU3kCAk+fNiKYaxbBy++6D6QnW0L2j79dPmewHc9ndzc0l0/eLB7sVKAiy4qX3ukwijk iIiIBLK1awvfPvPMwq+rXdv+nD/fvS8x0UpIHzpUYc0TydejR4EAHZSbCwMH2nAwf/buLd9zvvii u1rgiSfCTTeV7voePWDBAnjgAXjjDXj33fK1RyqM+pxFREQC2XnneS+MOHiw+/E119g34vPm2VCd 9evdx3Jy/M99cA3tEaloGzZA375WbS07270/MxP+9z+b3O/5Hg0JsfdweVx5JZx2GuzbB126QERE 6e/Ru7f9SJWikCMiIhKo1qyxD47XXAPh4dCrl83L8XTDDVZ84L//9d6flnb02ikCVtFv7lz/xz74 wP6sXx/uv9/Kn59+Opx6avmft2VL+5GAopAjIiISaDIzbc2bKVPc1dEuu8w74MybZz9duhRfmhds fZLSzlcQqWgJCdChA1xxRWW3RKo4hRwREZFA88gjtiiip1mzbJJ1QoIVIxg/3j3puk2bou8XEaFh alJ1tGpV2S2QakAhR0REJNAsWVJwX7t2EBdn1dK2bfM+5rvtKzOzYBUqkaOtYUMrI92njxW/eOgh 2Lq1YC+lCAo5IiIigef00+HXX93bxx4LX3xhP8UFGl+tWsGOHRXaPJEyWbTIhqqBzTP7+mt7PHeu Dbm84YbKa5tUOSohLSIiEmieeQbGjoVLL4U334QtW6BzZ1vnpqTCw+HVV+GSS45cO0VK6vbb3QEH vEubA4wbV/i1H35oVQZvu83KoEuNoJ4cERGRQBMcDI8+WnC/a1hPcnLx98jIgDFjrPfnjTdUdEAq RUqHDkRdcIG9p3/6Cb791spL16sHhw+7T8zOhltusfljDz8MTZva/jlz4Lrr3Oft3u3uAZKAppAj IiJSUwQFwbPPwj33lOz85GRo1Mg+FD7+uJWjLklAEqkgkdu2wWuv2carr7rDdv364HDYXDGHwxYF dRXbmDcPVq2yRT5956ctXlzwSVz3kICi4WoiIiI1yd13w/vvl3zRwwcesGC0dKkCjhx1QVlZ7g3P 3sSEBFsMNCQEhgyBlBT3sfXrrccGbHFRT1FR4LpnZqb1boaF2UKjf/99ZF6EVAqFHBERkUCTmmpD e9as8X981ixITy/ZvX780SZ8i1Q1WVk2TO3rry2ouBxzDEydCj16wMSJcMop7mOePUNvvw0zZtg9 NmyAkSN5r2+LAAAgAElEQVSPZuvlCNNwNRERkUCSlGTV1Vavtu2XX7YV4j2pHLRURyEhVnwgLAxW rnTvdzph9Gj45ReIjLT3/2OP2bFly2z+jqetW+3PAwe89/tuS7WmnhwREZHqYvt26N7d5hqcd57/ 4WOffeYOOGBzaXyNGVO6SmsiVUF2NqxbB02aFDz27rswcyZ89513QQKwuWiej4cOtcfDh0Pt2u5j t9xS8W2WSqOQIyIiUl3ccw8sX24f9r7/Hl58seA5nsN2wEpB79sHf/7pnrdw6qmweTP8/jsMHnzk 2y1SkTzXgHKJjYW//rLHgwZ5FxK44gr4+GN45BEbfnnuubb/xBOtp+ftt22tnQcfPPJtl6NGw9VE RESqi/37i94GuPJK+0A3d64FnFtuscVA09KgXTtYuNDmLDRoYMHH9cFQpLqIiYFduwruHzUK+vWD s86C2bPhyy+hfXu4914b6uZPhw7e6+/88osNhTvjDDjppCPTfjkq1JMjIiJSXXhOjA4Ph2uvdW+n pVnZ3JQU6+VZuBDuugs++MCOgS0KOmiQldG94gqrtBYXd3Rfg0h53XknnHkmNG7svX/tWgs6YD2U 775r1QELCzi+PvwQ+ve3/y569oSff67QZsvRpZ4cERGR6uLGG+2b6dWr7RvrLl1s/549tr1lC9St C9Om2erue/cWvMfq1dCnj4oPSPXVvj3Mnw85OVYKPTvbfeyTT2z4WVlMmuT+7yIry74gGDCg3M2V yqGeHBERkeqkXz+44w53wAF45RULOGDV1UaP9h9wXBRwpDq76y64/Xb455+C6+AEBVkv5vLl0LGj rYtz220le88fc4z3tr8CB1JtKOSIiIhUd56LJIIVHwjSP/ESoPbuhXfesRDzyy/exxISbD7NOefA xo22ZtTEidbDU5xXX7VhamFhVpzAVYZaqiUNVxMREanu7rnHyufu2AG1atnaOLt3w7PP2jfZhw+7 e3rCwmyld5Hqzjfce4qP994uqmfTpXlzm68mAUFf84iISI23NyODRYcOkeQ5tr+K25CaypVr13LJ mjX8ER0Na9bAH39YmDnnHLjuOvsm+/zz3QEHYMgQm7fjEhlp6+6IBKroaBg2rLJbIUeZQo6IiNRY uzMyeGDzZo794w9OW76cE/78k22uSmSV7OP9+3lwyxZmHzxY4Fh6Tg6nL1/O9NhYZsXFcfbKlewN C4NevQrOK9i40Xs7KcnKS194IZx9tk3ezso6gq9EpIJFRJT83OBg651p1869SOi6dVZ8o21beOaZ I9NGqXQKOSIiUiNtT0+n+19/8fKuXaTnTUrelZHBa/7W3yin5YcPM2zNGoatWcMK39XY/Xhl506u XreO8Tt3csHq1cyMjfU6vjQ5mTiPYJKam8tfhd13yBDv7Xbt4IQT4Ouv4dJLix66dsEF8MMP0KZN sW0WOeIcDrjoIkhPL3jM1TtZq1bBa4KD4fjj7ZyTToKhQ63Xc9s2ePxx+OabI950OfoUckREpEb6 7MABDvjpwQj2XCm9AiRkZXHOypV8GRfHl3FxDFy1isRiek5m+axd85XPdqqfYXXRwcE4/VWQuvZa +OILq8oGtnZInTpw8skFA05wsPf2t9/CwIH2YVCksoWFFQwxLklJ1sMzY4a77LPDAePGwaOPwoYN tm/lSu/hmwBbtx65NkulUcgREZEaKcbPPJT2kZGMatmy3Pd+dvt2uv75JxetXs0fSUnEe4SSuKws tqan82NCAueuXMnQ1atZn5LidX2HyMgit0+pW5eGPgscDli5kroLF/LRvn0FGzRsGCxb5r1vxQpb /NBTTo59QIyKcu9TuWmpKjIy4NNPCz+enm7FNr7+2t7vW7bAfffBoUPe57Vo4X4cFWWV1Mpi1iwr 1/7VV2W7Xo4oVVcTEZEa6domTZiXkMD0AwdoHBrKy+3acWmjRkT49maU0vQDB3jsn38AWJ2SwqHs bBqHhub3Gh0TFkYIcOHq1aTnVYdampzMll69CMsr+/xKu3Yczslh+eHDnFW/PqNbtfJ6jvqhoYxv 147rXd9OAzlAck4ON27YQP/oaDakpdEwNJRutWvbCZGRkJzs3Vh/hRYWLCi6apVIVfbbb1Zo4M03 bX0cgLvvhh9/tLlnkZHw/vs2L2ffPrjsMitFXVqTJ8PNN7u3338frr++Ql6CVAyFHBERqZFCgoL4 b+fOfHj88YSWYk2ZKXv3MipvuMsr7dpxQ9OmXsfX+fTKbEpL4+eTTuK57dsBeLR1a7amp+cHHLC5 QAcyM2kREcHujAw+2r+fs6Kj+ahTJ1YlJ7MqOZlutWuzOS2NJmFhNAgNpXFYmN/2ZTmdnLNyJRvy Cig817YtD7duDe+9B1dead+Gu4waBRMmwJIl7n0KOFLdZWfDnXfCv/4FDRvCeedZz+WqVdCjB3To 4B7SVlazZhXcVsipUhRyREQk4P126BDfx8fTqVYthvusYu4ZcHKdTv4XF0dqbi4XxcRQ22dI2I70 dG7ZsIGcvO2RGzZwTv36tPSo9nRugwaM3b49/5xsp5OXdu7k+WOPzT/P6XRSJziYwzl21nEREdQK CiIuM5NeS5eyO2+uzDPbt7M373H9kBASsrOpFRTEzBNOYEsRVeA2eBx7ats2RrdqRdDQoRAXx+Jf f2XOoUN0a9aMi/v1g86dbdV4VViTqq5ZM9izp2Tn5uRASoqFHLD3eefOFdeW9u2L3pZKp5AjIiIB 7eeEBAauXJkfOjanpfF4IdXChv/9N9PzKpnVDQ5mxSmn0NZjPkxcVlb+fcCGiB3MyvIKOX3q1eM/ HTtyy4YNZAOxWVlM3bePP5KS+PvUU5m6bx+3bNxIttNJ6/BwTq5dm9+SkohZtIgTa9XKDzhAfsAB SMgbWpaam8v9W7bQx3OtmyKEBQURlFdM4buMDC6MjCQ3MhJyc3n9q6+4+5JL1Hsj1UNsLNx4o83L SU0teDwyElwB/7LLoHXrI9eWsWOtPb//DqedBk8/feSeS8pEhQdERKRayMrN5YHNm+m7bBn3bd5M Zgk/mM+Ki/MKJp/7lGN2OZCZmR9wAJJycrji77+9zukSFcWpderkbzuAVT7D0wC2pafjO9tlfWoq +zMzuS0v4ABsz8hgTUoKsXm9KGv8fXDzI9vpJKyIKnCuI2EOBxOPOy5//2exsXj+1h4KD2dtBRRa EDkqsrJgyhT/Acd1/KKLYPbsogsUVITateHjj60y27Rp3sU6pEpQyBERkWph7PbtvLxrF78nJfHa rl08WcKyxm19Fg48tpCFBGsFBeFbcmC35/wVbGjbtR7D3ZzAqM2bC9yrWXh4gX3HRUZSLziYLJ9q ZclFhDXPtkbnDZ0LAbpFRRUa1lztur5JE86OjiYlxx3xfEtXp0VEsLJdu0LvI1LleRYKyc6G//3P qgb++qt7PZ2cHPj8c5g6tWClNQlYCjkiIlItrPSpDLbCt1JYIe5q3pxbmzalRXg4A+vX512Png0X p9PJwexs7vMsLQsMc43n97DPZ22ZRD8Vyk6tU4fGoaE4gAiHgyExMczt1o3IkBBGehQq6FmnDvc2 b56/7fuP8iOtW7Otd2+29+7Nzt69WXjyyZxUpw4z4uI46PO8ER49O8dGRDB1/36+S0hg5MaNfHbg AIlZWXxz8GCBtib7lKcGC0kiVV5UFHTrVnD/p59C//421yw5GYYPh8svhxtugD59oAQL8kr1pzk5 IiJSLZxdvz5feXxIP7t+/RJdFxIUxLtFlIjNzM3lotWrmZOQQCgwqkUL0nJzOa5WLe5s3jx/gU1H Xoj4MynJ6/ps4LK1a/m0c2eCHQ6cTicXrV6dXzI6w+nkyTZtaB0Rwdz4eKbmrWMT6nDwZOvWTPCY SJ0LdI2KomFoKIMbNOAmn8ptidnZ/FXIB7QB9eszokkTagcHM9pnscNFhw5xWr16BYbQAawfNoy0 efOIzAtvuegbUKkmPvoI/vyz4BpQLsuXW+/NZ5+5961bB/Pnw5AhR6OFUokUckREpFq4q0ULwoOC +O3QIXrXrcttzZpVyH0/PXCAOQkJAGQBL+/aRe2gIIY2asT4nTt54p9/CA0KYkKHDtQLCWFuYmKB e8yIjeX57dt5rE0bDufkeBUPcAIbU1PpXqcOE3bvJjMvNGU5nfxn3z5+zHtul90ZGXSqVYt+0dFe ++fFxzNk9epCX8f38fFsSkvjx27d6FOvnleFtd5169I8PJxLGzZkZlwcAA1CQhgSE8Owbt1o2KwZ 5/75J+GZmdQ/fJjmBw9y/+efE5mZyb7oaJokJlL4DCCRI6B27YLrOvkaNcrmxBR3H8+CBOCuuCYB TSFHRESqjVuaNeOWCgo3Lhl+5sQk5+by0f797nNycrhh/Xra+xna5bL48GFSc3K4Zt06HLiHfIU7 HPlza6J9SlLXDwmxymce83QOZmczPTaWGbGx/LtVKx5p1YoJe/YwfseOIoeRObHKcW3/+IMIh4OO kZFkO53kOJ38lJjIkIYNaRMeToTDQbbTSXx2Nh/s38/vSUmc0Lgxs/r1s3bk9Vj93rkzD06fzrwe PRj7/vtF/g5FKlxaGkyZQvY99xBS2PCy4gLO4MEwYgTUrWtV2VJT4aGHbMiaBDz1SIuISI20NiWF XkuX8tS2bYQXUanMJRfYWMTaNKk5OYzdvp3/HTzoFUYynE7OXbWKn+PjeaZtW7rkVWHqGhXF2LZt /c77AStP/fyOHZz01188tHUrcX7m/gAFiiXkAqlOJxvS0tiSns62jAz+s3cv/1q9mpd37ybd6fQa trYxLY0RjRvbhsfv4du+fen/+utE+6keJ3LE5eTAP//gDA31f7xbN6/3q5cWLWDNGvj2WwgNhUsu gcREK0Rw7bXw2mvwxRdHru1SJagnR0REaqTL1q5lXRElmx1YL0y6s2D/SduICBqFhLDEYzjNT4mJ hYalxJwczlq1iiDgvY4dubJxY2oFBfFTQgK/+8zx8bXFVSGqEM3DwtjhUwzBn7+KGPrjO4fH06zT T+eemTMJzckp9ByRI+KZZ/AbcTp1svVp3nkHRo+2sPPQQ7BpEzRtCo89Bg0aFLxu82bo2dNdYe3f /4YXXzySr0AqkXpyREQk4DidTibt2cPoLVv41c8cGoB/fMJDVJD3P4lOyA840cHe/SUXNGjAk23b eu0LBoY1alRku3KBmzdsoOfSpZy2fDnnrFrF1mJCTHG9TCUJOACHCukJAsgo9Ags6tKFK8eMYV90 NClhYWjZUKl069bBjh1w//02BG33bpg1y6qqvf02LFjg/7ovvvAuIT1lytFpr1QKhRwREQk4D23d ysiNGxm3cycDVqzgFz9B5zKPQFInOJjZXbtyZyHzfYIdDq+w8daePcyMjeWimBjA/jF9tX17RjZr Rv969Ypt39+pqcX24Lhk+OlJKous4k8p1BdnnsmM/v159Oab9cFBKl9wsIWZtDRbE+eCC2x4GkBG Bjz4oP/rfKoVUsHz+6Rq0XA1EREJOLPyKoiBzW35+uDB/Gpl7+3Zw0f799M8LIwX27YlNTeXyxs3 pnNUlN8wBDYkbJXP0LbJ+/ZxfGQk5zVoQExICJfnzWvZVcKelerm7rvuou/ateQ6HATlBa+00FCW dOzIma4PmCIVISTEFvYsTE4OvPGG9d7s3Fny+15zDSxaBB9/DC1bwrRp5W+rVFkKOSIiUm38kphI Sk4OZ9WvT3hQEDNjY1mbksLA+vXp49GD0j4ykk0eRQIahoQw/O+/WZ+aynKPuSn7s7L46aSTAJif kMDT27b5fV7fgOOyPi2N9XnPsyYlhV9PPpksP9Xa/AmCajX0yxkUxG9dunD96NHcPHs2WcHBPHzT TZy9fDl7GjXiqp9/ruwmSqDwF3DCwuCss+D77937/AWcsLDC59kEBcHEifYjAU8hR0REqoXbN27k nbyFM/vWrcsFMTE8+s8/ADyzfTtzu3ZlQN4CoZM7duTGDRvYlJrKxQ0b8umBA6zwUyXMM/BM2bev XEO6VqSkEL1wISWdnh9K0XNhqqpp557LtHPPBaBhQgIvnHACMYcOMWzhQiKyyvMbFMkTFga+PaI9 e8J113mHHF/DhsFVV0HXrke2fVItaGitiIhUeQezsvIDDsCipCQm792bv53tdDIjNjZ/u2l4ON91 7crm3r0Z166d34ADUC84mFd37uSvpCQ2FFFpraRKGnAcVM+A4ysuL1QerFeP6f37V25jJHD4G/KZ nAxXXglvvQXh4d7HjjkG2re34WuXXw7HHQe33XZ02ipVlkKOiIhUeeEOByE+VcaahoV5bbfOW3DT U3J2No/98w+NPNbaCAJC8+61PSOD+7ds4dRly1hS2IKDR0DFlBKoWm7+9785e/x4fu3SpbKbIoEm KAhGjbLHxxxjxQU8nXKKlYf2NHEiLFxo6+L06GFlpUs4lFQCg4ariYhIlVc7JIQJHTpwx6ZNZDud XN24MePatWPEunX8nZLC4AYNuK9FiwLXnb96Nb/mlYx1AO0iItiSnk5WBVUsE7fskBB+6tGDPzp3 Zt1119HKo2dNpIAmTWxYWjGFA5K6d6fumWfCrbfaT5MmBU/65hv/Fz/5JPz4oz1etsyqq91xR/na LdWGenJERKRauKVZM67L+4Dz0YEDnLliBefUr8+evn1pHxlJt7/+4rxVq9iZt+7MHRs35gccsN6T zenpAdmLUpWkRkYy9IknqlVRBakEcXHQp0+xpyX17Quvvmrr4aSmQt48vBJxBRyXtWtL2UipztST IyIi1cLyw4eZvG9f/vamtDQe/ecf1qak8MmBAwCsS01lxLp1fNulC297zOGRo2t/w4b6FlWKFhIC n39e7GmpnTqV/J49esDSpYUfHzSo5PeSak//DxIRkSotI28cfWFDzJb5zKVZlZzMVo/y0b4cQK/a tfO/5XMAwRXQTnGLj47mQN66RGC9aJMGD+aRG2/k986dK69hUnVkZEBxw0br1iW5Wzc48UT/x2+8 EQYMgO7d4eWXobD3Vv/+8MUXMHRouZos1Yt6ckREpErKzs3lqnXrmBEbS5PQUJ5s04amYWHs9am8 dHb9+l7zbA7l5NBr2TJ616nDH36KCTiBxXmlox152yWtiiYlkx4eznkvvMD4d98lMiODu++8kz/z PoC+OHw4059+mn/98kslt1KqvKQkGs6aBY88YoUFxo51V17r0wcmT/Y+f8MGG6Lm24s7cqSVl5Ya RSFHREQqRY7TyeS9e9mTkcG/GjXixNq1vY5P3bcvvyz0/qws/m/TJq/j3aKiOCYsjMENGnBVkybc vnEjq/JKRWc4nRzKKT66aH7OkbOsY0fOevXVAvtzg4OZfP75Cjk1zfjx9uMx5LQkWr38sj1o1w4W LICZM6FuXbj33oInd+xoQadFC/CYj8f27eVouFRXGq4mIiKV4tYNG7h140ae2r6d3suWsc5nLZt4 f6uee1iZksKchASGrFnD5wcOcFbemi0uGytg3Rs5MnY3bEhcnTqV3Qw5mvr2hU8/hbL+vW/ZYhXS XnoJxowp/D61a8PFF7u3Q0M1F6eGUsgREZFK8ZlHieGU3Fxmx8d7Hb+ycWOaeKxvU5TXd+8GyD/f gYagVWWr27XjnrvuIq2Ef78SAC65BIYPh5KsR9WtG/hZ94oZM6w3qJgvQJg0yebo3HsvzJ9vBQmk xinXcLWNGzdyxx13cP311zNixAj27dvHgw8+iNPppFGjRowbN45Q/Q9MRET8aBsRkT+8zLUNsC83 l/E7dhATGspfPXrwc2IidYODeWnnTn5LSir0fm/s2pVftljD0Kq+TwYO5NeuXQnOzWXslCmM+OGH ym6SHEmlGaa2cqX//T//bD9//AGnnQYnn2xFBXyFhsL995epmRI4ytyTk5aWxtixY+njUeP89ddf 55prruGjjz6iVatWzJw5s0IaKSIigWd65870qlOHFuHhPNa6NZc0asTujAyuTU3lwa1buXHDBkZv 3UqXqChu27SpyIADaF2WamhnkyZsa9qUW++7j3n6tl1KauZMCzEDBsBjj0Hv3lZh7auvKrtlUoWU OeSEh4czadIkGjdunL9vyZIlDBgwAIABAwawaNGi8rdQREQC0vFRUfzRowc7+/ThmbZtAZgbH0+8 R1nZTw8c4O5Nm9jnU1FNAktKrVpc+tRTZIaoHlLAczhsjZyoqBKd7gTrtSnMiy/C4sWwfDlcfjls 21YRrZQAUOaQExQURFhYmNe+tLS0/OFpMTExxHqMtxYRESlOi/Bwr+0Qh4Nfi+nBkcBwOCqq+HVT pPpzOm1OjU+hEaKjvefOREfDqFFsnDgRFi6EZ56x3pqOHb2v85yfk5kJ//xz5Nou1coRKzzg1P+o RESklAY2aMDIsDAahobSMCSEzBL8W1In2P9SnmGAZoVWHyFZWSzo1q2ymyGVoVMnK/P811/w008w dSqsXQvjx5PsCj6PPQZLl8KSJXDeeRAZaRXbPENPs2Zw0kmV8hKk6qnQfuGoqCgyMzMJCwtj//79 XkPZCrN06dKKbIJUY3ovCOh9IHBreDi3Am9lZDC1iPMcQC3gcCHr4WiAW/WSHRrKtY88wpobbiDG owKXE/u7lsB1OCKCja51sOrWhRNPhL177Qc//y4880z+w+DERJp8/DGO7GxiL7uMzK1bj1azpYqr 0JDTp08f5syZw5AhQ5gzZw5nnHFGsdf00ERDwf4HpveC6H0g4H4fjE5J4cvly0nMzsYBnFGvHr94 LPDnBFIKvYtUR/tiYjjx/fd595VXaLdnD522bydYI0MCS1AQHH88/P13/q46vXoV+v/+Ev27cPbZ ABxTYY2Uqqi0X4KWOeSsXbuWF154gT179hASEsKcOXMYP348Dz30ENOnT6dZs2YMGzasrLcXEZEa 6Ou4OL7MyOCygwcZHBPDqlNOYUFiIu0jI5m2f79XyJHAtC8mhqHPPktIdjapgwcTXEhPnVQTQUGQ 61H7cMoUGDECHn7YhqadfDKce67ta9oUrrrKyk2feiqUYESQSGHKHHJOOOEEpk2bVmD/lClTytUg ERGpHB/v38/Y7duJDArijfbtOT06ukLvv/zwYUZv3Up6bi6Ptm7NuQ0akJqTw4f79pHtdOIE7t68 GYApq1fzwfHHMzc+nllxcbSLjCzxwqASGLJDQrj/9tt5bcIEgnNVILzKuvNOuPpqOP30got0jh8P 8fHw3HO23bEjhIXB+vXw0ku2788/oU8fcIXZV16x4gSNG8Nvvx291yEB54gVHhARkepjfUoK161b x/rUVJYnJ3PRmjWkVeA36Gk5OQxetYp5CQn8eugQQ9esYXNqKgNXruT/Nm3irs2becSnKtLLO3fy 8YEDpObmsjolhS3p6RXWHqke3rrkEtr89798ctZZABysU6eSWyQFnHIKxMUVDDgAgwbBs89aWHnv PTh4EIYPh27dwPVF+cKF7oAD7gp7Bw7AO+8c+fZLwFLIERERtqWn4xlpErKzOZiVVWH335eZyQGP +6Xn5rIgMZFFHuWhk31CVUSQ9z9Rif4+REnA29W4MSPGjKHXhAmc/J//EF+7dmU3SVwGDLDhZfXq +T/+7bf2Z9++sHWrhSGw4WsvvGCPu3e3tXP8qVWrYtsrNYpCjoiI0LNuXZp5rH3Ws04dmvmsWVMe LcLDOd7jA0u94GBmx8cXOG9QdDRNHA7Ojo4mxOHw+kcqVXMzarQlnTuzs0kT/nPhhV77d8fEMOCV VzjvhRcUgCpaVBT4K9EeGQnnnw/9+kFsrM2l8ef55+3P9HQ7z9PBg/bnmWfCBx9YYBo8GBo0sP3d u8P991fM65AaSUsLi4gIDUJD+b17d97bs4fI4GDuat6coMK+XS2D0KAgfu7WjRd27GBlcjLzDx3i C9e3unkcwNddu/Lc4sU8nZiIb02tDFXZEuDJ66+n5YEDDFixgpygIHq9/TZ7GjUC4NKnnuKnUaNU crqinHYaTJoErVp5709Lg9mz7ef992HWLP/Xp6VZmOnXz6uaGgD790NqqvXWXHON/QBkZFiPT9Om VrRApIwUckREBIBWERGMPfbYI3b/Y8LDea1DB85cvtzv8b5169L699/Zn5VVIOCIuKSHhzNizBgA Wu3blx9wAOZ3787uhg1p4ROgpYz+/htuvLHoc3bsgPnz/R8bNszm4vgGHICICCtC4Cs8HJo3L3VT RXwpIouIyFHlOwxuaEwMr7Rrx29JSexTwJFS2HGMz8ooTifbPUKPlNOuXfDDD8Wft39/wX0vvQTT p/s/3+GwHqAQfdcuR45CjoiIHBXz4uPp+uef/HX4MMfXqkVUUBAXxsQwrVMn6uvDjlQEh4PbRo1S UD7aJk+Gnj3d27feCg884H7csKH3+e3awZVXHr32SY2kf1VERKRcViUn8/H+/TQJC+OO5s0J9xlH v/TwYS5evZrdmZn5+0KAhd2706tuXZYdPsz/4uKIcDhIz5t34/lYpDTWHHsszw8fziOffAJAZnAw oTk5mqdzJB08COvWwZIlULu2FRNwadDAykSffrrNtQkKgkcfrfg2fPMNfPIJtGwJY8ZYO6RGU8gR EZEy25iaSt9ly0jJW6xx0aFDzDjxRK9z+i1bRqpPYMkG+ixbxpNt2vDKzp0cyquc1iAkhJHBwfxf t27cuWULmbm5XNWoETdu3Khv56VkHA4eHTmSuaeeSovYWOZ368bOK66o7FZVL5ddZmvb7NlTsvPP Px8aNYILLvB/vGNHm5ezaBEceyx06VJxbQVr68UXW2lqgE2b4IsvKvY5pNpRyBERkTL7MSEhP+AA fHXwIE6nE0deZbbD2dkFAo6LE3hq2zY817KPz87mp9xcXvvzz/xqamtTUuhcqxZrU1OP1MuQALTg pJMAiMjIqOSWVEPLlpU84AQFwfffw4gRcN99tjioP40aWRA5En791R1woPBCCFKjaE6OiIiUWfvI yB2xiaAAACAASURBVALbDo/S03VCQoocJuQEIn1KVf+Zm+tVLnp3ZqYCjpTZNXPnaqhaafmuaVOU 3Fz7+eQTOPVUdynoo6l7d+/tHj2OfhukylHIERGRMhvYoAEvt2vHcZGRnFGvHrNOOKHAOd2LGBv/ ZJs2fNetG4MbNCBSa2LIEfBl3748fNNN9Hz7bfa4FpqUojVu7K585nAUrIJWrx6ccYb/az/6CFat OrLt8zVokK3nM2CAhay8+VhSs+lfFBERKZf7W7ZkQ69e/HLyyRwfFQXAv7dsIWbhQk5YsoQxrVvT p27dAt+mj2jcmH/S0/l4/37ePe64IsOQSFnFxsTwwtVX82enTszu3buym1M9XH89LF4Mb71l82jO Pdf7+LBh8OSTFoD8qYxqiTfdBD/9BB9+aEPjpMbTnBwREalQX8bG8tLOnYDNsbln82a29enDoJUr mZeQkH/e57GxZOYNS/vm4EHiPKqviRwJIx98kLZ793L28uU4oeoOYwsOhrxiHEfdnXe6q59t3gyv vALt28M558CKFdaD89ZbEBUFc+bAq6/C1q2wYYNdc8890Llz5bRdxINCjoiIVKhdPhO9t2dksCs9 nU86deLuzZuZFRdHem5ufsAB2KuAI0fJOa+8QsPERLqvX8+LkyZx0pYt/k8MC4PKel+GhUFaWuU8 t6tC2pw54FmV7qqr3HN1nE7IzoaBA+0HYPt2m5vTtu3Rba9IITRcTUREirUlLY2pe/eyOCmp2HP7 RUcX2PdbUhINw8K4t0UL0j2rIOWpHRxcIe0UKYm46Gjm9u5Nj4kT6T1hAn916ABADpDrcNiaLkcz 4AwebMHGpTL/e7jjDqustnCh9/5ffrE/v/vO1r4JD4e77nIfb926YgPOggXw73/TcNYsC1UipaSe HBERKdKKw4c5ffny/FLR/evVY063boQFBbEkKYkNqamcUa8e6bm5bEpL49Q6dWgcGsqBrCzAhgR1 iIzE6XTSMjycEIeDbI8PLfWDg5nXrRvjdu7ks9JUdRIpp9zgYBZ37sxpb71F77Vr+eXkkwnNzGTa 889zGUfxm+ClS71DVXJywXNq1YJ+/axcc3Fq1bLQsW5dwWN16sDhw+7tkBBbt2b5ctveuhVefx1O O837ulNPtbAxfDgkJtq+t96yNXLOO6/4NpXG/Pk2PC4nh9YAWVnw4osV+xwS8BRyRESkSFP27fNa C2f+oUM8u307rSMiuHnDBpxAMJCLlYRuGBrK5I4dGbdjB0k5OdzXvDmT9+5l4p49OIBQh4Nsj/u3 jYyke506DIiOZk58fP7CoCJHS2ZYGL+cfDIAWWFhXDlmDG8OG8aYadM4Z+lSgtu3twUmfVXU3JmS hPvTTrNFLz3Vrw8e89zyhYRYaHn+eQstDRvCu+/aEDjfHqp+/fyHqosugvfeg88/tx6aF1+0sHHo kPd5Bw8W3/bS+uYb79/rl18q5EipKeSIiEiRGviplLQuNZWv4uJw9cd4fsyLy8pifmIiC/PWrvgi Npa3PRYW9OzFcQCjWrZk3M6dPLR16xFovUgZBAXxW9euDH7pJa77/numTprk/7xp06BpUwsOH34I H3/s/7zwcCjvoqTp6d49MFFRcO+9sHcvTJzoPaQrKQmGDLFwUKsW3HCDe45PRga0a2fXt2kD77xj PT4XXwwpKXDssVY8AGDkSPvxdOutFpjArj///PK9Ln/yhg8Wui1SApqTIyIiRXqgZUs6RER47bsg JoboIsrE1vJY82Z/EXMbgh0OPty3j4m7d5e/oSJHwPL27XntzDPJPuss7wOhodC/v/0MGmQhoTBl CTi+60a1bOm9nZICTzxhc2UyMiA+Hk480X183jx47TV7HB7ufW2nTrByJXz1FTRrBj17Qt++EBlp oa2oNateew3yer2IjYU//ij9ayvOyJEwahR06EDi6afbGjgipaSQIyIiRaodEsLG3r2Z1LEjdzZv zmedO3NFo0Y0DA0lxM86GV2johjl8YEsqohJ1NlOJ3MSEvinvN9yixwJTier2rfnvrvu4pyxY3G+ /747MOTkQPfu7oUnBw+2wFARmjaFzz6z3haA226zHhd/C3D+/Tfs3m1D13yHzsXH25+PPmploF33 fv557/OeecZCUVqaDYkbNarwtk2b5p6/k5JiPTsVLSgIxo+HjRvZ8tprcMwxFf8cEvA0XE1ERErk pqZN8x8/vHUrM+Pi8rfbRUTQqVYt7mzRgoH16xPkEX4mqJdGqiuP9/GCjAyS9+yhjiuQ5+bCvn1w 3XU2X8Y10b9PHwsepXkOz6FmxxwDq1bZPJqhQ62XplYtO/b66zYh3xVeXOLjLWC5CgK47nv55fa4 ZUtYu9bCUNOm4NMzi8dwUr/bLuvXu6usuaSmlux1ihxl6skREZFSW5eS4rV9XK1afN21K+fUr8+i Q4dY4lFqOqyooS8i1YQDOPO449jUvLn3gexsmxcDULcuXHll6W7sGXC6d7cg0fD/2bvv8Diqq4HD v9mmXfUuW7JVLXfLxnIFU0MoAQIkYFoooTrEtCQEPkIoCSUJJdQACT2ETigOxaGY2NiAca8qtiVZ Vm8rrXa1fb4/RlpptWo2siTL530eP+zM3Jm9k2ilPXPvPSdR29brOwOcjz/WppV1D3AA8vO1rGcd /ei4btcRUpNJSyDQPcABuPji4LTVl10W2mbFCpg1SxvJ6eqOO/q8PSGGi/zlEUIIsd9OT0gI2j4t IQGfqnLm1q0cvWkT8zds4BdFRQD8JTubuD7W7wgxUk0wm4lt//KvAhsTEzn3rruCG02ZAnl5ndtX XdV3vZiu9XC6270bYmK0wOmee7SRmH/8Qzv23HPa/t68807ovoF+7k4+GdasgYcegi++0Eanunvq qeCgae5cbdpaR5ICIUYY+asjhBBiv12ZmkqUwcDq5mYWREdzYUoKq6xWPuzylPnpykp+mZrKwpgY 9i5YwLKGBq4qLMTu96MnOCObEEPJrCg4B1Bg8rjYWJ6trg7atyU7myU33cR1VivTpkyBK67oHG0B bbrZpk2wYYM26vLTnwZf9K234LHH4PPPQ1NQd4zg/N//aWtSOtqbTJCUFHydRYtCC3bqdNo0OoDI SG3kZaDmzdP+9aZ7kd+JE/fv+kIMMRnJEUIIcUDOS07msdxcLkxJAXqelvbL9toikQYDF6SkcFJc HCABjhheAwlwAF7sFuAAqDodz/z4x+x78EG4+WaIjw89MTpay7p21FGdyQM69i9apC3yP/bY4AAn JQUef1yrQ9N93cv//qclB1i0SAtkFiyAt98OnlZ2wQXw2mtaYc9582D5ci1b2mD5wx9g5kzt9dSp ockLhBhhZCRHCCHEoJgfHU2CXk9Dly9uK5ub+balhfnR0bxWU8N7B6NwoBAHSR+TwzixPWDvU0qK VtjyV7/Sth99VAuKWlu1wKWrWbO0mjN6vZbOuas5c7RRnlWrtLU2iqLVyHn5ZW0U6e67tYxoXZMN dPjmGy1d9KJFMG1a/33uTccIld0eHLgJMULJSI4QQohB82BHmtou9jqdANy8ezfdn5/H9JFeWoih FtZDSvSeHB0Tg36AbXnvPW3tysaN8MQTWpASHg7JycHtli/X/uvzadPQliyBE07QRkx+8YvOdoqi TXV79FFtaprDAXfd1TlNratXXtECpiVLtOQE3ae3HQgJcMQhQoIcIYQQg+asxERMXb786YH5UVEA KN2+FF6YnMy+hQuZHRk5lF0Uolf/yM3l5vHjGddLcgBL+5TMYoeDra2t/V+wvFwLRjq8+SasXatN OVu2TCuqmZ0NS5cGn6eq8Pe/a/9dsiQolTUQmmHNbu+54Ogzz3Rmb3O54Pnn+++zEKOEBDlCCDEK Vb1QxdcZX/PtxG9pXN5Dytk+NH/TzNeZX7PSspKia4tQB7h+AWCb3Y67S3sfUOl2A/BgTg7G9i9r kXo9ETodiqIQI5nXxAhxaVERD5SXU+vx9Hi8rX20pNrj4de7d/d/wZ5GezrWrs2bpyUn2L0bHn5Y W8PTld+vpW2+++7Qa5x0Ekya1Ll95ZXByQ86dE9W0H1biFFMghwhhBhlHIUOCq8sxLXXRVtxG9vP 2Y7X1tfqgmA7L9qJq8yF3+mn8qlK6t6uG/C50T0ELKXt09XOS07mT9nZALT6fPyjuprri4vZaLMN +PpCHEwd4bl7AIH9DrudozdsYElhIS29pXYeN07LlNbhssu01MvdGY3w3/9qNWjaRz4DampC28fE aGttXnlFGxH6+997fv+//lVLFqDTaVPffve7fu9LiNFCHp8JIcQo4yx3Qpfp+b5WH54GD4aogf3K d1e7g7dr3D22+6ShgUq3m1Pj4xkbFgZodUWMioKny5fE3C5PmHe3tQVdY1l9PVaf5FoTh54Kt5sK t5uvWlqwer08PGECVxQWUuxwcGZiIg/k5KBTFLjvPq12jtsdPPrSndGo1cLpGvTr9XD55T23j42F iy7qu5MZGVqyAL+/cwRJiMOE/MQLIcQhzGf34Sxzovo6g4roedGYszurmkcfGY05vYcq570Ye9XY wGtjkpHEHyeGtPm/PXs4detWrigsZPb69exzOlFVlUsKCgIBjh6YFh7OnSUlrLRaeaW6Gm+3J+R1 fRU3FGIEGEgygu9sNq4sLOSTxkZ2O508vG8f/6iq6myQldV3gNOhPeV6wBVXwIkn7mePeyABjjgM yUiOEEL0QVVViq8tpuqFKsJSw5j6+lSi50UPd7cAsH5lZdsZ2/BavUTOjmTm5zMxxhoxRBuYvWY2 VS9UoQvTkXp1KopugJmggNxHcok9NhZ3lZuEMxIwjw8NkJ6sqAi8rna7eae+npPi4ninvj6w3wds dzjY7nDwSWOj1MYRh6SHcnI4Pi6O12pquGfv3h7bLIiO5rtu0y53dRu1HJAzz4S//U17bTT2Pooj hOiXhPZCCNGH2jdqqXy6EtWl4ixxsvOincPdpYBdN+7Ca9VGQlo3tFLxeGfgYUoxkXFrBuNvGo8+ Yv/TNCednUTyBckY441B+6tfqmbjMRuJaQwekfGrKuF9pIOWAEccqk6IiyPBaOS85GROiIkJOT4/ KornJk3i7MTOEU89cEZCwv6/2WOPwZNPakVGv/wS5s8/8I4LcZiTkRwhhOjDQNenDAe/M7guhr+t hzoZB6hoaRGVT1aiGBRyn8ol9cpUrCutFPy8AFT4bRPc8ScFa4QW7Ny2Zw+zIiO5LyuL35WUoKLV wGmW9TbiEBZrMLDCauWGXbvwqionxMSwcuZMYoxG7D4f4Xo9M9tToP8pO5uJ4eEUOxyclpDA0bGx getUuVzcWVpKs9fLtWlpHNvlWBC9Hq69dihuTYhRT4IcIYToQ9LZSey9dy+eei2l7Ngrx/ZzxtDJ vCOTnRftRPWqmFJNpC5JHZTrWldZqXyyEgDVq1L8i2KSz0+mdVNrIP3UjG1wxHcqK47Ttp2qyoPl 5XyYl8e1aWmoqkqj18sfy8pw+/14/H7e6jKVTYiRbIzRSIrJhFFRuK64OJDH44vmZjylpayYNSuk GKiiKFwxtuffD6ds2cIWux2ADxoa2DxnDhN7SvkshBg0EuQIIUQfzBlm8tfn0/CfBkypJpLOGjl1 JpIXJxN5RCTOEidRc6JCppYBqH4tKulrTY7X5kUfqQ8U6/S1Bo++qF4Vv9NPzDExKEYF1aNdMybW BHQZ2drhhDwCdW9iDAauGjsWBXiovDzkfRU6U/YKMZL8ODGRt+vqaOwhMcaq5mZerq7m570ENN3Z vN5AgAPg9PtZb7NJkCPEQSZrcoQQoh/mdDNp16YdlADHWeak6csmPNaeiw/2Jzw3nPiT4jHGG3Hs drDviX1Uv1JN7Zu1lP6xlJXhK1lpWcm+J/aFnOtt9rJh0Qa+iv6Kb7K+wb5D+yIWd0Ic0Qs6kyvE HBND40eNREyNIPPuTG3BAXDRY17S25cBja2EC3/toOY1raZHi8fDlLVrOWrjRo7cuJGiHhZhdw1w 0nqpMC/EUIvW6zktIaHHAKdDb8VCexJlMDC5S0BjUhRmtU9xE0IcPDKSI4QQw6T+g3q2L96O6lIx pZmYvXo25ozgTGbueje272xYsi2ETwrH7/FT+0Ytfqef5MXJGKK1X+NNnzex+aTNQfVxutp13S5a vm1hzKVjsGRbKLuvDNt3NuxbtMDGVeZi1w27mPnpTHRhOmaumEnjR43s/u1umlc207yymZp/1mDf aQ9kEUgs8fP8JdAcAzHNoPdD8S+Lcde4ufCYOgq7BDZb7fY+1+gkGQwYgDL3yFnzJA5P48PCSDIa yTab2dNeyDZcp8Ph1z5c8QYD5yRpDzz2OZ08VlGBAtw4blygXhSA0+djeVMTFp2Oj2fM4HclJTR7 vSxNS2NKRMSQ35cQhxsJcoQQYpiU3lWK6tLGM9wVbiqeqCDngZzA8bY9bWw4cgOeGg+KQWHyPydT 888aGj9qBKDi0QpmfzMbfYSeouuLeg1wOtS+Ukvtq7UYE414akOfRHubO59c6816jAlGnLudgX1N nzWFnKP3Q3yX3d4mL0W/2k3eT+CrpcFt+0pCsNnhkKlrYkTY7nBw7KZNvDhpEiuam3H4fNyVmcnG 1lY+bGjgyJgYssxmWr1ejt60idL2QOiN2lruy8piSkQEU8LDOW7TJr5tTyt9SUoK/5o6dThvS4jD jgQ5QggxTBRjt4XLpuDtymcq8dRowYjqVSm9q5S2ws7REfs2O81fNxN3fBzOXU4GxE+PAQ46GHfj uKBdxmRj8MIZHf0GUgB1yXDuO1CfBG+ep+3LLIGKNPD0MitNAhwxknhUlb9VVrLWZsOjqtR6POx1 Oilqa+Plmhrer6vjunHjAgEOQJnLxUUFBYFRnW+71M15uaaGv+TkkCLTMoUYMrImRwghhknOQzno Y7QFLuHTwkOCDJ0l+Fe0PlKPEhYcCLVuamXvg3tR3aFhQkReBLl/zyUiL3hqTPfgyjLRQv66fFIu TAnsU1UVv8tP+v+lo4vQYYg1MPbqgS20jmnR/vuLp+HNc+Gtc+CFy+GEz5FoRhwyOgIcgM+amoLW lX3c1MTZ27ZhUkITeqjAv+vqgvYZFAWLTr5yCTGUZCRHCCGGSeyiWBaWL8S510nz6mZqXq4h+fxk wtK0ef3jbhxHw38aaF3fiiHBQO4TubjKXRRdU4Tf6Sd8Sjh7bt6jXaxbqrIxl49h8nOTtfc5JpY9 v92Da6+LpHOSsO+wU/tqbaBt+ORwoo6ICmyrfpXt52yn/l0t5XPY+DAiZkRgTjdjTDLiqescCTLn mIOmtMWeGAufWQPbSe1Zo/93DCw/dVD+ZxPioPtBTAyrmpv7bONSVcaHhTHGZKLK5WJfl/VkKSYT P01K4uF9+zAqCk9NnEi0oe+vXJ83NfFpYyMzIiO5KCWlz7ZCiP5JkCOEEEPItslGye9KUL0qGbdn EHt0LKW/Lw0EFOUPlzNn4xxMySaMsUby1+bjqnRhTDSiN+thASSfm4zP4WNVxKrOC6sQNiEMnV5H 2rVpjLteGxUq+kURlU9XohgVYo+Lpf79esKnhRM5K5LWTa0Yk4xYV1hZFbuKqDlRWHIshE8JD/QH wFXuwlXuCqwF6soQF/xnpGVtS4/3XTk4JXyEGBJXpKZySkICN+/RHiLkR0ZybGwsj+zbFzRjM0Kv Z21+Pnafjx9t2cLK5maSjUaezM1lTnQ0d2dmYtTpCOtnFOfDhgbO2Lo18Jyi3Onk1oyMg3NzQhwm JMgRQogh4LF6KLikgIYPGwLrWlrWtJC/KT8ooHBXumn6oomU87UnuYpOwTzOjKPQQdVzVRhiDKTd kIY+XB+yRib5J8nk/DkH+047xTcU0/BxA85ibZRF9ag0faplCLB9Z2PcTeOY/Mpk1uWtC1zD+rkV 6+fW/ZrI7Cp1BW37W/zozDr8Tu2i5hwzrr0ufviFyvvnQE2C1s7kALeUCREj1OMVFayYNYtTExLY 1dZGpE5HXmQkv01P5/hNm9jpcGDW6bgtPZ3zt29nt9PJTxITeW/6dKINhkCh0Mh+Rm86vFdfHzST 89/19RLkCPE9SZAjhBD7wWf34ShyYM4w91h8szd7bt5Dw7KG4Gu1+nDtdWFIMOBt6MxsFjYuLKid q8LFhiM34G3U2pQ/XE7KhSnoLDr89s4op+XbFgqXFFL7ei2+5t4zmQHYt9q1dTw9JRIYQHKBDuHT w2n+ssu0HoVAgKOL1BE+KRznbieJtfDKJQpvnKkS1QqnfQi33wPfLBz4ewkxVL5uaeGoDRtYnJzM /Xv3YvV6iTUY+DQvjw35+exwOEg1mbiysJAPG7URznU2GxlmMxcewFSzHHNw6vgJFsug3IcQhzMJ coQQYoCcZU42HrsRV5kLfYyevI/yiDkyBne9m5ZvWrBkWYiY1nP9i7aS0GKYxiQjkXmRTP/3dAqv KMRr9TLuV+OIXRQb1K55dXMgwAHwNnqpeKICJTx40XPz/5pp/l/f6wg6xP0wjojpEUQviKblm56n mPVHH6MPDnAgaF2Qv9UfNMXN4FC56LXO4/fdpiUleOM8aEw8oC4IcdCsb21lfWtrYNvq9fLbPXuI MxjQKQp3ZmSwzW4POqf79kD9evx4SpxOPm1qYnpEBI9NmPC9+i6EkCBHCCEGbO8De3GVadOzfM0+ Sm4vYfILk9mwcAPuKjfoYPLzkxlz6ZiQc00pwalj9XF6ki9KxphgJPaYWOYXzwe0NS3VL1UTsygG S46F2rdrqX6xusf+qI4DS1Wmj9FT868azFlmpr03jY1HbsS5Z4ApqLvob7SoPwqw+G2Yuw4uf+F7 XUqIIfFVc3Mg49oqq5UfJSTwQrX2+VSAE+PiDui6Rp2OZyZNGqxuCiGQIEcIcRiq/mc1Nf+swZRq IueBHExJA6xd0S2mUP0qVc9WaQEOgB/K7isLCXLq/l0XlM0MwNfko+KRCtqK2sj7ME/r10vVFPy8 AFQtXXTW/Vnsum7XAd2jPlaP3+5H9YQGQr5mH/YtdnYs3oEp04S71N3DFTTRC6KJnB2Jq9xFw8cN 4O216QEbUwUGF/gMoOoH//pCDIZYvR5rl4K2NR4Pr1VXc0ZCAqkmE2clJnLCAQY5QojBJ0nbhRCH laYvmii4pICmT5uoeamGHRfsGPC5438zPrBeRh+lJ+uPWegiutWyCQ/9lm77zhayr0Pj8s7pXBVP VAQCKV+rj/KHygfct+58Vl+PAU53fQU4AKbxJsw5ZlKXpJJ9f/YB96cvPh18egp8cgos+RvM2HJQ 3kaIA6YHVsyaRUK3RAJO4D8NDVw/bhynJCQMS9+EED2TkRwhxGHFtj444OgrAOnOkmVh7o65OHY6 MGeZ8dR7qHuzDsWooHpUDPFaLZvuohdG93pNnbkzSOqejrl75rLutXCGQv1b9dS/pWV/MyQcnD8Z ke3LlUxeOO8t7d9r58PfrzkobydEj4yAp5djt6WnMysqis9nzeJ3e/YEkg2A9pGsdbuZGtHzejwh xPCQIEcIcViJOSomKPVyzNEx+3W+IcpA9DwtaNly0hZaN3UuTM59LFe7fjcJpycQNScK27puAZUB oo+KZs24Negj9aQuTaVpRVPIlDBLrgXLJAuNH4bWqRlKXTPAHWyL3wC9FzwmeGMx2Pbv/yYh9psH OCE2li+t1pAEg/+ur+fL5mayzGZemDyZi3bu5NMmLSV7XkQE86J7f5AhhBgeEuQIIQ4rMUfGMP29 6dT8q4awtDAy78w84Gs5S4MX67sqg0devC1etv90O01fNBE+NZyMO7S6FykXpuC1edl0zCas/7UG 2u++brc2L6YbfaReC5CGeBRnOOlULSkBQHKNlolNJliLg22vy0X5woXkffcdDd7OoH67wwHAquZm Gr1e/jNjBq/X1uLy+zkvOZlwvSwmE2KkkSBHCHFIcpY5Kf9rOYqiMO7X4zCPM/d/UrvEMxJJPOP7 5yxOPj+ZyqcrAdBF6NBF6th6xlaMSUay7sui4tEKmj7TnvY6tjmo9dZiybagM+nwNHnwt/VQkKaH hGWtG1tDd45yHcmxq1Pg4V8jAY4YErkWC/+qqcGr9v5EYaPNhkmn45IxoVkUhRAjhwQ5QohDjtfm ZePRG3GVayMn9e/XM3fb3B4X/R9MuU/mEjUvCtc+F+GTw7UkBu1Bin27nYgZwXP02wraaCtoo/Gj RqKPkuktA7EnG5xSF1EMgSyzmfOSkrissLDPdsdLBjUhDgkS5AghDjmOHY5AgAPgLHHSVtxG5MzI Ie2HolMY+/OxAGy/YHvQKIztOxvpt6RrNW56GJ1pWd2CYlZQXephNQ1tf2XvAXObBDri4FKAJq+X /7avs+mgA64aO5ZjY2P5qLGRLLOZ29LTh6WPQoj9I0GOEOKQY840o4vQ4bdr07300XrCxocN2vVb t7bi2OkgekE05vT+p8HVv19P3et1wTt1UHRtUSDA0Ufp8dmCox3VqWq/hYduPf8hZ0wN/OW38OZi aIyHHdNA8YMq09fEIFIBq9fLW3XBn2MF+PX48eSGh3NBSsqw9E0IcWAkyBFCHHJMKSZmLJtBye9L UBSFrPuyMMYbB+XatW/WsuNCbdqZPlrPESuPCIwQeaweCi4rwLbORuyxsUx6dhJ6i566d+tCL+QD T01nQlqfzddzCmgJcPo1Y5v2z2WA2hRIrIevF8If7xzunonRxtNtLY4P2NDaSm54+PB0SAhxwCTI EUIckuKOjyPuq4HNjbeutLLz4p14Gjyk/TKNnD/n9Nq2/KHywOiLr8VH5d8ryX0sl6rnq6h8ppLW 9VoSgNpXawlLCyP6uGhq/lnTfyeGocbNaBPmhfEV2usTvgSjB+68G1RJbCUGyfyoKKxeL4VtWvGm MEVhVuTQToMVQgwOGfAXQox62xdvx7XXhd/up/wv5TR80hB03NPoYdevdvHdjO+wrQ2uZaOPd28i 4AAAIABJREFU0FPw8wKKri4KBDgdyh8qZ/tp2wkpqtHOkmshMj+SiNkRmFJNg3pPAo5eDY9dB1c9 hQSQok9K/00A2NjayqUpKRgU7YzpERFkmgeeuVEIMXLISI4QYlRTfSqeuuA65u5qd9D2llO3hAQ3 HSqeqcDf0ksU08vuDopRwVHg0NYODfRbltgv03eC2QX1/waPEb6bCzVjh7tXYqTpHgOfnZCAW1X5 sDG4wK5bVbm9tDTw0V7f2srL1dVclZra67UL7HZ+sn07u9raOCsxkVemTMGkk2fIQgw3+RQKIUY1 Ra8w5pLOehb6eD1Rc6IC2z67r9cAB+g9wOn1DTtfOnY4AskRZKTh4MkqgeufgF//Ff5+DaSVg9HV /3ni8PVuQwN7XS5OiInB0i0g6f6Jd/j7/h1wVVEROx0OPKrKW3V1PFlRMci9FUIcCAlyhBCjXtJ5 SZjStOlivkYf6/LWUf3PakCbjmaZMHj5iRWLDNkMNX2XADLaBkevAs/gJdsTo9RWu50vmptp8/vp uqwrTOn8DOeYzVyYnNzndWrc7j63hRDDQ4IcIcSoVr+snq0/2oq7ossXDxWKlxYHNvM+ySPhzASi F0aTem0qGXdnHHCwojpUlDAJdIbTvnEQ1whX/gOmbRnu3ohDwViTiUidjii9nocnTGBDfj7/mTGD 9XPmkGTqez3d1WM750dG6HRcKKmmhRgRZE2OEGJUq3iyosepYqqnc6clx8KM92YEHR972Vi2nbWN 1o2t3U/tV/jUcOwb7ft9nvj+/MBlL2pBTnwzPH/ZMHdIjBgK8Nvx43m5RsuGWNVlxKXS7Q5MU7uj pITyhQs5Iioq9CI9+E16OjMjIylua+PEuDgmSrppIUYECXKEEKOaIbbnX3Oxx8eG7Gv8tJHKv1Vi iDWQdU8WMUfFHFCQIwHO8NEBOSWd2zKmdvj5aWIiP46P5436ej7qklhABX6SlMSfcrQU8n8tL+ez piai9Hre6FIEtMHrpdbjIUM/8NzkP4yP54eDdgdCiMEgQY4QYlTL+XMOrZtbaStoC9pv/Z8V1aei 6LWvwfYddrb8aEugOGfLuhbyv8nHXeOm7q0ein2KQ8LxK+Czk4a7F2IovVNfT6XbzcbWVoyKEijw OSU8nBkREYF2N40fz03jx1PvdvOl1UqNpzML42179vDKlCkoioTJQhyqZE2OEGLUaNvThn27HVVV ce5z0rqtlbBxYczfOZ/JL08Oauu3+/G7tQkqfq+f8kfLAwEOgGObg+KlxeQ8nEPmHzOH8C7EYLrt fvjFkzChuP+2YvT4uqUFp9+PR1UJ1+m4PyuLVUccgaWH0ZlEk4llM4Knq75aW8vq5mYAXH4/95aV cU1hIV80NQHwP6uVpUVFPLB3L55+sq8JIYaHjOQIIUaF0ntKKf19KQARsyKwb7GDH2JPiCXv4zwS f5xI+ORwHAUOAMZePRa9RY/f42fLyVuwrrCGXLP6xWqqX6xGH6Un6cIkrJ9Z8dR6QtqJkUsBFr8N Z70Pf74F1s4DSxvU9Z0wS4wiDr+fR/ftY350NMfHxQUdq3O7MSoK7h4CFW/7CNDlBQW8WlsLwHNV VTw9cSK/KC4OHN9ut/PilCkH+S6EEPtLghwhxCHPY/VQekdpYNu+qXNNjPULK3X/riPl/BRmfzOb mldrcJY4iT81nrJ7y2j6vKnHAKcrn81H3asyZe1QZvLA7+/RXn9+HNxz57B2Rwyxao+HM7duZdPc uWRbtJTxS4uKeLKyEgUwd6uVc0ZCAsfEauv2/ts+egPgA16vrQ0EOAAfdysoKoQYGWS6mhDi0KfS d7HN9oe03hYvZX8oo/yBcjafsJmS20v6DXDE6JO/HqZvhj/fDMYumcWzd0NC/fD1SxxcNr+fnG+/ 5Zxt21httfJkZSWg/epo6zaS8+bUqeja1+NM77KOB2BOt6xrUySbmhAjkozkCCEOecY4Ixl3ZFD2 hzIAwqeH49juABViFsWQ+JNEAGpfq8VdLYX6DnexNrjrD5DQCH+7Fr6dD+P2wbErwauHFcfBAzdL QdFD0RSLBZeqEqXXo1cUNrSGZkd8p76ead0Cl67Sw8Iwd1m78+qUKSwtLqbc5eKC5GRuGj+eOKOR 12trSQ8L428TJx6UexFCfD8S5AghRoWsu7NIuSgFn8NHZF4kzlInFY9XUPtOLRsWbGDSs5N6TSct Dj8J7TOMJuzW/nUw+OCHn0PRRHh78fD0TRy4nW2dWRQnh4ezYfZs3q+v5569e/F1aZdhNnN8bCwr rNpI7oLoaOo9HuINBv4+aVLQNceGhfHO9OlB+25JT+eW9PSDdh9CiO9P/uILIUaN8Imd00Zc+1zs e2QfAO5yN9vO3MaC0gU0ftxI/Xv1GBIMGJOMIamlhQA4/zVY9mNwmYe7J6I3eRERbLFr6+8UIM5g oNHbmSKxwOGg0efjruxsFJ2Ou0pLAZgREcG5SUlcnJLCCqsVi07H0bGhdbOEEIc2CXKEEKOSs9QZ tO2udIMfpr87HZ/Dh86iY+sZWyXIET1KsMLj18Ft90K9ZGIbcX6fkcFD5eWBbZXQ5AEAMe3Tzu7M zOS0+HjqPR6Ojo0lon3/SfHxQ9JfIcTQk8QDQohRKfaEWAwJnc9xEs5MQBem/crTh+tRFIWo/Kje TheHKT/QFK29zt0Fb50Hz10+rF067BnQRmpMisIJMTGUzp/PH7KyGGMyBbXrKWBJMBoDr+dER3NK QkIgwBFCjG4ykiOEGBVavmuh7J4yFL1C5t2ZRM6IZPY3s6l9tRZDvIHUq1Oxb7dTtKQIT4OHtF+m kfH7DCoer8Db5O33+uLwoAPiWoL3ZZdAeCs4IoelS4c1HfD7zEwuSE4mt0sWs5K2NlJNJipcLnxA vMHA+pYWwhUFR3t652i9nsQuQY4Q4vAiQY4Q4pDnrnOz+Yeb8TVrS4ubVzcz6YVJ2NbaiDoiisQz texqW8/YirNEm8ZWvLSYiLwIlDBl2PotDh1HrYZPTx7uXhx+/MCdpaXcW1bGBIuF+dHRPDphAmdu 28ZWe2c9rFqPh1qPB4PS+Xlu8fm4u7SUBydMGIaeCyGGmwQ5QohDgs/ho+mzJgwxBmKPDV4k3FbU FghwADy1Hradvi1QOyf9tnRiT4gNWaez96G9KDoJckT/ljwD1WNh6wy0uVNi0FkUhSyzmR1toevk 3KrKDoeDHQ4HOmB7lwCnq65FOgE29ZBCWghxeJA1OUKIEc9n97Fx0Ua2nbmNTcdtovjG4qDj4ZPD g9bfAEHFQffet5ctJ25BFx78K6/x/UYtIYEQ/YhvgsduAL2v/7biwLSpKslhYcyPiiJKr8fUS7sd Dgc/iIvr8Vj3LzW9tRNCjH4S5AghRrzGTxpp3dj5RLbi0Qp8js5vm8YEI7NWzCLulL6/0Pjtfvmt J76XlOrh7sHo9qXVym/Gj6fl6KM5v5f1NCfFxfHOtGnclp7OnKjg5CFZZjP/mDiRi1NSeGzCBG6V WjZCHLbkz70QYsTTRwZnQ1LCFBRj8JwhnVlH1OwBZEvzD2bPxOHmNw+B2aG9TiuHY1cMb39Go44p Z1N6yIJ2R0YGd2ZmEmUwcG92NndnZgbW4eiBh3NyuDI1lZenTOG6ceNQFJlbKMThStbkCCFGvLiT 4hhzxRiqn6tGMSlMfm4yOqMOVVXxNnppWdvCtrO3obpUbb1E+1S1uJPjaN3aiqfSM6z9F6PHEZvg jfOhIQHSKsDkgadq4M3zh7tno8OCqCjOStQShRxtMDDBbGaXU1tLd2R0NHdkZgYFLtcWFQWCIh/g 6rYmRwhx+BrUIGft2rXccMMN5ObmoqoqkyZN4vbbbx/MtxBCHIYURWHys5PJeTAHXZgOvUWPu9bN 5pM2Y99sR2fWaQEOgApRc6JIXZIKemha3jS8nRejTrRN+9fhiufhrPfgjrth16Th69ehSkfnAGuk wYCxvainWVFYN2cO/6qpwaQo/CwlBX23kZlaj6fP7b78t7GRF6urGWMycWdmJjEGee4rxGgy6J/o efPm8eijjw72ZYUQAmNs5xz9snvKsG/WMiz5ncFz0KLmRDHm52NYGbGy5wt1/VYF2jwXWVAuDpDJ A2Nr4G9L4fLnYd/44e7RyDPGaOSurCxu2b2bZl/nhy0zLIxSlyuw/VlTE9vtdvIitaJEMQYD16al 9Xrda1JTeWTfPgBSjEbOTEgYUH/W22yctnVrYBRom93Of2fO3O/7EkKMXIO+JkeVoWIhxBDwtgQX 8NSZtV9n4dPCybgjA9Wnojp7/n0UNTeK3KdziTk6RgIcMWiMXnh6CVz7JORtGpr3VBjejNaJBsOA v0hck5rKpWPGBO3rGuCAdi8dIyp+VeW3u3czZe1azty6lVp3aCbEv06YwLvTpvH0xImsnzOHcWbz gPqyprk5KN30/6zWAd6FEOJQMehBzu7du7n22mu56KKLWLNmzWBfXgghAEhbmhZISKAYFaa8MYUj a49k7ta5hI0NQ2fUEb0wOvik9m+Dtm9tNHzQQPZfsiXAEYMqwgHnvg0P3Aw/XH7w308lKFv6oOge NCX0MY3LB2yeM4dHJ0xgeV4ei9vX03RnaU8i8KfsbH6RmsqU8PCQNgZF4a8TJqAHCux23vV4eKC8 nAKHgw8aGri6sLDHa2dZLCQYDPsV7B0RGRnUPj9qAElLhBCHlEGdrpaRkcHSpUs59dRTKS8v55JL LuHTTz/FIPNchRD7ydvqpXVDK2HjwrBkW0KOR8+JZu62udjW2QifFk7E5IiQNlPfnMqGeRtwV7lR wpTOdTtA40eNxJ8UjxKhoNplBFoMLpNXKyD66cnD3ZNQZkXBp6r0tnql+6ehwevtsR2A0+9nemQk 09unl8UaDLxZXx/SzuX3U+xwkBsezt8mTuSjhgZO27o1qM3e+fN5va6O9G++QQXGdVt/U9hDkdB/ VldzWUEBfiDeYGDN7NlM6iGA6m5RbCyvTJnC81VVpJhMPJiT0+85QohDi6IexPll5557Lo888ghp vcynXb9+/cF6ayHEIczf5MdxuQO1XAU9mO82Yzyl55oZHdQ2FYygGIK/GKl2Ff8eP6pJpe1nbYP/ 2FuI3kTA5Y9BSfZwdyTYbJ2ODf7ByaV+sdHIDWYz67xe7nI6aVJVXH20z9Tp+LPZTJpOx5UOBwXt /TjdYOBWs5ljWluDlst1SZYYeK+uzrfb2dXlXnpqI4QYPfLz8wfcdlCHWJYtW0ZdXR2XX345dXV1 NDQ0kJKS0uc5+9NZMXqtX79efhZE4Oeg7P4ySspLtJ0+8D/lJ+fYHKIXRKMzBM+yVVWVwisKqX6h GnRgiDWQdG4SuU/kdrY9RvtPSWEJZX8oG8I7Eoc1O1z2Itx5FyOqKl2D0UiCz9frCM1Ui4Ud3UZN jIpChE6HtUvSgJvS0ni4PZvqyatX0zCAZ6alfj8P6/V8k5/Pep+PjxoaiNTrOTk+Hoffj7pqVVD7 P2Rm0uj1MtFi4erUVHTdRndSNmxgV0tLYHtCWhr5mZn99kMcOuT7geiwv4Mjg/pr94QTTmDt2rVc dNFFLF26lLvvvlumqgkhBqRtTxver7y4a9whhT7dFW42Hb2JLSdtwe/x43f7ce5z4vf6afigQQtw APzgbfRS9UwVBZcVUPfvOnxtnV/Kxt8yHsUkxQHF0DlmFTxzjVY4NDAk0fvsr16lGI3cOG7cgNv3 9ZfXrNPR1McUtN+kp/OzlBTyIiLIDAvjiMhIHpkwAWe30Z9/t09Lc/n9fU5p666mPc1zuF7POcnJ nJKQgKIoROj13NUlQJmn13NLejoPT5jAkrS0kAAH4LHcXMaYTIBWR2d//jcSQoxugxqBRERE8PTT Tw/mJYUQh4GGjxrY9hOtmOfaP6wl76M8ouZEYVtnC2pnXWGl6tkq9t6/F1e5C8tEC0mLk3q8Zu2/ aqn9Vy1Rc6IY96tx1PyzBkehA9Ut89XE0Jq4C165BOzh4DJBuB1++TeYuhOMHvj0h9Daz7r3U+Lj OTEujtdqagJBQl96Cjl0wKyICDba7b3O2kwzGjkzMZGfjx0btP8XhYU4u43UVLhcvFJdzR2lpUHT yjpkmc0sTkpip8PB8sbGQKHOK7tdu6s7MjM5NykJm88HRUWBmjm9mR0Vxb6FC2n2eok39j6ltdHj 4briYgocDs5ISODObkVFhRCjjwyzCCGG3d4/7Q0kBfA2eql6oYojvj4C+3Y762evD6ppU/NKDa5y bdZ/W1Ebe+/Z2+e1bets7Lxw50HruxADFeHQ/gHcezuMqdFe/+Q9uPEhaOgWrx8VFcVmh4M5UVFc kpLCyV3quhyI5ydO5Kbdu0OCkZPi4lCAI2NiuCY1NRAs7Glr48rCQsqcTup6CKy8wMUFBb2+3y9T U/l1ejoAxe2BTo7Fwqn91LKZEqElEVk/wCBEryh9BjgA1xQV8XZdHQAbWlsZbzZzRR/BlhDi0CdB jhBi2OkswU9r9RY9OoOOqJlRTHhkArtu3AV+SFqchLf5AOb6CDHCdAQ4AOPK4e3F8Pp58MwSbZ8e eGv6dMaGhQHw2L593yvAMQJHx8bS5AvOmT7ZYuGDGTMI62HE5MIdO/jWZgvZP1AdfQfIDQ8ndwBZ zw6WbXZ7n9tCiNFnBC2FFEIcrnL+koNpjDavPnxqOOm3pgeOjbtuHEdWHsn83fOZ9sY00m9JDwmK eiSPcMQh5vw34IJ/aa876soAlDmdfNBDWuau+hrHiNXrOScpCYtez1HRnbWjEg0GPps5s8cAB6C4 h5TNfQnX6YjV61GAn6WkcH5y8n6dfzCdHBcXtH1St20hxOgjXwOEEMMucmYkC0oXsP6z9eSfnB+S Qc2UYgq8jjs+jrk75uLY7qD+/Xqq/lHV4zUz78qk4T8N2L458CfRQgy1q5+FmjHwxQ98fNPSwgcN DbxYXd3veX2t0rH6fLxWV8enTU3Ud0kQcEdmJml9pFs+OzGR59rfu2PNjQ64IyODTxob+abLKI8O +PqII5gRGYlbVXsNnIbLQxMmkGE2U+BwcHpCQr9T5oQQhz4JcoQQI4IuTIdujC4kwOnOVeWi+Npi 7Dvt+Jp9vbYr/X0pGXdmSJAjDjlz1sGXx0Hph7W8mFk3aNet75YB7bOmJq7rIxvZ0xMnMisyknKX i7MTEzEoCglGI1kWC3dmZfHzggLeqK0lTFF4dtIk8qK07AlhI3BBv15RuGn8+OHuhhBiCEmQI4QY Udz1bnRhOgxRPf96KrisgKb/NvV/IRWM8X0vRhZiJGqJgv+7H/xNdfBQ8LEfxsZi0es5Mjqar5qb +U9j44Cv2z0DWprJxNbWVjLNZqJ6KPdg0OlY2kcQ9MLkybwwefKA318IIYaSBDlCiBHDeb+TNe+s QTEo5D6ZS+rVqUHHi28s7j3A0RGUhS1yViS2tTKKI0a++FPjMY010bymmbaCNs57S9vv08GJYTF8 5moG4MZx4/jrhAmB824BriwoCEwp66BHW9PT2p5kwKgopIWFcev48SxvauLrlhbyIiJ4t76ep6qq SDYa+XTmTPIiI/H6/RhG2FSz72s03pMQon8S5AghRgTrSiued7SVBapXpfiXxSRfkBwY0bH+z0rF oxU9nquYFMLGh+Hc7ezcF67Q/HXzwe+4EN+XASY/Nxm/18/WU7fS9JkWyI/5aRIv7o7nvcdtGO1+ TrnUBDcHn/rs5Mncm52NAlyycyfLm5rwARMtFiaHh2PR6bg9I4NMiwWAa9LSoL1tdXta6FqPh7tK S8k0m3ls3z6iDAb+OXkypycmDtX/AgdFtcvF6Vu3sr61lTlRUfxnxgxSTKb+TxRCjAoS5AghvrdS aykvb36ZmLAYrplzDWZD74uZe+OzB6+vUb1qUOFOrzU0dfSYq8ZQ81INqlvF0xi89Nq2RkZxxKHB sd1B0xdNGJONZN2fhaqoeJu8OCucFF9SyLT2j8Ge3+4h4UcJREyLYIfdzuMVFYTrdPw2PZ3/Wa0s b+oc5dzQ2sqfs7M5MT6+x/f0dUtHXe1y8W57Bjer18uFO3diXbQI3QhcXzNQ/1dSwvrWVgDW2Wzc XlLCPyZNGuZeCSGGigQ5QgyDipYKylvKmZ48nUhT5HB353upaa1hwbMLqLFrhT8+2vURy3+2PHDc 5rJxxQdX8PW+r1k4biHP/fg5osJCy7vHnRCHLk+Hf4s25yx1SSrGhM41NXEnxhGRF4F9i1bfYszl Y3BsdwQCIV9T70kIhBjJvFYvm3+wWVs0YwJcvbf11Huocbs5ZuNGGtoTCbxXX0+Z0xnSNkKvZ5XV ygcNDWSbzVyTmhoIWm5NT+e/TU3UezzEGgycnpDA112ypdl8Plx+f1Aq6+5q3G7uKi2l2evl2tRU FsXGHtD9HywN3QqYdt8WQoxuEuQIMcSWFS7j3LfOxeVzkROXw1eXf8WYyDHD3a0D9r+y/wUCHID/ 7v4vzc5mYswxANz+xe28tUNbZPDWjrdIjUrlkVMeCbmOLkxH+NPhZDVnoY/QE3t08BcmfYSe8b8Z T8VjFRjHGsl5MIetZ2w9iHcmxMETNj6MhNMS8NR7qHu7PYOaSp8BTuTsSKLmR7HGZg0EOAB7eghw rktLww8cv2kTHeF/ocPBI7m5AMyIjKRw3jwKHA4mWiwYFIUXa2oCtXEuHzOmzwAH4JQtW9jUPlLy Xn09m+fMGdaCn90tSU3l48ZGvKqKUVG4euzY4e6SEGIIyUo8IYbY7774HS6f9k1md9Nunlz75DD3 6PvJjM0M2k4MTwwaqSmxlgQd39O0p9drKSaFhFMSQgIcgKYvmyi4tADbOhuNyxrZefFOsu/LRjEN YDqNJFkTI40RMv+YSfxpPU8n6y7pgiQybsug/t16cvwmTF2mkcV2y4y2MDqax3Jz+aihga7jm+83 NAS1izcaOTImhkSTiVijkW9nz+bFyZN5b/p0nu1nWpfN6w0EOABtfj/f2UKniLr9fv5YWsrFO3fy Zm3tgO51sPwoIYF1+fk8O2kS6/LzOUVq4whxWJGRHCGGmE4Jfrag1/X9tHSkm5c2j8dPfZwH1zxI dFg0z5z+TNA9njP1HJYVLQvaPhAt37QE5b9tWd1C7DGxxBwTg/Uza98nyywVMcJ4G7ysSVqDzqLD NNaEu8qNEqaQcmEK1f+shi5L0CJmRaAYFbafsx2A8KnhvLV8Cn+p3YdFr+eB7GxWNTfzSk0N48LC eLx9tCa3PdlAh+7b3cUZjVw6ZmCjylEGA5MsFgrbR36MisLMyNCptzfs2sXTlZUAvFJTg0Wn44wh TGgwMzKyx34JIUY/CXKEGGIP/PABzn7jbOweO1OTprJ03tLh7tL3tnTe0qD7eHHTizz09UPEhMXw 5I+e5D8X/Idv9n3DwvEL+VHujw7oPaLnRwcV+ohaoI0WxRw5gCBHiBGmo5Ctv82Pu81NyqUpROVH 4drnYtob09BH6jGlmtCF6TAmGVkdtzpwrmOHg4VrFb76yezAvllRUSGFPS8dM4aitjbeqasjx2IZ 9EX3n+TlceuePTT7fCxNS2NaRERImxVNwSnfV1itQxrkCCEOXxLkCDHEfpjzQ8puLKPSVsnEhImE GcKGu0uDakPVBi5//3LU9mjkR6/+iH037eO0iad9r+vGHR/HlFenUP1cNbZNNpo+aWL9gvVMfGYi tnU27NvsmMaYpDaOGDH0KXp89T4YQE4M6xdWal5qX9umh5mfziRyujYC4ff40Vl0+Ns6C0EZ4vr/ 860oCvdlZ3NfdjYOn4+/7N1LldvNz1JSOHoQkgRkWiy8Pm1an22OiIoKjPYAHCGjKkKIISJBjhDD ICE8gYTw0Tk/vKihKBDgAFTaKrG5bUSHRfd7rsfvYUXJCqLDoslPzQ85HjE1gtYtrXjrtbk8tm9t bJi3AdWtYog3MPGZiXhqPey5fQ+t37WGnC/EUPLVDDzjn9fWZX6aD3ZcsAPVrZJ4ViIT/z6RyS9P puCyAvwOP2nXpxF3fFyf11P9Kj6HD0Ok9mf+op07ea89RfSL1dV8O3s2s6JCsxwOtqcnTiRCp6Oo rY0zEhK4eIDT4YQQ4vuSIEcIMagWpS8izhxHk1ObpnJMxjEDCnBcXhdLvl7C5qbNANx61K3cf+L9 geOqqrL1tK14aoMX2HSkkPY2etl7/14m/X0Szj2h2aaEGGn0sXriTozDEGug+tnqoGOeGu3nvPqF aqLyo0j7ZRpJP0lC9ajowvrOGdT0ZRPbf7odb6OXxLMTmfrGVJY3NgaOu1WVL63WIQlyYgwGnp08 +aC/jxBCdCfZ1YQQg2pc9DhWX76a3yz8DX847g98eOGHAzpv+e7lgQAH4E+r/4TdbQ9sV79UjWtf t/y63RKrNa9sxrrKirchtHCoECPN9H9PZ/pb0/HUBQfuiiH4B7vj517RKf0GOACFVxTibdQ+A/Xv 1lPzzxpmdFsvM72H9TNCCDGayEiOEGLQTUmawgMnPbBf54Tpg9cmGXQGDDrtV1RbaRtFVxcFn2CG iY9PZPevduOzadOC3NVutv90+4F3XIghohgVvM1aIBI2NvhnP2JmBK3rtemWSphC/OkDSzPdoeO6 XbffnjaN64qLqXS7uXzMGE6M379rCiHEoUZGcoQQw2Jl2UruWHEHj699nOrWak7KOYmTU08GQK/o eeLUJ3B6nTy45kH+9NWfsBqDM6hNf2M6qVemknRBUtD+julrAIp5ADV0hBgGqkel5HathlTWvVnE /iAWnUVH7PGxzFw+kwmPT0AfrUd1qexYvIPWna00fNRAzWs1eFv6Hqkc/+vxgdemNBPJ5yUz3mzm vRkzWJufz5K0tIN6b0IIMRLISI4QIsjKspVsqdnCMRnHkJeSd1De48VNL/Lz938e2L7989tZfcVq 7p19L/9Y/A/CjeFEh0Wz4LkFbKjaAEDGNRk89cRTWDwWIo+IJP7UeLwtXi2o6ZJauisOuj8GAAAg AElEQVTV2cNOIUaIjmlpxngjsz6bFXSs5esWfC3tI5SVbradvi2w1ix8Sjizv5mNIbrnP+EZ/5dB zNExuCvcxJ4QiynJdBDvQgghRiYJcoQQAc9vfJ4rPrgCAJPexGcXf8bRGUeHtLO5bLy0+SVUVeXS WZcOKLFAV89tfC5ou8XdwuPfPs7VqVczPkZ7Cr2jbkcgwAEoiymj7Y42phmnkbokFZ1Rx6bjN9Gy uiXQpnuaXSFGLB3kPJjT62HVExygd02m4djpoPG/jSSfk9zr+bGLvn+KaCGEOJTJdDUhDhNNbU3U tNb02ebZDc8GXrt9bl7a/FJIG7fPzXEvHcd1H1/H9Z9cz3EvHofb5w5qs6psFYvfWsyVH1xJRUtF YH9hfSEnvHQCW2q2hFzXYgyuxu70hGZIizg/gvRb0jHEGPA0eoICHNAKK+qj9X3eoxAjgc6sCxQE 7Un6LekYYrXnkLpoHTpz8J9rY5zxoPZPCCEOdTKSI8Rh4PFvH+fG5TfiV/1ck38NT5/+dOBYRUsF 7+x8hwRLAskRwU+Gu2+vr1zPi5teDBph2Vi9kWVFyzhj4hmY9CZ2N+7m5FdOps2rFQD8et/XbL9W SwZw5utnUthQGNK/yYmTuW7edbyz+h0+bfuUUyacQmRYaNHABEsCn+z6BLfPzUmZJ2EaY6Ktpg29 2hnYdEzxEWIk8zv87Lx4Jwk/TkBnDH3eGJUfxbzCedh32ImYEkHz6mZ2XrJTq5OzNI24H/RdJ0cI IQ53iqqqwzZpff369eTnhxb8E4cf+Vk4eKxOKwl/ScCvdk7jWvXzVSxKX0SVrYrZf59NdatWo+Oc KedQYi1hS80WLEYLLa4Wjk4/mvfOf4+ihiKOeeEYPH5Pj++Tl5LHiktX8PzG57n505uDjn135Xf8 8qNfsrZybdD+tKg0vH4vJp2Jclt5YL9JZ2LV5at4et3TvLDpBQDOnXouekXP69tfB2DO2DncqruV hKsGVlRVMSlE5EXgrnLjrnD3f4IQQ2BhzULCksP6b4hW4HMgdXJGC/m7IEB+DkSn/f1ZkJEcIUax rTVbOf+d84MCHIA2jzbK8vGujwMBDsC/C/6N+3Y3F797Ma9tew2AVXtXcdeXd+FwO3oNcAC21Gzh 18t/zctbXg7ar6Bw0isnBYqDdlVhqwjZB+D2uznr9bPY8ostXJN/DW9uf5OixiL+U/SfQJt1Veu4 puUa3uRNdAOYeau6VVrXtfbbToih5NjhQFEUCq8oxLHTQfxp8Ux4aAKKPjQzoKJTUMIkY6AQQgyE BDlCjGI/ffOnFDcWB+07LvM4os3RvLDxBQrrg6eOxVviWfDcgpA1M3WOupC2Pfmm4puQgEpF7THA 6U9VaxW3fnYrW2q28F3ldz22aYhu4OmTnuaaT69Br+pZl72OOWVzQGasiUOEKdlE0ZIiGpY1AFDx aAXmdDPjfzW+nzOFEEL0RYIcIUaZnXU72dW4i/nj5rO7aXfQsQunX8gZk87gqOeOwqcGRwJh+jCi TFGsq1wXtN+oM3LFEVfw4JoH+3zfBEsCs1JmUVBfEHLMYrAE1ujsj9e2vYbD4+izzVtHvsWy/GXo VT1hsWG8XvQ6xudlUbYYgQyQ8+ccyu4pw+/2k3VPFhFTI2grDv5s7P71bmwbbEx5eQqKTkZuhBDi QBweE3uFOEy8se0NZjw1gx+//mOmPTktZFRl9tjZ3L/q/pAAB8Dlc1FiLQnad/bks1l39TpOzD6R G+ffiELvX7ianc0snraYnLjgtLgzkmew4tIVpEam7vf99BTgLExbGLLPGebEbrbT6GzklHGn0BDZ sN/vJcTBFjEjgvG/Gs/C8oXkr80n9SrtM5F4ZmJI29p/1VL7eu1Qd1EIIUYNCXKEGEX+tPpPgQCm vq2emLCYwDEdOn6Q/YOQ6Wu90Sk6LAYLhfWFqKrK3LS5qD1V3GznVb1c8M4FIaNHW2u3cteXd1Fy Ywl7rt/D3NS5RJmiDuDuNHkpeX2uwfHr/Ly94O3Adl99FmIoOUucNK9p5tuJ3/LdtO/4Nvdb7Dvt ZP4hk0nPTUIxBj9E8DQGr4Hz2X0U/bKIjcdupOy+MoYxb5AQQox4Ml1NiBGu0lbJDZ/cQKWtkktn XsrV+Vf32jbcGB60fWzGsaBoNXKun389s8bMIsIYMaCpY37Vz6vbXuXVba8SExbD9fOvJ8oYhc1j 6/Ucl8/V4/5Pdn9C6kOpfHHpF3x04UeMeWhMv+8PoFf0IaNOz2x4pt/zXl/0OuUJ5UyqnMTFqy4e 0HsJcbD5rD723LYHd6WW3c9d5ab0rlKmvTGNsZePpW1PG3vv3QuAKc1E0k+Tgs7fdeMuqp6tAqB5 ZTPGBCOp1+z/CKkQQhwOJMgRYoRb/NZiVpevBmBN+Rqy47I5MfvEHts+cvIjHP/S8dg9dgCWFS3j ncXvcPaUs/Grfl7a9BKL0hfxQdEH+FU/8eZ4Gp2N/fah2dXMH1f+8XuNwDS0NXDT8ptIj0nvcbpc d0eNO4pKWyUlzSX9tu3J6imrWT15NTPLZpK3N++AriHEYOs+WuNv65xSmn1PNnHHx+GqdBF/cjym ZFNQW9v64AcMVc9X4a5xM/bqsYSNGVgaaiGEOFzIdDUhRhCfP/TL/+aazUHbL29+OaRNh7lpczli zBGBbRWVdwvepc3TxlUfXMVl71/Ge4XvBdbqxFn2r6Cgzd37KM5AVNmqaHX2n8ZZj54d9TsOOMAJ UOCWn93CMyc+w5vz38StD66PI1PZxFBLuTAFXUTnn96GZQ1sPHYjriptFDTuB3GMuXhMSIADEHtc bNC2ba2N0jtL2XjkRrw278HtuBBCHGIkyBFiBFi+azmJf0nEfK+ZGz6+IejYgrQFQduvbHmFDVUb Attev5dmZ3Nge1z0uKD2dfY64v4cx/Obng953+7rZw62nfU7QwqC9sSHb7/TTmfHZpM/NrRImNPk 5PVFr/PUqU9x97l3Bx3rK5GCEAfD3vv3hsyhaF7ZTOEV/adoz/5LNln3ZhF/enzQfmeJk9YNUgNK CCG6kiBHiGGmqioXvHMBDW0NeP1eHlv7GB8VfxQ4PjdtbnB7VLbWbAXgsz2fkfCXBGL/HMtP3vgJ Xr8Xrxr8RPeT3Z/0ulbmYOspiNjbsvegvNce6x7WV63vs82ayWvYm9D5/j5FCuqIodVW3Ia/1d/j /v7oDDoybstg6itT0UfqA/sVg0JYukxXE0KIriTIEWKYef1eml3NQfvqHfWB1+OjQ4sCvrzlZaY+ OZWzXj+LFlcL/D979x0eVZU+cPw7NZn0XkggCUlIIEAIRXpTQVRAXQSxogiuWEBdVH6oqIi66lpw QRQVsYLYpSpI7x3pEAghlZBG2iQzmZnfH7NMGGZCEkihvJ999nm4555z7rlKzLxzznkP8MuhX/jX H/9ixfEVDTtgrAkB3DXuNda7HJeDPXv/s6xot4JNsZuYdO8ktkU7P2hUiAbjJLYOuN0xjXR11N5q En5OwK2NG7oYHfFfx6OL0tXjAIUQ4soniQeEaGIalYaxHcfyyQ5r1rBIn0huib0Fi8XCx9s/ZmvG VjqEdGB39m40Sg3NPJuxMmWl074+3Ppho4zZZDHZkhtcaXJ8cnh92Ou2670t9nLn5jvxKvNi+Obh soRNNApthBa3WDcUKgWBwwIJHRNqu1d5ppKyw2XoonVo/J0fbOs3wI/r9l/XWMMVQogrjgQ5QlwG Zt06i1tibyFfn09uWS5JnyRRXlluN6OjQIHRbCT1TGq9PVeB4rKcbWlMFdoKvu3zLVggNjuWpBNJ NTcSojoKqM2PlMKswP9mf4ynjXh190KhsAbXZYfL2Nl9J5UFlSjdlXRY2QGv67wadsxCCHEVkuVq QlwGFAoFQ+OGkhSSxHPLnyO9KN0uwIGGWfp1rQc4dhTwzKhnKNZeWgY5cY2r7Y+UCo796xgn/32S XT12oT9m3ZNzeMxhKgus++rMpeZaJSQQQgjhSIIcIS4jCw8vrFXg0SGkA490fISRCSNr3bcsw6qZ zqDj8TGPczhUPliKhlVxoioZiKnYRMFf1myC5SfL7eoZTtmnPRdCCFE7EuQIcZnIKc3h3xv+XWO9 xKBEPrrlI34+9DPz989HgQKlkx9ljdJ+Lb/M2tRM76InLSiNZ0Y9w5u3v8ne8L1NPSRxldKG25+D Y8w3AuA70P7sKp/r7c/GEUIIUTsS5AhRSx9u+ZDB3w3m/1b8HxWV9Z+S+eSZkw6b+e9sfadDvfTi dKZvmW5bzmbBghnHlLRqpWy5u1hlrmX82eFPxo8ez8FmB5t6OOIq45bgRrtf2+HRycP2Wzjl/1JI mZJC7PRYAu8ORBumJWBYAHGfxTXtYIUQ4goln4KEqIXPd37OhGXWQzoXH11MmbGM6TdPr9dntA5o TZRPFCmFKQC4qFw4XnjcoV6ePo/v939fY3/6yprP3RA1UMKE0ROYM3MOGpMGnzIf1CY1Kouq5rbi 2qQCzDjdm+N9vTcBQwIIeTAEjY+GoOFBlOyoOsQz8+NMoqZGkfBdQqMNVwghrlYS5AhRC5vSN9ld b0zfeMH6/7fi/5i3bx4RPhHMvW0uUb5RTuuZLWb2ZO/BXetOmGcYt8XdxrLkZRzJP0KFqYKdWTur fYZkRmscRrWRJx9+kkK3Qtu37u/NfU+ysAkAVF4qTEXnHHxzgfNlW89pjWuEq+1aE2i/pPT8ayGE EBdPghwhaqF7eHc+3/W57bpHeI9q63639zvb3prUM6nc98t9bBi9AYC9p/aSVZJF9/DuuGncuG3+ bSw+uhiAWL9YjuYfrfWY3DRuV+xZNVeaQo/CqgsLnPQ/KUGOAMB3kC8BgwM4Mu4I5lLHZaNn6WJ0 oAKT3kTmx5mYik0E3x9M8P3BnPruFC7hLsR/Gd+IIxdCiKubBDlC1MLDHR+mzFjG/H3zOZp/lIVH FtI+uD0Pd3zYoe6x/GN218cLrEvOPtzyIU8tewoLFuL845jWf5otwAHqFOAAuKpdJchpCgr47MbP uG3HbbaiXI9cLEoLgUWBTTgw0RRKtpfQ9vu2FK4uJHtOtrXQyVk5+mQ9u3rswjXKlTNrzwDW5Wmd 93Qmfm48CqVkPxRCiPokiQeEqKVHOj3CgdwDnC47TUphCo8seoR9Ofsc6g1uNRgXlYvteljrYQC8 svoV2/Kyw3mHWZW66oLPC3ILwl/nX+39PH1etfckXXTDMivMdn9+ZfgrjHl0DJm+mU04KtEUjHnW rGitPm5F9H+iCXsiDL/Bfk7rVqRV2AIcAEOWgYMPHCRjRgYWkyw9FUKI+iQzOULUUkF5AYXlVcuW zBYzJwpP0DaorV29pNAk5t85n+mbpxPmFcZ7N72HxWLBbLFfytIhpANhnmFkFGc4fV5OWc5Fj1X2 6jSspOQkvu35Lfub7+ek/0kyAq3/DlcnrOae9fc08ehEYzKdMbHOZx2+N/rS+uvWqHQqjAVGDtx9 gKLNRZhKTVD5v8pKUHmqMJ2p2rhTsKyAgmUF6I/rif0gtmleQgghrkIS5AhRS8HuwfRq0Yv1J9cD 0MyzGd3DuzvUSzuTxpjfx9hmWgwmA+Fe4ZypqPoGt2tYVx5o/wBrT6zlm73fNM4LiHqzoe0GNrTd 4FDuVebVBKMRDc2rlxclO0swl5lRaBRYjPZfIpjOmMj9KZeTbU8S9UoUGl8NicsSAShYVUDyhGTM ejMRL0egi9JxZNwRylPL7RIW5C/Jhw8a9bWEEOKqJkGOELWkUChYdu8yZm2fxenS05woPMHwH4Zz V8Jd/LPzP231lh9fbreU7KeDP9HMs5ldXwNaDkCtVOOmcUOr0mIw2Z9qrlVqMZqNMiNzBQkoCuDm 3Tc39TBEAyhaX2T7s8VoQeWjwlTomEatIt3x/Czf/r50+buLXVmXv7uQ9XkWh8cctpW5tXGrxxEL IYSQIEeIOnDXujOxx0SGzBvCoiOLAFh1YhWhnqEMjRsKQIR3hF2bUI9QonyiSC9Kt5VF+0Xz/ub3 mb1zttPnGMwGp+Xi8uRa4conH3+Cyizn51wLnAU4CrWC4LuDa91HyOgQylPLyf0tF12sjlazWtXn EIUQ4ponQY4QNTCYDPxz0T9Zfmw57YPb8+XtX7Ijc4ddnR2ZO2xBzg0tb2Ba/2l8tP0j/Fz96Bre lROFJ2jp2xKDycCINiMYlTiKB397sAneRjSEcpdynn3gWQbuGUi5ppyQ/BBQQnJIMkknkuhxpPqU 4+IKo6Zqj83/NJ/cnMDbAvG6zrpc0WKyUHqwFLWPGtdwV8c+sM4MR02NImqq8zO0hBBCXBoJcoSo wdsb3mbu7rkAZBRnMGHZBPpG9mX+vvmANZNZn4g+dm1e6PMCL/R5gWf/fJb/bPqPrdzX1ZdY/1iW HF1ywcxp4spzPOQ4H4d8bL2wwNkEdz/2+JF/bP4HTy57ssnGJuqHJlSDa3NXircV26WIdm/rbgtw zAYze2/dS8GKAlBC7H9jCXsszK6f/BX5pL6aikKtoOVbLW1thRBC1B8JcoSoQUpBit318YLjzBs2 Dze19TDOuxLu4oaWN7A2dS2vrX0NtVLN69e/TsfQjmxM32jXtqC8gHGLxzXm8EVTOC+D929dfuOJ ZU9Iau8rmRKMWUaMWUaHW5Wnq6Z2cn/NtQY4AGZIfiaZZo82s52DU5FRwb6h+zDrrdkW/775b7qd 6IbaU34dCyFEfZJzcoSowZ1t7kSpqPpRqTRX0vLDlszZPYc/jv1Bp2adyCrO4tbvbmXF8RUsS17G wK8HUlxRTLewbk04cnG5UJqVGKn6cGxWmDFjvkAL0ZTcO7o7Flbzr0sTpCHgjoCqgvNzhVjsy/TJ eluAA1CZX4khU/bgCSFEfZMgR4ga3Bx7M890e8Z2vSOraj9OYXkh45eOJzk/mRJDia08T5/H2tS1 vH7D6406VnF5cq1wpUhXxMfXf8wDjz/A0OeHMvClgayLW9fUQxNOxEyPqV1FJSRtTMK1edW+G7WP /YyM7w2+KFRVM3ju7d3Rhmht17pYHa6RzvftCCGEuHgS5AhRCxvSHM9EOavUUEpCUAJB7kF25YPn DebNdW86HBYqrj3FHsWMeHYE3/f5nrTANEpdSzGpTOxvvr+phyacUOlqmSXPDEceOYIxv2qWLm9R nl2Vigz7tNIaXw0d1nWg2ePNCH8qnA6rO6B0kV/FQghR3+S/rELUwvnn3JylVqp57frX8NP5sebB NQxoOcDu/tS1U9mXs68xhigucxal45lHLXNaNsFIRE0yZmTUum7hykK2tt6KSW9NK+0aZT8rc/41 gFuMG61mtCLm/Rhcmrlc2mCFEEI4JUGOELUwfdB0uoV3Q6fWMaTVEL687UumXT+NY08eo1u4dd9N fEA8T3V7qolHKq4keyL2NPUQxHmCHwzGVOx4Ds6FGHOMHH/hOABh48MIHRuKNkyL7wBf2/k3hlwD +X/koz+ur/cxCyGEcCTpXISohTCvMDY9vMmuLF+fzz0/3cPWjK10COlAvH88ni6e3BxzM0uTlzbR SMWVZEmnJSgtSjqmdCTfLZ/Wma2Jy4qTQ0UbkXsHdyJejEDppiTj/QxOzT0FgNJdibm09skhMmdk Yi4x02pWKyJeiMCrmxeuLV1xCXWh7GgZu3rtwphjRKFVkPBjAgFDAmruVAghxEWTIEeIOvp85+ds Tt/MkfwjrE1dC8CqE6tYdWIVAO2D2zN90HSeX/485abyphyquAIs6ryIRZ0X2a5VJhWJKYm89ONL +JT7NOHIrg2lu0s5cOcBVN4qTGeqZnDMpWaipkWR8mLKBVpXsRgtZH2ahTZUS8Z/M6gssKaVbvlO SyrSKjDmWPftWAwWUl9LlSBHCCEamAQ5QtTB9M3TeeqPCy9J+/vU30xaMUkCHHFRTCoTO2N2srjT Yu7dcG9TD+eacW6Ac1bAsADy/8jnzLozAKh91YQ8HIIuWkd5ajmVZyo59dUpuxmfgr8KbAEOQObM TAJHBNr1q3SVleJCCNHQJMgRog7+OPZHjXVUChX6Sll3Ly5N0JmgmiuJeqVrrUN/SA8WiHgpArc4 NyKnRqI/rsczyRPPJE8ADo0+RPYX2dY2rXToj1h/3hUuCry6eVG0ocjWp9pfTfOJzclfkk/pvlI0 ARqi341u/JcTQohrjAQ5QtRBu6B2DvttOoR04FTJKbJKsgAwWeq2aVkIZ3xLfe2uLVhQoKimtlB5 qTAVXdrPnlKtpFdBLyxmC2ofNQdGHuD0gtMA+N/mT8wHMRRtKbIFOAD6I3oiX4tEoVSgi9OR/m66 bT+PSwsX4j6LQxuopdOuThgyDGiCNLVPUS2EEOKiyZy5EHUwtf9UWge0tivLKcmh1FDaRCMSVyOX ChcsWNgetR2wBjirElaR5p/WxCO7fJlKnAQ458WEah81XCC+KDtYhtpbjcZXQ9mhMluAA5D3Wx5b W23l4MiDDu38B/sTMTmClP9LoWhTkW35WvwX8Xh2sM7+KNVKXCNcJcARQohGIjM5QtSBi9qFH4b/ wGOLH+NA7gFyy3LJLMls6mGJq0yFSwUvjXyJCpcKQgpCMKgN5Hvm8+msT5t6aJcvJ4nQXCJdqEip OoyzsrASz86eFG8vdtqFJkCD/oQeXaQOs8GxQ4vR8ayjsCfD8OzgicVicUgPrU/W43u9r0MbIYQQ DU+CHCHqYPWJ1dz63a2UGctwUckhfqLhVLhYP5xn+1qXRvU+0JvoU9Fk+GbwTZ9vMClNjNwwUg4U vQCf/j7kZOZgqbAGJ7pWOkoPVT/rasg2sOfGPVx36DqnAc25mj/bnPCnwm2HeSoUCgKGBpD7Sy4A Kk8VvjdIgCOEEE1Fghwh6uD1da9TZiwDoMJU4XDfQ+tBiaGksYclrnJuejde+PEFDGoDzzz4DDne OQBsarWJb/77Dd5l3k08woahCdIQ92kcae+ncWb1mVq3U7orCb4vmNgZsQSPDCZ9ejpqLzUt32zJ 3tv2Urqn+kCn/Fg5hmwDumgdan81lXnWTGkqbxUWkwVziRn3tu60mNQCjZ/Grm2beW3I+CgD42kj QfcEoYvWXdyLCyGEuGQS5AhxnuySbL7c/SVuGjfGdByDTlP1QUWr0l6wrQQ4oiGU6cp4+463uWv9 XbYAB6BEV8Krw17lva/fa8LRNZxm45oRMDQA/TG90yBH20xL0L1BpL+TXlWogo4bO+LR3gMAvwF+ +A3ws91O+D6BQ6MPUX6inMqCSsx6+2VprpGuaIO1KDVKElckkjotFYDIlyJxiXCxBkAtdSi1jlta lS5Kmj/dvD5eXQghxCWSIEeIcxToC+j2WTdSz1g/2MzYNoNAt0DCvcKZPXg2b1z/Bjsyd3Cq9FQT j1Rca1a2W8nKNivBgt2G+t2RuylwL3DIxnY1OPnWSbx7ehNwewDHnjlmd6/5c82JfsuaijlzVibm kv8FKybIW5yHS5gLR8cfRX9MT8DQAILvD0YbqsUtzo2OGzoCYMg1UHawDGOBkezPs1G5qYiaFoVS Yw1gPDt40vbHtnbP1fjYz94IIYS4PEl2NSHOsTFtoy3AATiSd4QNaRv4fv/3BL4TyLLkZRyfcJw3 rn+jCUcprlkqHDKGWVQWxvxzDMnByVi48D6SmqgD1ZfVV1+Wcgt/3/Q3pQdLCRgWYCv37uVN1LQo 8pbmkfyvZLSB9jOsZ9ad4eBDB8n5LofiLcWkvJDC5hab2d5+OxVZVctMtQFafHr7EDg0kHa/taPN vDZ1WmJmMVkoPVhKRbbj0lUhhBBNS4IcIc7R3Lt5tWeRGMwGJv01iXl75zEgegBKhfz4iCZkAV25 9QN5vlc+X/T/4pLP0ak8XQmVta+v0CpwiXRxCLzqlQXyfs8jYUECbRe2JeGnBBJXJJK/JJ+9t+wl /b10ylPK7X6b5S/Np3iTYwa1soNlnHzjZL0My1xhZs/APWxrs43NzTeTNTerXvoVQghRP+RTmhDn aB/cnmGth6FSqFApnJ9nsTVjK52bdebbf3yLt8vVueFbXAEUYFKaaHOyDaNWjeKFn15osEdFvRXl tNy7jzeGTAPnTyAp3ZSgBoWufqKfskNlbGy2kdRXU3Fr44bSRUnuwlz7SudlfNYEOl9WZtLXz2G9 OQtyKFxZCICl0kLyk8n10q8QQoj6cRktTBCi6W1M28iPB3+0XWuVWgxmg12dXi16YTKb+GL3F5yp qH3GJyHqm0Fr4ECLA5zyOYVPmQ/uenf8SvxwNbqyvP1yIvIiuGPrHRf/AAV4XudJRWqF9Sux8wKJ wrWFYHBs5jvAl+KtxRiynNysy+NdFfj09qFgeQEAxlNGDt57kM47OmMqunCwUp5eXnXxv7GrfdWE Twi/pDGdZTHZR3YWswWLxYJC0ZDTWkIIIWpLghwhznGi8ITd9fkBTpx/HFPXTmXq2qkk58s3t+Ly kOeVx/RbpwPgUeFBiUtVlj8zZoZtHVan/tw7uKMJ0VC0pojiLcUUb3F+eCYW0ARrMJ4y2o/ntzyn 1RVaBRZD7fcNRUyKoGSvfcZC/XE9lcWV5P5qP5PjeZ0nxVut43RLcKNsf5ntnjZUS9zsODySPHAJ rZ/zrYJGBJE5K9P6TAW0fKulBDhCCHEZkeVq4opnsVjI1+djsVzapmuA/pH9CXQLtF0HuAXY3T+c d5jk/GQJcMRl69wAB2BP5J4691G6u5TCZYUO6ZXPF/Z4GEnrkwibEIY6oObvzBL/TMSru1eN9RQB Clq+05KIlyIo2W3/PrqWOsx6s8NhnSovFf5D/Gn7a1uaPdrM7p42SIv/Lf71FuAAqNxUJK1LImlT EtcduY7wJ+pnhkgIIUT9kCBHXNGO5R8j5r8x+L/tT/uP25NVfGmbf0M9Q9kyZgtT+03lPwP+Q1JI ku1edXt0hLictcpq5VBmxIhCU7dZB7WfGqWHErWvGu9+3sR/HU/s+7HoonVUFqG0mU8AACAASURB VFRSmWufsUDlY//z4tnFE5++PkS+GnnB5/gM8MFjmQdqTzXbk7ZjyLafTQ24IwBtkJbgB4JtZQq1 gsIVheQtzCP56WSCHwgm4PYAUIBLuAtxn8bV6V1rS6lV4t3NG7cYtwbpXwghxMWT5Wriijbpr0kc LzgOwL6cfUxdM5VZg2ddUp9RvlG81Pclxv4+luXHl9vKn7zuSebtmydn5IgrhtagpfOxzoB12drR 0KO4GlxpkdfCYSZEoVE4lKEAj04euDRzIea9GFt65bLDZST/K5ms2Vn4XO/Dqa/O+ZlQQutvW+N/ qz/5S/MpWF6AJlBD82eth2R69/LGo4OHwwwNgNJDiWdHT05vOs2RJ4843Pfu4034U9YZk/i58QSN DKJoaxGpr1SlfS9PKceYbaTtL20xG8xOD+0UQghx9ZMgR1zRiiqK7K8NRdXUrLud2Tvtrk+Xneb1 G17nuT+fI788HwWKSz6XRIiGZNAaGPfIODzLPDGqjJS7lPPFTPtU09pwLR4dPMhflO/QPuqNKCIm RdiVWSwW/h70N+UnrBv7z2w8L/mGGfwH+6P2UBM0IoigEUF2t1U6FR3WdSDnuxyO/NM+kDGXmEl7 Kw1VF8dZU9+bfElclmi7VigU+N/sj0eiB2nvpGEutS6t0wRpcAmzLkuTAEcIIa5d8htAXNGe7vY0 WpX1IEB3jTtPdHmizn1kFGWwOX0zuWX2G5n7RfSzu16wfwFjfh9Dfrn1w6AFC346v4sbuBCNqNit mHIXa1BS6lJqd2/fdfvI/TPXoU3k1EgiJkVQuL6Q7Z23s7XtVnIW5FBZWGkLcAAwgS626gDN8H+F o/a48Pdnag81oWNCcQl3vkfGkm9x+O2kDdY6revSzIX2S9rjO8AXv1v8SPwzEZW7LC0VQohrnczk iCvaoJhB/P3o3+zN2Uun0E5E+To/z6M69/98P9/s/QYArUrL7yN/Z2D0QMwWM28NeAt/N3/25exj Q9oGTp5xPEQw0C2QNgFtWJ+2vl7eR4hLVdMM4/RbpvPmd2/iX+LPnhZ7WGhZyIuGF+3quES4EPlS JKZSE/uG7KOy0Lrf5uC9B+lyoAseHT0o2WldbqbyUNFuYTvKT5aj9lLj1bXmxAIACqWCdkvbkfxU MvqjeipOVtjuqRJVxL8dz5FHjlCZV4lbWzdavtGy2r58+vjg86dPrZ4rhBDi2iBBjrjixQXEERdQ 943Ffx3/yxbgABhMBsYuHEu+Pp8KUwUv9n6Rl/u9DEDHTzo6DXIO5x0mtTCVFfev4Mavb7z4lxCi ntS0hPJos6OM/NdIXMpdKNWV0jy3OQaVAa2paqakIrWCLa22UJ5RjqWsqj9LpYXylHLa/9Gek2+c pLKokrBxYSi0CtReajw6eNRprB5tPeiwogMWi4XU11IpWF6Ae3t3iu4pIqhnEEH/CMJUbkLlKjMz Qggh6kaWq4lrVqmx1KEsrSiNUmMpleZKXlnzCjsydwDw1o1voVU6Xy5TbirnrQ1vSfY10ahGdxh9 0W0rFZWU6qx//9MC0nj5rpfJd7ffk6M/qrcLcMB63oxnZ0+0AVpi3osh/rN4incWsyVmCzu77WRn j51UlthnWTur9GApp38+bX9I5/8oFAoip0SStC6JVjNboXCt2jNUXYBjLDBy+NHD/H3r35yaJ8lA hBBC2JMgR1yzBkYPpENIB9u1syAlT2891DCjOMPhYNBzLT++nBCPkPofpBDV+Hbvt/XW1+ZWm/mq z1c11vPp74PSxf7XxvHnjsP/jtMp2VlCznc5Du1O/3Ka7e23s3/YfrYlbCPllRRO/3Ta4Wyr3IW5 ZMzMwJxhxlxp5sSrJ9h7217S3k9zqHvw3oNkfZJF/pJ8Dt57kIKVBXV8a+f0J/ScmHaC9BnpmCsu fE6QEEKIy1e9L1d788032bNnDwqFgsmTJ9OuXbv6foQQ9cJV7cqmhzex5OgSTpeeZmjcUJ5Y+gQ/ H/wZgDj/OL7a8xU/7P+BgvKaP0BlFGc09JCFsKkwVdhde2g9KDE4pmWujqvKlXJT1azK4k6L8ajw IKY8hpFxI8n+ItuhTc68HHK+y6HZ481oNeN/5++c/1WZk6/O0t5Jw1JpDVJMRSZSX7WmfA55KIT4 OfEApLyUQuq0/6WC9oSjdx8la7b13Ku83/NQapWEPR5m67No8zmZFC1QtKUI3+t9a/3+zlRkVbCz 606MOUYA8pfl035R+0vqUwghRNOo15mcbdu2kZqayvz585k2bRqvv/56fXYvRL1zVbsS4BbAxvSN /Gfjf5g9eDY/Dv+RmbfM5HTpab7d+y2f7fqMlSkr7dq1D2qPj4tsdBaXjxJDCa5q11rXv7vd3awa tYqv7/iahMAEKtWV/Nj/RxI/SyR+TjxhT4U5/ob432RK5sxM28xJzPQY28GiXj29CL43mPOpPJwv Ocuem22bLcmcnVl1oxjy/7RfPndmg32qaq8e5yQ4UIBX99olPLiQwlWFtgAHIH9xPqZS0yX3K4QQ ovHV60zOpk2buPFG6+br6OhoioqKKC0txd3dvT4fI0S92Z+zn4FfD7R9K74jawfTB03nyz1f2lJF AxSUF+Ch9aDUUIpSoeTvnL/RKDVNNWwhnCqvLK/V+U2eWk9e7fcqzb2tB3QObzOcQ7mHCPEIIdjD GqTEvh9Ly9dbkvlJJoVrCsn7Lc+uj8oi696bkPtC8L3Rl8r8SnStdCjVjt+dRb8Xzd+D/saQ4bjk c1ffXbT+pjXaYK1dgOEW70bFiarZqvODmDbftiHlpRQq0ioIuicI336XNosD4BppHyRqgjQo3WRV txBCXInqNcjJzc2lbdu2tmtfX19yc3MlyBGXrY1pG+2W/axNXUvvL3pTbCh2qHt2KZDJYv1m12g2 OtQR4nLg5+pnF6SfK8Q9hEc6PWILcABc1C4khiQ61FW5qWj+dHOaP92cw/88bFs+5t7eHb8BVWdE uYS44BLi/MwbsGZR657aHWOBkZP/Pkn6B+lgAixQvKWYQw8eIv6reA4MP0D5yXJUN6lou6AtqdNS KdlZgk9/H8KeCLPrU+2tJvbD2Lr8Y6mRdw9vot+LJv29dNQ+alp92gqFQlFzQyGEEJedBk0hff5G USEuN4khiSgVSswW65IZN42b0wBHiCuFBQuf3/Y5Q+OGsjNzJ72+6GUXyGeXZjN17VR6R/Tmxpa1 T3se90kcgcMCMRWb8L3Jt84HbipUCmtWtv/EoNQpOTmtKiV7xckKPDt40vVoVwC2b96OylVFy2nV n43TUM4GdUIIIa5s9RrkBAUFkZtbdXJ2Tk4OgYGBF2yzY8eO+hyCuII1xd8FFSrubHEnC1IXAM7T SgtxpTl27Bi7SnehQMHMrjNZlLaIhWkLMVG1v2TkgpFEuEcwqd0kWnrWMpjwt/7/5GHHM6PqwhRv Ahfgf7GXpb+FHTt2YDFaKJ9cTuWqStYErkH3Hx2qBEnNfi2TzwgC5O+BuDj1GuT07NmTGTNmMGLE CPbv309wcDBubm4XbNOpU6f6HIK4Qu3YsaPJ/i5EFURBatW1j6sPheWFTusqUNA6oDXdwrsxZ/cc u3s3Rt3IipQVDTlUIWrUL6IfySSzdP9S9EY92zK3EewRTM8WPVl7cq2tXl5FHnkVeUzeO5mjTx5l w8kNjF82njJjGS/0foH72t/XcIPsBCVtS8hblIdrS1eC77buA8qYlcHRVUcBsJy2oHhXQac98jvi WtWUvxfE5UP+Hoiz6hrs1muQk5SUREJCAiNHjkSlUjFlypT67F6IBnFD1A28veFt22btEPcQhyCn X0Q/TpedRqlQ0im0E52adeLLPV/a9ueoFCpy9bkOfQvRmDqGdmRb5jZWp662K08vSqfUUEqkdySl xlJOl5223TuWf4wSQwlD5g2xpUp/8NcH6RTaidaBrRtsrB6JHngketiVVeZXXvBaCCGEqK1635Pz zDPP1HeXQjSoAdED+HXkr/x66FeifaPRG/W8vr4q/bmXixf3tb+PMQvHALA3Zy9z98y168NkMfF3 9t+NOWwhHOzM2lntvYLyAlsQc+4+tEExgyiqKLI7C8pkMXG84HiDBjnOBN0dRNr7aVTmWYObsCfD amghhBBCONegiQeEuNxUVFbgonbMAjU0bihD44YC1ixqmzM281fKXzTzbMaye5cxe+fsGvs2I6ej iyuDxWLhmW7PEOgeyISuE3BRu9AtvBub0zcD4K5xr9PBovVF11JH592d2f35buL7xePTV86iEkII cXEkyBHXhHx9PoO/G8ym9E20DmjNknuXEOkT6bSuh9aDFQ+sQG/Uk1mcSZB7EHqjvnEHLEQ9UqBA q9Lasqz1jezLuze9a1fnz/v+5I7v7+CvlL8oNZYy8qeRuGncGBI3pFHH6hruimawBp9OEuAIIYS4 eHLKmbgmTFs7jU3pmwA4mHuQiX9OvGD9An0BPeb0IOa/MYS/H86B0wcaY5hC1Av1ed9fDWs9jOX3 L2dU4igmdp/Ir3f96tDG08XTYS/aoiOLGnScQgghREORmRxxWSoxlJBXlke4Vzgq5aWnkM3X51/w +lyF5YU8tewpdmfvBqCoosgWIJ1LhcouJa8QlwuFUgFm0Kq0PNHlCdusTe+I3hds18q/FTuyqrLX xAXENeg4hRBCiIYiMznisrPi+AqavduMyOmR9PqiV417A04UnmDWtlksPrK42jpjO47FVe0KWDOh PdblMaf1dmTuoPXM1nz191fV9qVSqEgMTpQAR1yWFCgwmo0AGEwGliQvcahTYihh0opJ3PvzvXY/ NzNumcGw1sOID4hn/HXjmdB1QqONWwghhKhPMpMjLjvjl46n2FAMwOb0zXy8/WMm9nC+vCw5P5nr Pr3OlhnqpT4vMbX/VId6PVv0ZPc/d7M5fTPtgtvRMbSjQ505u+Yw5vcxtlTSZ52biQpgQtcJTO49 mbgZceTp8y76PYWob1qVlse7PM77m9+3lZUZyxzq3f/L/fx6yLpk7bu939EhpAOfDfmMTs068eOI HxttvEIIIURDkZkccdkpryy/4PW5ftj/g13q2092fFJt3biAOEZ1GOU0wLFYLIxfOt4hwInyieLI E0d468a3uCn6Jib1nMSLfV6k55yeDgGOSiEns4umZTAZuKfdPTT3ag5YZ3Ve7P2i7f6y5GW0ntma 3w//btdud/Zubv72ZioqKxp1vEIIIURDkZkccdl5ue/LPPz7w5gsJiK8I3g46eFq6wZ7BNtfuwdX U9PeyTMn2Z29m7ZBbWnp2xLAdrDnuYoripm5bSYPJz3Mcz2fA2DNiTUczjtsV69vRF/WpK6p1bOF aCgapYZg92B2P7qbTWmbaOHdgnbB7QBrMo1hC4Y5ndkBOF12mtyyXMK85GwaIYQQVz6ZyRGXnVEd RrH/sf38ed+f7Hl0D6GeodXXTRzFA4kPoFFqiPKJYu7tc2vsf0v6FhI+SuC2+beR8FECK1NWolAo eOvGt1CgsKubq8/l/c3v03NOT1ILU6vtc03qGrxcvGr9jkI0BKPZyBvr3sBP58etrW61BTgAp0pP OQQ4akXV91yJwYmEeIQ02liFEEKIhiQzOeKyFBcQV6vMTiqlii9v/5K5t81FoVDUWB/ggy0f2JIZ lFeW8+6md7k+6nrGdx1PRWUFz614zqHNmYozrDu5jgifCFvWtfMVVRQR5x9HRnFGkxykKARAkaHI aXmUTxRRPlGkFKYAEOMXw/d3fs+Xu7/ETePGxB4T6yWToRBCCHE5kCBHXBVqG+CA9TR3Z9clhhJe X/e68/5R0Mq/FQABbgHV9n3+MjYhGpNKoeLxLo/blS0+spj/++v/SCtKs52D4+vqy+jE0byz8R3a B7Xn2Z7PolbKrwMhhBBXD/mtJq45w9sMZ8nRJWSVZBHpE8kbN7wBQG5ZLmcqztjVbRdkXe4zoesE rgu7DoD4gHin/erUOvSV+gYcuRAXNrHHRI7mHeXpZU9z8sxJov2i2Z65nQqTfUKBgvICJq+aDMB8 5lNQXsDbA95uiiELIYQQDUKCHHFNmbd3Hvf9ch9mixl3jTs/Dv+RGL8YAJp7Nadzs85sz9wOQIhH CI93eZwuYV3sMrIFugeiRImZqrTSOx/ZyZTVU+SEeNHoFChICk1iQMsB7MraxVsb3rLdyy7NrlUf q0+sbqDRCSGEEE1DEg+Ia8r7m9+3nXlTaizli91f2O6plCpW3L+Caf2n8XCHhymqKOLRxY/S5dMu zNs7z1avhXcLXrv+NdRKNUqFEq1SS/fPu9Pav3Wjv48QFiw82+NZHu38KH8e//OCdVUKFVqVlgEt B9iV++n8GnKIQgghRKOTIEdcU7xdve2vXbwd7r/Q5wXUKrUtE5XZYubDrR/a6lgsFmZtm0WluRKz xYzBbKDCVME7m95Bp9Y1/EsIcZ6t6VvxcfVBq9Q63HNVu/Ji7xeZ0mcKWf/KovyFcn4e8bPd39VV J1aRUpDSmEMWQgghGpQEOeKaMn3QdCK8IwDo0byH7eyb82mUGrtrX1df25+XHF1CenG603Z1SYAg xMUI8wzDU+tpV3Yw9yA+rj58849vHA6lLa8sZ2zHsXRq1ok/jv1BUUUROWU5dvvHDCYDxwuON8r4 hRBCiMYge3LENaVNYBtSJqRQYijB08XTaZ2c0hx+PvSz7dpD68EHgz6wXb+65tVq+9eqtNUetihE fcgoznAo25q5lRJDCcMThhPtF02n2Z1s97QqLZP+msS8fdYll60DWrN+9HraBrVlX84+wLr/LCk0 qXFeQAghhGgEMpMjrjkKhaLaAAfgj+Q/yCzOtF2XGkqJ9IkEwGgysiNrh/N+UdhS9FZHKT9yogHk 6/N5csmTFOgL6BjakSl9pqBRavDQejDzlpm2AAessz6rT6xm5QMrmdRzEk93e5oNozfIvhwhhBBX FZnJEeI855/67qfzQ6uy7nVQKBSoFCpb8oKzvLRe1R7CeK5zM7IJUZ/m7pnLxvSNxPrGsjh5MQDD YocxKnEUE5ZNsJth9NP5EegeyJs3vtlUwxVCCCEalHytLMR5BkQPYFLPSbhp3Aj3CueH4T/Y7qmV aj4Y9AEK7PfenB/guKpdG2WsQpzrSN4RW4ADMH//fEb9Oopv7vgGD42HrXzc4nEczTvaFEMUQggh GoUEOUI48eaNb1I6uZS0p9PoH9Xf7t5jXR7j5NMn6dKsS7XtyyvLG3qI4hrXPbw7c2+bi4vK5YL1 5u2bh4+rDxN7TLSVHco9xONLHm/oIQohhBBNRoIccU0qMZRw63e3on1NS8dPOpJamFqn9uFe4XQP 795AoxOiZi19WzKqwyhaeLeosW6+Pp88fZ5d2emy0wDkluXy/b7vWZe6rkHGKYQQQjQFCXLENemt 9W+x5OgSjGYju7J3MX7Z+Dr3Mb7reIdla0I0FleVK2+ue9MheFEpVIR5htmu4wPiGRA9gFGJo3DT uNnKx3UeR3ZJNh0/6cjIn0bSZ24fpq2d1mjjF0IIIRqSJB4Q16RTpafsr0tOVVOzemlFaQS5Bzn0 BdYPoF3CurApfRMeWg/OlJ/BguWixyuuHS4qFypMFTXW++rvrzCajQ7lJouJ53s+T4RPBEUVRQxp NYSMogx0Gh27/rmLNSfW0DqwNb1a9GL65umkFaXZ2r676V1e7PNivb6PEEII0RRkJkdckx5IfMCW MQ1gbMexdWr/3qb36P9lf06VnnI6m1NuKqdzs864a9wpLC+UAEfUWnUBjqvKPpmFswDnrOMFx+kQ 3IGiiiIe/PVB2nzUhoSPEnhnwzuM7TSWXi16AeDt6m3XztvF21l3QgghxBVHZnLENalXi15sH7ud talraRvUlr6RfevUfsbWGbY/W7AwImEEvx/6nXJTVcKBD7d8iMliqrcxi2tXkFsQOWU5ta6fWZxJ 9H+jqTRX2pV/tuszJnSbQNugtgDc1/4+Fh1ZxE8Hf8LH1Yc5t82p13ELIYQQTUWCHHHNahfcjnbB 7S6qrb+bPymFKbbrHuE90Cq1fLP3G1uZBDiivlwowAn3CqddUDuWJi+1lS05usQhwHFGrVTz44gf KTGU4KZxQ6mQyX0hhBBXB/mNJsRF+GzIZ0R4R6BAwe3xtzOuyzhZkiYaxIUCj57Ne3J8/HEW3bOI dkFVAXuJscRp/TFJY2yzOOfy0HpIgCOEEOKqIjM5QlyExJBETjx1gkpzJWql9ceoZ/OefLv321q1 D3QLtKXwFeJCzBaz0/K72tzF1//4Go1KA4C71t3uvlKhtLV9tNOjPNn1SdoEtmnYwQohhBCXCQly hLgEZwMcgHFdxlFeWc70LdNJPVP9uTtuGjcSgxNZnbq6VkuKhHBmdMfRtgAH4JGOj7AlfQsWLLio XPjlrl8oM5YR6xdL+5D2TThSIYQQovFJkCNEPXq6+9MUG4p5efXL1dYpM5axImVFI45KXE00Sg3P 9XyOgdED7cofSnqIGL8Y9ubspU9EH6fL0oQQQohrhSzCFuIifbXnK9rNakfPOT3ZmbXTVv5sj2e5 Pf52XNWutA2UD5ri4i24cwFtAuyXmBnNRm6Oudlp/d4RvXmsy2MS4AghhLjmyUyOEBdhT/YeHvrt Idueh1u/u5WMZzJQKpToNDp+uesXW93B3w1m8dHFTTVUcQUb/dtop0kEHl38KGXGMu5rdx+v9n+1 CUYmhBBCXN5kJkeIi3A0/6jdhvDskmzOlJ9xWveXu36hT0Sfi3rOA+0fuKh24upQXZa0fTn7OF5w nKlrp9JzTk8+3v5xI49MCCGEuLxJkCNELX28/WP6ze3Hg78+SHxAPP46f9u9ns174qvzddpOo9Kw 6O5FjEgYga+r8zrVSStKw1XtWnNFcdVRoKhVvY1pGxm3eJzdAbVCCCHEtU6CHCFqYeHhhYxbPI41 qWv4cs+XPLf8OTaM3sDE7hOZ2m8qS+9dWm3bNSfWMODrAaQUpDBv2DzubXtvrZ+76sQqyivL6+MV xBVEq9QyoesEu7Kagp5Pd3x6yc81mAyM/HEkLtNcaDOzDQdPH7zkPoUQQoimIHtyhKiFcxMLnL2O C4jjnYHvXLBdvj6fIfOGUGwoBuCO7+9wOPfEx9WHwvLC+h2wuKIZzAY+2/UZE7pOYFvGNiJ9Iuka 1pWJyydiNBvpFNqJA6cPoK/U29q4adwu+bkfbfuI7/d/D8DB3IOMXTiW9aPXX3K/QgghRGOTIEeI Wugb2RfFGgUWLAD0i+xXq3bpRem2AAdAX6mnmWczMoszbWUfDvoQLxcvfF19GfnTSLJKsup17OLy EO8fz9H8o5gsJqf3NUoNRrPRdl1iKGH2jtlk/isTH1cfAEZ1GEWpsZRmns349/p/839//R9gneWZ 2n/qJY/xVMkp++vSU9XUFEIIIS5vslxNiFroF9mPX0f+yr3t7mVyr8nMuW1OrdrF+sUS6xdru47w juC7f3xHmGcYSoUSH1cfNqVvItwrHLVKLQHOVUCr0jqU+br6su6hdXx1x1confxnV6VQ8eXtX6JS qOzK9ZV6cstybdfert4082wGwKRek/hx+I+82u9V1o9ez4DoAZc89nva3YO7xt12Pbbj2EvuUwgh hGgKMpMjRC0NjRvK0LihdWqj0+hY+9Ba3t/0PmaLmQndJuCucedMxRnMFjOF5YXM2j6L2Ttm83zP 5+s8Jq1Si8FsqHM70XAMJsd/H8/3eJ4iQxFnys8w7fppTF452e6+t4s3d7e7mxbeLRi2YJhtBqVb eDeifKKqfdawNsMYxrB6G3u74Hbs/OdOlh9bToxfDDfF3FRvfQshhBCNSYIcIS5BXlkec3bNQa1U M6bjGDxdPB3qhHiE0CWsC5NWTOLXw78yoesESgz2qYFNFhO7sncR6xfL0fyjgPXb/4Lyggs+//Ub XifKJ4o317/Jjqwd9fdiolZUClW1y8/ONWnlJCatnGS71ql1dvtpfHTW5Wg9W/Rk32P7mLt7LlqV loeTHkalVDn015Ba+beilX+rRn2mEEIIUd8kyBHiIpUaSuk5pyeH8w4DMG/fPDY+vBG10v7HKr0o nXt/vtf2Df+zy58lzj/O1u6sUI9Q3h7wNiN+GMGRvCM1BjhqpZrPdn6Gq9qVPaf21OObidoyWUwo qNqrVVvnBjg6tY4PbvrAdr382HK+3vM13q7e9G7Rm6TQJNu9HZk7eGHlC1SaK5nSd8pFn78khBBC XO0kyBHiIu3K3mUXqGzL3Max/GO08G7B0388zbbMbfRq3otQz1C7JUzlleV8MvgTFh1ZxPz988ks zuS6sOt444Y3eOi3hziYW7u0vZXmSodASTS+ugY454rxjWHL2C346fwA+OnAT9zz8z22+4O+GUT6 M+loVBqKK4q58asbKaywZuLbkrGFI08cIdQz9NJeQAghhLgKSZAjxEUK8wyzW66kU+sIdA9k8l+T +WTHJ4Bj6mmA9sHt6Rbejb6RfXln4DtYLBYUCusZKMcKjjXeC4gGpVaqifSKJLkwudo6PVr0sAU4 AC+vftnufk5ZDnn6PEI8Qvh4+8e2AAes2deS85MlyBFCCCGckOxqQlykKN8o5t4+l+ZezWnp25Lv 7/weP50f+07vq7bNuM7jWPPgGlzULrayswEOwLDWzjeR3xF/B/1a9LvgeNzUbnaZsUTjUyqq/pPq r/Pn3UHv8myPZwlyCyLGNwYVVftrIrwjaBPQhu6fdSfonSCG/zDcIfNaoFsgQe5BAMzfP9/unk6t IyEooQHfRgghhLhySZAjxCW4r/19nHz6JMfGH2NI3BAAboquPiPVE12esJ154swrfV9xKLu77d38 NOInVj20itvjb0er0uKh8eDmmJvx0noB4OXixQOJD1BqLL20FxKX5NyDXk+VnmLEDyOY0HUCp549 xdhOYzFRlaQg9Uwqk/6axOaMzZwuO82PB34k1j8WtcI6wa5T61h490Jb4O/J7AAAHgtJREFU4OTr 6mv3rFGJo+xmgYQQQghRRYIcIeqo0lzJjK0zmPzXZHZl7XK4P7HHRD4d8imPdHyEpJAku3t/HPvj gn1r1Vpa+ra0K5u3bx4/H/yZzOJMVqasxGAyUGIsYWnyUooMRdwQdQNHnzhaY6IC0fgqTBWkFaUB 0DqgdY31D+Ud4sDjB1h8z2JOPHWCruFdbfemD5pOC+8WAPRo3oN/3/jvhhm0EEIIcRWQIEeIOhrz +xieXPokb65/k55zerIvx3F52piOY/hkyCe2pUZnrT25tsb+377xbYeyJ5Y+wZ7sPRRVFDnc+yvl L1IKU6pNNaxVOh5OKRpHhHcE7YLaATj8XXAmoyiDWP9Ybom9xaF+QlACJyacoGhSERtGb8Db1btB xiyEEEJcDSTIEaKOfjn0i+3P+ko9y5KXVVu3S7MuF7x2ZlDMIAJ0AXZleqOeNoFt0Kl1TttUmCow m81O78lhoRdPgaLmShfg4+qDu9a6T6o2SwkjfCLsro0mI2+se4MHf32Qnw78hEKhcHoWkxBCCCHs SZAjRB1F+0bbXcf4xVRbd0rfKUzuNZkbom7g5b4v83zP52vs313rzspRK/Fy8bKVPdfzOSJ8Ilh8 z2IGxQyyO6xxdNJonl/xvG1juofG45I/nAsrH1cfMp/JZN6weQS4BTitE+kTSZCb81maE4UnbH/u 3aI3PZv3tF13Du1MxYsVjO04FjeNG3H+cXx1+1d27Scsm8ALK1/gyz1fcucPd7L4yOJLfykhhBDi GiAppIWoo+/v/J4xC8eQUZTBA4kPcHv87dXW1ag0vH7D63V+Rrvgdhwff5xVJ1bRzLMZPZr3AKB/ VH/6R/UHILUwlUpzJSaLibgZcba2JcYSHurwEF/s/uKCz2gb2JaeLXry+c7PqbRU1nmMVxsvrRdF BvvlgC/2fpEnlj7Bzwd/dqgf4R1BUmgS7w58F1e1K38k/4HRZGTCHxMorywHsPu7oVFpWDVqFX+l /IVOraNvZF8AZg+Zzewhs+363pm1k+ySbJYfX25X/lfKX9za6tZ6eV8hhBDiaiZBjhB1FOsfy5oH 1zT4c/zd/LmzzZ3V3j+7tKlAX4BOrUNfqQdApVAxufdknu/5PAv2L2DK6ilO2+87ve+C6a6vVIFu gZwuO+30nrfWmzOGM07vnR/g3BB1A/GB8fxr+b8c6qoUKo6NP2a3D+qhpIeoNFfSPqQ9n+/8HE+t J69d/5pdO41Kw6CYQRcc/9sb3ub5FdYZP0+t/dK0DiEdLthWCCGEEFYS5AhxhfPV+bJg+ALGLx2P vlJP+6D2PLb4MbKKswj1DGVKnylMXTu11v0pUGDBYv8MF1+aeTXjUO4h2+GnteGqdrXNajSWPH1e tfeKjcW17uevlL9smdHO1zuit0Oih9k7ZvPk0icxmowAWLCwIX0Dq0atwk3jVuvnvra2KjAqNhTT Pbw7CoWCoa2G8kDiA7Z7c3fPZcbWGfjp/Pjvzf8lLiDOWXdCCCHENUn25AhxFRjcajA7/7kTlULF n8f/ZPnx5ew7vY/lx5ez4MACxiSNuWB7BQq0Ki3x/vFOz/EpqCiguXfzOn1YV6Bg9uDZqBTOs75d qhCPEDRKjUP5uWfVOLsX6hFa62ccyTtCj/AedmUuKhdev95+CeKpklM8tvgxDCYDlv/9D2BrxlYW 7F9Q6+cBDv+MH+38KBtGb+D5XlX7uTanb2b0b6PZkbWD5ceXM3je4Do9QwghhLjaSZAjxFVi76m9 ZBRnOJQfzj3MdWHXXbCtBQuzbp3Fx4M/pm9EX6d1/kz+k2KD/UzI2YMqz6dAwf3t72dvzt46zfzU RV5ZnsNYa5Nw4ZbYW4j0iaz1c+5pdw97Ht3Dd//4jlm3zmLHIztse6TOKjYUV/ueamXdJsw/HfKp LdAZ3Gowd7e926HOwdMH7WbbkvOTMZgki54QQghxlixXE+IqEege6HSpmbvWneEJw3l8yeMYzUan bRUoePj3h4Hqs8Wd3y/AzJtnknomlX9vsD+YUqVU8dXf1kxhWpW2Vh/ANUoNT7V5inf2vVNjXQCj 2Ui4V3iNY9QoNXbv/dWer2zXoR6hZJVkXfA5rfxb0T64Pe2D21dbJ9o3mqFxQ/n98O9A1ZK/G6Ju YETCiFq9z1lD44Zy+tnTFFUUEeIR4rRO74jeuGvcbWmpr4+6Hq1KzkMSQgghzpIgR4grxLy98/hw 64f4uvrywaAP7NJIAyw/ttzph3w/nR8+rj4svWcpA78d6LCcS6VQ2c1CJOcnO32+s77bBLUhISjB IcipNFdlazOYDPi6+lJQXlDtu/m6+jKxx0TeX/9+tXXO56fzo01gmxrrnR/YnXudVZKFm8aNMmOZ 07YapYYbW95Y4zMUCgU/j/iZhUcWYjQZ6RrWlbLKMmL9Yqs9pPVC3DRuF1waGOMXw9qH1vLFri/w 0/nxbM9n6/wMIYQQ4momQY4QV4CdWTu575f7bAHKkW+PkDw+meKKYmZtn4XeqHf6YVqBghd7vwjA q2tfdbpfZdPoTVz3+YWXsznTL6If7YLakfBRgsO982dPZt4yk1dWv8KR/CNO+yooL+CFlS/U6fm9 m/dmQPQAEvcmsufUnmrrBbgF0DqgNetPrifCJ8Lu7BqdWmdLFODMHa3vILskm8N5h0kITCDQPbDa uiql6oLpxOtbx9COdAzt2GjPE0IIIa4kEuQIcQXYn7PfLkA5VnCMUkMpN31zE5vSNwEQ5hlGUkgS u7J3WZd+dX2Ke9vfS2JIInqjnnUn1zn0O7H7RLqEd+HVfq/y8uqXAXjyuif579b/1jim165/jV3Z uxyWez3S8RFGth3JmIVjKKooYmL3idzd7m40Kg3Dfxhe53dXosSMY3D225HfWHh0oe2fi1qpts0g NfNohrvWnZSCFHLLctmTvYe7Eu4ivzyf9sHtWZe6jsLyQvSV+mr3FQF0D+9O3Iw4ig3F+On8WPnA ShJDEuv8DkIIIYRoXBLkCHEF6NG8h90ejJ7Ne5Kvz7cFOAAZxRl8PPhjIrwjCHQPtNvPodPoaOHd gpNnTtrKpvWfxgt9rLMnU/pOYVzncZgtZoI9gpm/b77dWTNqhdruwNARbUbQq0UvThSesNtz4+Pq w38G/gdPF0+OjT9m9w7B7sF4aD0oMZTYrk+VnnJ4V6VCSZB7EB/d8hHuWnfi/ePp9nk3p3tnzg38 zl0il1mSaVevyFDE/P3zbdddw7qyJWOLrY9Qj1Ce7/U8Ty17yq7dl7u/tCVbyNfn8/bGt/n2H986 jEMIIYQQlxcJcoS4AkT7RbP6wdV8tvMzfF19eb7X82hVWrxdvDlTYT3cUqVQEe0bTevA1k77WHT3 Ih5f8jgF5QVM6DqBMR2taaVTClIoM5bRJrANCoU1O9mmhzcx6tdRnC47zdNdn+bRLo/y26Hf2JKx hR7NezC4lTVlcaRPJAvuXMAra15Bq9Ly7sB38XTxdHj2Twd+4u6f7rYtYfPX+bPn0T3M2DqDbZnb WJmyEqPZiL+LP5vGbiLWP9au/R/3/cGTS59kY9rGapMn1EVxhX2WuKySLP69/t8Mjh3MoqOLAOsy txDPEDgnDpPN/UIIIcSVQYIcIa4QnZt1pnOzznZlv438jSeWPoHeqGdK3ym2AGfxkcXM3DYTtVLN o50fZWD0QNoFt2PtQ2vt2k9bO42XVr0EwLDWw1gwfAFKhZJov2jWj15vV/e2+Nu4Lf42h3FVVw6w J3sPd3x/BymFKXblefo88vX5vHa99eDL1MJUjhUcw5JtsQU4JrOJsQvHsmD/AqJ8o/j+zu/JKs7i Hwv+QVFFEQBx/nGkFKZgsVhQKVUOB4+eTSpw/h6hx7o8xsxtMzmYe9BWll2Szeik0dza6lby9fnc 3fZuyoxl7M7eTXZJNi28W9j2NwkhhBDi8iZBjhBXsL6Rfdk7bq9d2d5Te7nj+ztsH+oXHllI7xa9 WX7/clzULrZ6BfoCpqyaYrv+6eBPrD6xmuuj/r+9+4+qqsz3OP45goJCCEcFzV+o+IMstVgWekjR 0hQixyaUDCimWN1lYlMk5jhaOqZpP1wus2UuMFdl4yTmlCtnxLrFcLNCMco0s0tmXBwJDDMBFfDc P1ie8QilnIBtD+/XX+yH/eN7znrWZn/Yz372+CbXceL0CZVXlatfYD95tfNS5dlKnak7o8StiQ0C jlT/Qs2+gX1dy30D+8pms2nmf8/Ui8Uv6uGbHtbB8oN6ufBlSdIX33+hlLdS9MkDn+iHjB9UVVMl X29ftfdqr7pzdYpaH6WPSz52O8Yg+yClXJ+iee/Nc30XN/W8Sfdff79SI1L1wA0PqPtz3XXi9AlJ 9cPkBnYZqKnhU932UzS7SMU/FqtP5z7q2L5jk7+bfaX7lHckT9/++K1O157WpLBJihkY0+T9AACA y0fIAQxTeKywwZCuvO/ytOXLLZpx3Qy39ounhW5s9rVLeefQO5qWPU1VNVWK7BWp5GHJevifD6vm XI28bI1Pnzy8+3C3KZLPOc9p4qsT9dXxryRJ//j6H0q9IdVtm6M/1T9n49XOy21I3Jm6Mw0CjpfN S1lTslx3qc4bYB+glOtTtP7T9SqvKldmXKaW/s9SVZ6t1Lyoebo2+NoGtXZq30mDuw5uwjfyH7nf 5mriaxPd3hO0On+13kp4S3cMvsOjfQIAgEsj5ACGGdlzpDq066Cz59xfwJm5N1MrP14pR2+HVkxY oaCOQVowZoH+8q/6IWN3DL7Do7s4s/852/WemY//72Pll+S7wtKF7985z8fLR0+OfdKt7YfqH1wB R5Kqa6vVL6if20QFKSNSGj1+p/adFGYPc73fxyabNt65UVF9otQvsJ8+0AeudfsF9lPy1mT99Yu/ Sqp/7ubTBz9t8FLR5vJy4cuNvgh1+9fbCTkAALQgQg5gmCFdh2hH0g6l56Rr77/3utrf//Z9SdKe o3sU4BOgxeMWa/G4xUoclqiqmioNCxn2i9Mp/5yLL+Ibuxs0acAk/XnMn/VD9Q8K7xauMHuYJGnu zrlat3edQvxC1NO/p0pOlUiqf89O3KA4TQ6brO1fb1e/oH6/+A6a7TO269GcR1VRXaG0G9M0/drp kqTnJj6n49XHVXC0QNGh0ZrrmKvA5YGu7cqrypVTlKM/XP+HJn/uyxHiF9Jo+5CuQ1rkeAAAoB4h BzBQdGi0ts/Yru7PdW/09198/4Xr50FdBv2qYy0Zt0T3v32/6px1rvBy/q7KeYnDEuXo43Bre/ur t7Vi1wpJ9c/0dPT+z/MuNedqdKDsgOIGxzUYKuZ0OlVWVaZA30DXbGcDuwzUtru3NagtqGOQ3kp4 y62tu39319A3Seod0LupH/myzR8zX58e+1TvffOeAnwDFOwXrNsH3q60G9Na7JgAAICQAxjLv4O/ fL19G8w4JkkT+k9otuPcO+JeOfo4VHKyRB9+96Hmvz/f9TsfLx/Nvml2g2eBJKnkZInbcnVttdvy nqN7FDc4zq2tqqZKsa/H6oNvP1CQb32AubnvzU2q981pbyrlrRSVV5XroZEPacKA5vsuLhbgE6Cc pBw5nU7X9NwAAKDlEXIAQ/l18NOrU1/VA28/oOraak0Km6TgTsFy9HHovhH3NeuxwuxhCrOHKftA tlv74K6DNX3odDnWO3Sg7IBCA0P18pSXdX2P6xU7KFZd3u+i49XHJUn9g/rrm4pvJNU/VzOm75gG x1m7Z60++PYDSVLF6QrN3D6zwexyl3JTr5t04KEDHnxKzxFwAABoXYQcwGB3XXOX7rrmLp1znvPo eZtLOXnmpD4v/VyhgaHqFdBLd11zl9YWrFXtuVpJ0vjQ8XKsd+hM3RlJ0meln+nON+7U4YcPq0/n PtqdultvfvmmQvxD9Lshv1PaG2k63fG04q+J1y39b2lwvMqzlW7L5yclAAAAuBAhB2gDWiLgfPfj d4paH6Xik8Xy9fbVlmlbFDMwRnkpecopylF413CVV5W7As6F250PXf2C+il9dLrrd7PCZykiIuJn j3nfiPu0tmCtjv50VDbZ9KeoP3lcf+25Wnm34xQIAICJ+AsPwCOrP1mt4pPFkqTTtae18P2FihkY o8hekYrsFSlJrqFlF/p9+O89Dl29O/fWZ//1mT787kOFBoZqePfhTd5H3pE8xW+OV1lVmZKHJyvr jqwWCYEAAMA6/GUH4JGL74I0dlckOjRaa2LWaEiXIeof1F9PjH1CG+/c+KuO27VTV00ZMsWjgCNJ iVsTVVpZqnPOc9pQuEF/++Jvv6oeAABw5eFODgCP/DHyj/r7V3/XwfKDCvAJ0IoJKxpdb+bImZo5 cmYrV/fzjlcdd1+uPv4zawIAgN8qQg4Aj4T4h6jwwUJ9U/GNrr7qanX27Wx1SZdl1o2ztPzD5ZKk Hv49NHXIVIsrAgAAzY2QA8BjPt4+Cu8WbnUZTfL0rU8rOjRax04d06SwSeru3/gLUwEAwG8XIQdA mzMpbJLVJQAAgBbExAMAAAAAjELIAQAAAGAUQg4AAAAAo/BMDgDLbCjcoN0luzWm7xhNv3a61eUA AABDEHIAWGLlRyv1aM6jkqQX97yoqpoqDdMwi6sCAAAmYLgaAEts/9/tv7gMAADgKUIOAEuEd3V/ v841Xa9p0vafl36uiHUR6vl8Tz3x/hPNWRoAAPiNa7bhalu3btWqVavUp08fSZLD4dCDDz7YXLsH YJhltyxT5dlK7fn3HkX1jtL8MfO1r3DfZW8fvzleh44fkiQt/tdijew5UrcPur2lygUAAL8hzfpM TkxMjDIyMppzlwAM5dfBT1lTsjze/siJI7+4DAAA2i6GqwH4TbpwNrYAnwBNCptkYTUAAOBK0qx3 cvLz85Wamqra2lplZGQoPDz80hsBgAfW37FeUb2jdOzUMU0bOk0D7AOsLgkAAFwhPAo5mzdvVnZ2 tmw2m5xOp2w2m2JjY5WWlqaxY8eqsLBQGRkZ2rZtW3PXCwCSJK92XkqNSLW6DAAAcAWyOZ1OZ0vs OCoqSnl5ebLZbD+7TkFBQUscGgAAAIBhIiIiLnvdZhuulpmZqR49eig2NlaHDh2S3W7/xYBzXlOK hbkKCgroC6AfQBL9APXoB5DoB/iPpt4cabaQExcXpzlz5mjTpk2qq6vTU0891Vy7BgAAAIDL1mwh JyQkRK+88kpz7Q4AAAAAPMIU0gAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAAGIWQAwAAAMAohBwA AAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZADAAAAwCiE HAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxByAAAAABiFkAMAAADA KIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAAGIWQAwAA AMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZAD AAAAwCiEHAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxByAAAAABiF kAMAAADAKIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACjEHIAAAAA GIWQAwAAAMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAA AAAYhZADAAAAwCiEHAAAAABGIeQAAAAAMAohBwAAAIBRCDkAAAAAjELIAQAAAGAUQg4AAAAAoxBy AAAAABiFkAMAAADAKIQcAAAAAEYh5AAAAAAwCiEHAAAAgFEIOQAAAACMQsgBAAAAYBRCDgAAAACj EHIAAAAAGIWQAwAAAMAohBwAAAAARiHkAAAAADAKIQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAA AKMQcgAAAAAYxeOQk5+fr9GjRys3N9fVdvDgQSUkJGjGjBlatGhRsxQIAAAAAE3hUcgpLi7Whg0b FBER4da+dOlSLViwQK+//rpOnjypvLy8ZikSAAAAAC6XRyEnODhYa9askb+/v6utpqZGJSUlGjp0 qCRp/Pjx2rVrV/NUCQAAAACXyduTjXx8fBq0VVRUqHPnzq5lu92usrIyzysDAAAAAA9cMuRs3rxZ 2dnZstlscjqdstlsSktLk8PhaI36AAAAAKBJLhly4uPjFR8ff8kd2e12VVRUuJZLS0sVHBx8ye0K CgouuQ7aBvoCJPoB6tEPINEPUI9+AE94NFztQk6ns35H3t7q37+/9u7dqxtuuEE5OTlKSkr6xW0v nrgAAAAAAH4tm/N8SmmC3NxcZWZm6vDhw7Lb7erWrZuysrJUVFSkhQsXyul0avjw4Zo7d25L1AwA AAAAP8ujkAMAAAAAVyqPXwYKAAAAAFciQg4AAAAAoxByAAAAABjFkpCTn5+v0aNHKzc319V28OBB JSQkaMaMGVq0aJEVZcEiW7duVXR0tJKTk5WcnKyXXnrJ6pLQypYtW6aEhATdfffd2rdvn9XlwCL5 +fkaNWqUkpOTlZSUpCVLllhdElrRoUOHNGHCBG3cuFGSdOzYMSUlJSkxMVGPPPKIampqLK4QreHi fjBv3jzFxcW5rhEuvHaEuVasWKGEhATFx8dr586dHp0PfvUU0k1VXFysDRs2NJg+eunSpVqwYIGG Dh2q9PR05eXl6eabb27t8mCRmJgYZWRkWF0GLLB7924dOXJEmzZtUlFRkebPn69NmzZZXRYscuON N2rVqlVWl4FWVl1drSVLlmjUqFGutlWrVikpKUkTJ07UypUrtWXLFiUkJFhYJVpaY/1Akh577DGN HTvWoqrQ2j755BMVFRVp06ZNOnHihKZOnarIyEglJibqtttuu+zzQavfyQkODtaaNWvk7+/vaqup qVFJSYmGDh0qSRo/frx27drV2qUBsMBHH32kW2+9VZI0YMAAnTx5UpWVlRZXBasw4Wfb5OPjo8zM TLeXiOfn52vcuHGSpHHjxnFd0AY01g/Q9lz4z66AgABVVVVp9+7dGj9+vKTLPx+0esjx8fGRzWZz a6uoqFDnzp1dy3a7XWVlZa1dGiyUn5+v1NRUpaSk6Msvv7S6HLSi8vJy2e1213JQUJDKy8strAhW Kioq0syZM3XPPfdwUduGtGvXTh06dHBrq66uVvv27SVJXbp04bqgDWisH0jSa6+9pnvvvVfp6ek6 ceKEBZWhNdlsNvn6+kqSsrOzFR0d7dH5oEWHq23evFnZ2dmy2WxyOp2y2WxKS0uTw+FoycPiCtZY n4iNjVVaWprGjh2rwsJCZWRkaNu2bVaXCovwn/y2q2/fvpo1a5YmT56s4uJiJScna+fOnfL2bvWR 1bjCcF5ou6ZMmaLAwEANGTJE69at0+rVq7VgwQKry0IrePfdd7VlyxZlZWVp4sSJrvbLPR+06F+O +Ph4xcfHX3I9u92uiooK13JpaSm3Kg11qT4xYsQIVVRUuAIQzBccHOx25+b7779Xt27dLKwIVgkJ CdHkyZMlSb1791bXrl1VWlqqnj17WlwZrODn56ezZ8+qQ4cOXBe0YZGRka6fb7nlFj355JPWFYNW k5eXp3Xr1ikrK0v+/v4enQ8snUL6fBLz9vZW//79tXfvXklSTk4Okw60IZmZmXrnnXck1c+qYrfb CThtiMPh0I4dOyRJ+/fvV0hIiDp16mRxVbDCtm3btH79eklSWVmZjh8/rpCQEIurglVGjRrlOjfs 2LGD64I2avbs2SouLpZU/0D6oEGDLK4ILe3UqVN65plntHbtWl111VWSPDsf2JytfA84NzdXmZmZ Onz4sOx2u7p166asrCwVFRVp4cKFcjqdGj58uObOnduaZcFCpaWlmjNnjpxOp+rq6jRv3jxdd911 VpeFVvT8888rPz9fXl5eWrhwoQYPHmx1SbBAZWWl0tPT9dNPP6m2tlazZs3iwraN2L9/v55++mkd PXpU3t7eCgkJ0bPPPqvHH39cZ8+e1dVXX61ly5bJy8vL6lLRghrrB0lJSXrppZfUsWNH+fn5aenS pW7PccI8b7zxhl544QWFhoa6RvYsX75c8+fPb9L5oNVDDgAAAAC0JEuHqwEAAABAcyPkAAAAADAK IQcAAACAUQg5AAAAAIxCyAEAAABgFEIOAAAAAKMQcgAAAAAYhZADAAAAwCj/DyHbXuqPvoYDAAAA AElFTkSuQmCC ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3X1wG/d97/vPLkESEB9hKSIdC3xoHMs3FqVzxo2eehLH sXUbp9G07kw9mURScps7+aPtjZNp7CiS1SSNRVNyelK3PZ2Om/ikstpJZpo718eyG1dyYte1ZMlV zpEot0eyHAmg5JCWSAKURPAJ2PuHCGR3sQABEiQB8P2ayVRcPHBlCux+9vv7fb+GZVmWAAAAAKBC mIt9AgAAAABQTIQcAAAAABWFkAMAAACgohByAAAAAFQUQg4AAACAikLIAQAAAFBRfHN58f79+/Xz n/9ciURCX/ziF/XTn/5UZ86cUTAYlCR94Qtf0D333FOUEwUAAACAfMw65Bw/flzvvPOOfvjDHyoa jerBBx/Uxo0b9dWvfpVgAwAAAGDRzDrkrF+/XuvWrZMkNTY2anR0VMlkUswWBQAAALCYDKsIqeRH P/qRfv7zn8s0TV25ckWTk5NasWKF9uzZo+bm5mKcJwAAAADkZc4h58iRI/rbv/1bff/739eZM2fU 3NysO++8U08//bQGBga0Z8+eYp0rAAAAAMxoTo0HXnvtNT399NP6/ve/r/r6em3cuDH92H333adv fvObOV9/8uTJuXx7AAAAAEvE3XffnfdzZx1yrl+/rieffFI/+MEP1NDQIEn60pe+pEceeUShUEjH jx/XHXfcUdSTRWk5efIkP78yxs+vfPGzK2/8/MoXP7vyxs+vvBVaHJl1yHnxxRcVjUb15S9/WZZl yTAM/e7v/q6+8pWvKBAIqK6uTt3d3bN9ewAAAACYlVmHnIceekgPPfRQxvHf+Z3fmdMJAQAAAMBc mIt9AgAAAABQTIQcAAAAABWFkAMAAACgohByAAAAAFQUQg4AAACAikLIAQAAAFBRCDkAAAAAKgoh BwAAAEBFIeQAAAAAqCiEHAAAAAAVhZADAAAAoKIQcgAAAABUFEIOAAAAgIpCyAEAAABQUQg5AAAA ACoKIQcAAABARSHkAAAAAKgohBwAAAAAFYWQAwAAAKCiEHIAAAAAVBRCDgAAAICKQsgBAAAAUFEI OQAAAAAqCiEHAAAAQEUh5AAAAACoKIQcAAAAABWFkAMAAACgohByAAAAAFQUQg4AAACAikLIAQAA AFBRCDkAAAAAKgohBwAAAEBFIeQAAAAAqCiEHAAAAAAVhZADAAAAoKIQcgAAAABUFEIOAAAAgIpC yAEAAABQUQg5AAAAACoKIQcAAABARSHkAAAAAKgohBwAAAAAFYWQAwAAAKCiEHIAAAAAVBRCDgAA AICKQsgBAAAAUFEIOQAAAAAqCiEHAAAAQEUh5AAAAACoKIQcAAAAABWFkAMAAACgohByAAAAAFQU Qg4AAACAikLIAQAAAFBRCDkAAAAAKgohBwAAAEBFIeQAAAAAqCiEHAAAAAAVhZADAAAAoKIQcgAA AABUFEIOAAAAgIpCyAEAAABQUQg5AAAAACoKIQcAAABARSHkAAAAAKgohBwAAAAAFYWQAwAAAKCi EHIAAAAAVBRCDgAAAICKQsgBAAAAUFEIOQAAAAAqim8uL96/f79+/vOfK5FI6Itf/KK6urr0yCOP yLIsve9979P+/ftVXV1drHMFAAAAgBnNOuQcP35c77zzjn74wx8qGo3qwQcf1MaNG7Vt2zb95m/+ pr773e/qxz/+sT796U8X83wBAAAAIKdZL1dbv369nnrqKUlSY2OjRkdH9eabb+rjH/+4JOnee+/V 0aNHi3OWAAAAAJCnWYccwzDk9/slSf/4j/+oj33sY4rH4+nlacuXL9eVK1eKc5YAAAAAkKc5Nx44 cuSIfvzjH2vPnj2yLCt93P5nAAAAAFgoc2o88Nprr+npp5/W97//fdXX16uurk4TExOqqanRwMCA Vq5cOeN7nDx5ci6ngEXGz6+88fMrX/zsyhs/v4WXsCz93cSEehMJdVVV6fM1NTINo+D34WdX3vj5 LR2zDjnXr1/Xk08+qR/84AdqaGiQJG3atEkvvfSStm7dqpdeekkf+chHZnyfu+++e7angEV28uRJ fn5ljJ9f+eJnV974+S2O7nBYf33hgiTptURCt912m3a1t0u6GYD2RSI6NjKiTY2N2tnW5hmA+NmV N35+5a3QgDrrkPPiiy8qGo3qy1/+sizLkmEY2rdvn3bv3q0f/ehHev/7368HH3xwtm8PAABQNMdG RrJ+vS8S0e7pAHRocFCS0gEIQHmadch56KGH9NBDD2Ucf+aZZ+Z0QgAAAMW2qbExHWBSX6fkCkAA ytOc9uQAAACUg51tbZLkWJKWkisAAShPhBwAAFDxTMNw7MHpse3BeTQUkiQdjcU0YVk6GoupOxzO ujcHQOkj5AAAgCUl2x6c7nA4ffyFoSEd6O/XjtbWkgg7+TZHAHATIQcAACwp2fbguI+fjcfToWex GxHQHAEozJyHgQIAAJSShGWpOxzW1t5edYfDSlqW49h4Mul4fmoPTra9OHNpROB1LrNBcwSgMFRy AABAQUp96ZRX1UNS+pgkbQkGVWuajiYEqf97oL9fZ+Px9HM3NDSoOxzWT0ZH9YkC9+oUqwJDcwSg MIQcAABQkFJfOpVP1ePU9et6eNUqR2BJNSfY2damnkgk3Yjg2f5+nRsbkyS9VuDytXzOJZ/Q6O4O 90gopO5wuGSDJrDYCDkAAKAgpb50akNDg6PqsbGhQYZhOI69NzmZdb9NakHZ+XjcUdFJyfX3tQeW DQ0NGkskHI97VWDyCY327nCSHE0SSjFoAouNkAMAAApSjKVTqTCQqpbUGIY2NzU5KhLFWhb3SjSq WtPU/c3NOjYyohu2PTlegeWJcFh7Ll7M+n5vj45mbTGdbamcdHOJnH0+T7ZzyCc0lnrQBBYbIQcA ABQk12BNKb9wYg8DKS8MDUn6VUUi32Vx7u93LBZzPH4kGs36d/EKaAcHBjyf2ywpquxd1yaSSX23 ry/r96o1TVmSHr94Mf09QrW1ikwvhXOfU67/juzRAXIj5AAAgIK4l065ucOJ17yZbJUH+/F897M8 cPq0Dg8Pp79fdZ7VntWBgJKWpa29vVrf0KBXh4f1xrVriru6r9WZpna1t+ufIhH9q235mft8PtXb q6tTU1m/36bGRu2LRBxVIvtyuNWBgD6zcqV+Njyspy5dUmNVlc5PB6BDg4P677/8pc58+MP6s0uX 9Ho0qtv9fo0kElpXX58eaArgJkIOAAAoqnzmzbgrESmbGhvTFYy3R0czHnN7IhxOB5yUyTzbNLf5 /enA4XUu9u+7q71dly9fdoQc+7keGxnRUVcFye52v1+PhkJ68K23cp7Ta7FYuvL03uSk47HzY2Na 8+ab6eCTcnh4WPv7+tiTA9gQcgAAQFFlCzD28JNa4ua1J6fHtZRtdSCQrgS5ZVtalk2daWpVba0+ u3Jl3q+NjI0paVn6fE2NbrvtNh2NxTSeTOrvfvlLfbevL2v15hafT0PTj50fG9P+vr6Mpgh2Z+Nx nfdodOA4l/Fxz+PzuSen1FuGA14IOQAAoKiyzZuxV2JyLXnzumA/NjKinkhkzhfYN5JJnY3H9ReX L+dcWmZ3bmxMq48fV8v4uJZVVysyNubZdS2lbnr+TmRsLB1yJOmpS5e0tq4u5/dK5HxU8hmGJjwq VbmaIcxVqbcMB7wQcgAAQFG5581ka1CQ4q4UuKsdZ6dbOR8aHEx3Sku93/aWFj2WoxNaNvkGnJTz Y2M6L0mupXHZGIaRnq2T8t7kZM4mCNnc7vfrlxMTupFManR6v9Adfr/aA4F04EotCXwlGtVP1q4t atChkxvKESEHAADMi2zVGneosSwrHVQODQ7q/uZmrQ4E0s+3V03sDQZ+Njycbg3dNz4uy7KUsCz1 T0462kQvtBvJZMY+oUL5JVWZpgKmqe0tLfqH995z/HcwDEP/tHat7jpxwvG6w8PD+tCJExmNHuaC Tm4oR4QcAACwoOxzaA4NDmqFz3k5Yq92LDPNrO8zm6pIuRiTpGRSN5JJfSMczvjvMDg5qbtOnPBc NpetxbU0u/01M7UMB0oRIQcAACyI1AV2TyTiOJ5r6VhqeVbd9IyZ0UWs0Cwm99/76tTUjEvuvJaV 5bO/xisIsQcH5YaQAwAAiipbtcBrAKjbCp/P8+J9MZeflasNDQ2OrxOWpQP9/Y5jsw1CQKkj5AAA gKLyukj+aiik/9rXN+NrH161Sn/X358xCwaFS1iWusPhdNhMWFbG8jav/TU0GkAlIOQAAICi8rpI /lRvrwbz7Gh2x7JlhJwi+Ctbm+xDg4Oqdu29MSVNJZNKWpZjXw6NBlAJsu/mAwAAmAX3RfGmxkad un49r9d+6+JFvUHloChiCefUnUnXfJ2kpG+Ew/rE6dOaTCbVHQ5ra2+vLMvStzs69Knly7W3s5NG AyhLVHIAAEBReXXj+rM8lqpJ0pTkGKCJ2WusqsqrenZ4eFi/1dvraM+9t7NTz3d15fV9vPZgWVLB XdyAYiLkAACwBMymdfBcvseGhgZ9uL5eP3j3Xe0Nh5dsV7TFFJuakqmbFZuZ/K9r1xxfF7IPx2sP liSaF2BREXIAAFgCCumYNds789kudrE4CqmHNfl8umKr+hSyDyefRgUH+vup5mBBEXIAAFgCCumY 5RVWkpblGOD5s+Fh+auqHCHI3Z54Jj4VdiGO+XNHIKD/69ZbdTQW04Rl6Wgspu5w2DOYuEPwxoYG z0YF9mNn43H1RCJUc7BgCDkAACwB+XTMSliWngiHM4Z1HhsZ0dujo45jR6JRSTcvZL976ZL+U11d RnvimRBwSsfEdFOC8/F4+uf4wtCQXolG9ZO1ax1Bxx2Cv93Rob2dnY4qn3Qz9Nr/TdCKGguJkAMA wBLg1QzAbV8kkq7W2G1qbNQbsVjW9746OZkOPShPfePjnoNaDw8PZ1Rg3GHl4MCA/n39+oyKz47W Vsd70ooaC4kW0gAALAGmYehrbW3a1NioYyMj6olElHS1FPa60746ENAjoZBuuNoRo7L0jY9nfaw7 HNadx4/r8YsXlbSsjLCSWoqWGj66tbdX3eGwHg2FtLezk1bUWBRUcgAAWCJmaj7gXtImSdtaWrQv ElHcFYhQWXJ1v7uRTOpsPK49Fy/q1WhU/7R2redStEKaWwDzjUoOAABLxEzNB3a2ten+5mbHsVej UT1bYEMBVK4j0aj29/VpR2ur43iqQmjHHhwsJio5AAAsETM1HzANQ/6qKsexI9GoVvi4XFiKss3Y OTYyoufWrEn/ObXHqycSmbG5BbBQ+K0FAMASkLAsWZal1YGApJvL0Lz2SHgtWbvF59NV2wyVO/x+ tfn9NBuocNkWsG1qbJRpGBlL0fJpbgEsFEIOAABLwL5IRI/ZOqeZhuE5/2QqmVS1YWjStgfH3XJg e2urjl+7No9ni1JVpZszk5KWJdMwPAfHMvATpYCQAwDAEuDeH3Ggvz/jwvSJcFjfCIczXvtLV+et nkhEm5ua5vV8UZoSUroBgb+qSuPJpA4PD0ui2QBKCyEHAIAKZb/LPu7qnnV2euij/cL04MCA5/sE qqo0aluudmP6wtaQRM+1pSnbUsUD/f15V3OoAmE+EXIAAKhQ9pa+krQlGFStaert0dGM9r8Jy9Kg LcjYNZqmBj2OE3DgdjYe14dOnNCO1tYZQ8sT4XB6+OyhwUFZlqXdHR0Lc6KoeLSQBgCgArgHMSYt K2OJWq1p6vmuroz2v2+PjuqB06d1dXLS870vTEzM23mj8pyNx7X7wgX1RCI5n+euHD6bpZIIzAaV HAAAKoDXIMZsLaNTXa9SAx1T/wOK6WgsttingCWMkAMAQJlLWJYOuAZ2ZptlIind/vfYyAjhBvPm 7OiokpYlS/Lce7OtpSW9XE262dYcKBZCDgAAZW5fJJIRVrLNMklJWFZGMwKgmM6PjelDJ06oze93 dGB7JRrVT9au1a72dpmGkfdcHRoVoBCEHAAAypx7783qQCDrBWPqQjG1VC3lA36/3hkbm9fzxNLj tRTy8PCweiIR7WpvL6jdtNeSTNpVIxsaDwAAUOZSe21SdrS2Zr3DnbpQdF94RlyzcID5NJv9Ou4w 7/4asKOSAwBAmUtVbdzLfhKWpSfC4XQXq20tLTqW5eJy0qIhNBbOhGUVvPwsWyMNwAshBwCAMpdt 782+SMSxsXvPxYv6QG3tAp4ZlqI609SNGfZ7heNx9YTDesw2J0fKvfwsW5gHvBByAACoUF7Lefqz zMIBFtK5sbGMuThHYzF1h8NZKzu5GmkAboQcAAAqlHt5jySxKA3zbaYqTjYTlkVjARQNIQcAgAqU sCwlLUvLfT4NTk2lj1vsvcECMSUFTFNJSXGP4POZlSvlM8105cbdjIDGApgLQg4AABXoiXDYsR8n ZYyQgwWSVO6qzmuxmF5aty69JK07HNYLQ0Ppx2dqLMDcHORCyAEAoAK4L/gOuvY7pBBxUCqORKPp eTlS4Y0FmJuDXAg5AACUuHzuWLsv+FZUVzseN3XzzjpQSuxL0gptLMDcHORCyAEAoMTlc8fafYG3 3OfTVVsnNQIOFku1YWSdwzSXWTfMzUEu5mKfAAAAyM0dYA709yvpumh0X+Bta2nR3s5OrQ4E5v38 gFzaXLOZ7mtu1qeWL9fezs45zbp5JBTSlmBQK6urtSUY1KOh0FxPFRWEkAMAQIlzB5iz8bh6IhHH sZ1tbfp2R4dWBwJaHQjImD72wWXLFvBMgV9Z4fPp/uZmvTM25jhuWZaeW7NGu9rb59Qo4Mm+Ph0e HtZ7k5M6PDys/X19cz1lVBCWqwEAUOJ2trXpQH+/zsbj6WPu6k7qYjH1nNQkea9ZOcBCWFdf77lP 5qexmFYfP66RRELr6uv1YleXfGZ+993t+9PeHh11PHagv58Oa0ijkgMAQIkzDUM7Wlsdx7z2Hzzb 3+/4OnXR9wHXciE7LgcxX16ORrO2kD4/NpauwHyyt1cJy1J3OKytvb3qDoczlmOmpPanHRocdIR+ ybvCiaWLSg4AACUkWye1fNrrDtmGfqa+7olE1DcxkfFcU1KwqkqDicS8/D2AfB2NxdQTDqerj4cG B/VKNKqfrF2bUZVxV4bqTNMRpOiwhhRCDgAAJcTdSS1pWTINIx1unluzJutynOXV1bpqCzqxqan0 e7klJQIOFoVPkj2O30gm9YSrAnN4eNgxQyfFvfxyc1OTDg8POx4HJEIOAAAlxX0n+qlLl9LBJVv7 6IRl6Ylw2NEyWpKcXwGlYcrjmNeytqOxmLrDYUf10l3RfDQU0v6+vrwHiGLpIOQAAFBC3Heqr7qW oLlDUMKy9MDp04672UAlmLAsz/lQ7pBfyABRLB2EHAAASoj9TvXbo6MZm6vdy3H2RSIEHFSMZaap UG2ttre0ZAR69tugEHRXAwCghJiGoV3t7Xq+qyujo9qWYDBjOQ4Xfqgko8mkzsbjMgxDm5uaHI+x 3waFoJIDAECJ8uqoZkmOfQobGxqYg4OKc2xkRM+tWZP+M/ttUChCDgAAJSpV1bHrDocd+xS+3dGh LcEgS9ZQUd4eHVVPJMJwT8way9UAAFgk+Q5AtHMvT3tjZET3NDVpdSCgZXlOjQdKUZ1paoXv5v33 s/G4dl+4oE+cPp3X5wJwo5IDAMAicc/Ekbw7RdkHhI67Wu1OWFZ6iCJQzjY3NanGMPTC0FD6WLZ5 OcBMCDkAACySfLtH2cOQdLMBQa1palNjo47GYvN6jsBCOTw8rNv9/ozjB/r7WbaGglHXBgBgkbi7 RWXrHuUOP7Wmqee7urSrvT2jA9WWYFC/dcstuq+piTuZKDvnx8Yygs7ZeFw9kYik2S3xxNLE7z8A ABaJV/c0L+4BoePJpLb29qYnvqfeY0NDg5KWpX947z0NTk15TpYHSt3qZctUZRiOGVGpoJ/vEk+A kAMAwCLx6p7mxR6GxhKJdCe1Q4OD+rtf/lKfu/VWPbdmjXoiEe1hfw7K3IRlaUdrq2OJZqrK6bXE 075nLXWzgKVtIOQAAFDiUmEoYVlqff11x2Pnxsa0+8IFWZalN65dW6QzBIqnxjCyVjndVc1NjY1U d+BpTiHn3Llz+sM//EN9/vOf12c/+1l9/etf15kzZxQMBiVJX/jCF3TPPfcU5UQBAFjq9kUiujrl vQjtzy9f1pdvu43BoCh7E5al3z5zRpsaG/XcmjWOqoxX+PntM2ccr8/WwANLy6xDTjwe1+OPP65N mzY5jn/1q18l2AAAMA9yXbxdnZyUJemDtbV6e3x84U4KKKJlpulYjik5qzJeSzy9qjvArLur1dbW 6nvf+55WrlxZzPMBAABZzHTxdvzaNbUHAgt0NkDxTbq6peVTldnZ1qa9nZ361PLl2tvZmbWBB5aW WVdyTNNUTU1NxvGDBw/qmWee0YoVK7Rnzx41NzfP6QQBAChlC7XpeSKZ1M+Gh1VnmgpUVWk0kdCo azDopsZG/eCXvyz69wYWijvk5FOVybeBB5YWw7Lm1mD8r/7qrxQMBvXZz35Wb7zxhpqbm3XnnXfq 6aef1sDAgPbs2ZP1tSdPnpzLtwYAYNE9Mz6uv56YSH/9BzU1+v3a2qJ/nz8cHdXxRCL9daMk+z3u Rkn/XFen/3LjBq2jUVZMSfa43m4YCpmmJiVVW5bW+nz6fE0NHdOgu+++O+/nFrW72saNG9N/vu++ +/TNb35zxtcUcrIoLSdPnuTnV8b4+ZUvfnal5Zu9vZJtP0CkoUF3d3Wlv3ZXerZcuaIP//qvF/x9 Lrz+umQLOf7qaq2sqtL5sTFJNwPPyytXKmlruwuUA/fd9v+7vV3/EovpX6f35vzrxIRuu+22OVdr +N1Z3gotjsx6T46XL33pS+rr65MkHT9+XHfccUcx3x4AgJLjXk7j/jrV3vbQ4KB2X7igH9iqPvlI TXh3T3ZfV1+vO+vqHMeOjYyo0zUtHih19n/Zt0//+001H0jx2puT+mxs7e31/IxgaZt1Jeett95S T0+P3n33Xfl8Pr300kvavn27vvKVrygQCKiurk7d3d3FPFcAAEpOtnkeKe6Ls15bNSYf9hkgklRn mtrc1KQXu7q0v6/P0VVqQ0OD7q6r07cjESW93gwocZHxcR0cGMg47rU3h/k4yGXWIeeuu+7Ss88+ m3F8y5YtczohAADKyUybnt3tbbuqqgp6f3dIujcY1PPTy+HcASthWfpWJJLxHst9PsWmptirg5I3 YVk6G487jt3u9+toLKbucNjR2MP92WA+DuyKuicHAAA4uYPIlitXCnq9OySNJ5Pa2tubrhqlAlbC stT6+uuO15qSgj6fBrMMEAVK1Yrqam1sbNR4MqnDw8M6PzamF4aGJP2qWsN8HORCyAEAYB7ZKz0J y9KXLl/Wn9pCSq6OUfa20ZakgGF4DkpMWJY+ceqUrrrCTFIi4KAsLff59HxXl7b29jqO26s1My0V xdJGyAEAYIHsi0RutpseHMxrD8Gnent1JBpNfz3qejx1wbcvEnE8Dyh321paJOWu1jAfB7kQcgAA KMBchn8Wuofg1PXrOR8fSySUtCz2IqDsLTNNhabnS21raUmHF6o1mC1CDgAABZhLR6eZ9hC4A9Ta urqcFZoj0ah6IpGM95WkgKS498uAkjOaTGpHa2t6+WXPLG8kACmEHABA2ZtLdaVQs+3olLAsJS1L 7YYhv9+v7S0t2tnW5jj3eCKhl6dDzaHBQX2rvV2GYejU9etqrKpSbGpKV1x7bI6NjOi5NWtkWZae nW69+5mVK/VaLMYSNpSVo7GYJFpDozgIOQCAsue+KHolGlWtaeYVeAoNSIV0dLK/d6pLlCQpHtez AwMyDENJy9Keixc9X/94JKJvdnToJ2vXyjQMdYfDjpk5qe9vGoZ2d3RoZ3u79kUiOtDfn9GGFyh1 48mb053cNw4O9PdTzUHBCDkAgLLnvijy6kCWTba7xu7w80gopCf7+vR6NKrb/X6NJBJaV1+vR0Mh z/dNWJYeOH06Y3J7ytl4XLsvXNDqQCDruU1aVvrcdrW3a2dbm5KWlR6W+NmVK2VZVrqldK7ABJS6 vvFxSZk3Es7G4+qJRKjmoCCEHABA2fPak5Iy03Iy9+OpoYP2akiqOuQOLIeHh7W/r8/z4mtfJJI1 4BQqdY6mYeixjg491tGhiWRSd504ofNjY+lzzBWYgFJ3aXxc3eGwHg2FMqqRNNdAoQg5AICSMpv9 NfYOTI5lYZI2NDSoOxzO+n7ugDRhq57YpfYLuB3o73e895Rl6VO9vXo1z/0w21taZBiGjo2MaH19 vf4lFtOxkRHdmF66kzpHt0/19qYDToplWXl9T6AU1Jmm49/5jWRSuy9c0IH+frX5/Y6Qw6BPFIqQ AwAoKbPZdGyfl5F0dWZK2kKL1/ulAtLRWEwTlpW1bbP9YszubDyus/G4Dg0OKpFM6rWRkbwrOKsD AVmS3hgZ0Yfr6/VqLKY3RkbkNwxtbG6W3zS1uakpfY7xREJr33xTkfFxTXkEmkRe3xUoDRsaGnR5 YkKXxscdn6/UZ2pLMOjYWwcUgpADAFhwuao1s+1eluIeEOiemO7exJx6vtemfrdlhqHRHNWSv7h8 uaDN0YOTk+k9NPZq0g1JL0ej2hIM6tjIiHoiET0SCmnVsWMacnVXSwlWVaX3NADl4KdZqqMptaap 57u6FuhsUGkIOQCAeZEryOTa7D/uqpjMdplK6vu/PTrqOJ5tE3M+YcpfVaXRLCFDkuLJpFpravTe 5GRe53g1x3tJzgYKr0SjWQOOJA0nqOOgfKX2k9mXqG1saMh43kK2i0d5I+QAAOZFrmVn2ao17s36 W4LBWS9TsX9/t2MjIxkXS+sbGrI2L0gZmprSMtPUpGVp0qOik5QUdu2TKZZse4KAStDm9yvsanvu VTNlhg7yRcgBAMyLXMvOss2acb+m1jRnfZc2V2XmZ8PDuvP4cUdnsvuamvJ639Ese3Okm5Wc+ZJt TxBQ7m5f6ymQAAAgAElEQVT3+z33sR2/di3j2FyXs2LpMBf7BAAAlcm9zMz+9SOhkLYEg1pZXa0t wWB61kyu10g3l6p0h8Pa2tur7nBYSVc1xf64e9mb3Y1kMqMz2auLVClhoQ2WKlPSHX5/1otRr6Wq M/2OAFKo5AAA5oW9rbO7O9KTfX3pO7f2WTOPhEJ6JRrVqevXPQdtei1V+VpbW3rZmbt99JZgUKeu X89rj0zu3THzh6bPWKqSks55LO9cHQhoR2ur51LVXL9XADtCDgBgXri7nNllW3KSLfzkel2uvTen rl9XY1VV3o0AACyOFT6fNjY1zdhMINfvFcCO5WoAgAWXbcnJTOvt3a97e3RUB/r7s36f9yYnM5al AQAqH5UcAMCCy7bkxN2QYENDgx6/eFEHBwYkSZ9ZuVKPd3To2YGB9MBAAOWn2jAcHQqvTk3p0OAg HdNQNIQcAMCCy7bkxB5+NjQ06NVoVEei0fTj3wiHtbezUx9ctswRcFYHAhqemmJZGlAGtgSD+khj o/4kHPZ8nI5pKAZCDgBg3qVm0hyNxTRhWaoxDG1uatIjoZCe7OtLhxpL0t9PV23GEglHwEk50N+v QddQzB2trUpalvZcvLgAfxsAs2FvKPDbZ85kfR4d01AMhBwAwLzzag7wwtCQXolG040G3IM4sy1F cx//QG2tkpalZ3PszQGweHyS7mlq0k/WrZPPvLkd3L00dUswqFrTpGMaioaQAwAoilS1xr7PxpL0 RDisnkjE8zWnrl+f8/d9Z3ycCg5QwqYkvRyLqScSkWkYOjYyoo0NDfp2R4eOX7s2Y0c1YDYIOQCA ovCaYSMpZwBZV1/vOencbnUgoL7xcY3mGO4JoPQdnG4YIt38HbG3s1PPd3Ut8lmhUhFyAABFMVP7 55QVPp82NDZqc1OTHg2FtObNN2fskkbAAcrHr9XW6hfj4xnHLcs5+pYGA5hPzMkBABSF1+ybDQ0N Gc/7SiikQ2vXald7u3ymqR2trTnf95LHxRKA0nRfU5P+Y/167e3s1B2BgOOxkN/v+Hqjx+8HoFio 5AAAPPfTFLo+3j375pFQSJ88fdrxnPubmzM2Fae+PhqLaTyZVGRsTEOJhCzL0uDUlG5QxQHKxseC QX3n0iUdGxnRkKulu3sPnrOuAxQXIQcA4LmfptBhfO7ZN93hcEYL6MjYmJ4Ih/XGtWvpKs8bIyPp ttL3BoN6JBTSvkgka7MCAKXLvu/GLZZIOL4+fu3aQpwSlihCDgAgr/00hVZ7vN7j3NiYHptuROBu GS3dbCv9Z319GnLNwQFQ/hpNU4O2oMM8HMwnQg4AIGNmhdfFR6HVng0NDZ5BZiYEHKD8fDIY1G80 N8uyrPSNDLeHV61SlWk6bpQA84WQAwDI2E/jdfGRb/e0lCn20gBLxjtjY/oNSV9ra9Mr0ahjqeoK n0/Lq6tlGgbzcLBgCDkAgIz9NF7c1Z7xZFJJy8p6wfLf3n23qOcIoHSdjcfTld57mpsdIefq1JSu Tk3psYsXZeTxuwYoBlpIAwDy8kgopNttLWAPDw97NgeYSCb1f546patZlp1VcxcXKHvZPscH+vv1 Ro4qL7NxsFCo5AAA8rIvEtH5sTHHsWMjIxkNCX42PJzRVS0lWFWlYVeHJQDlZ09bm6pMUwf6+x3d 1M7G42pzzcOxo9kAFgohBwCQl4MDAxnHNjU2ZjQkqDOzLxIg4ACVIbXsbGdbmz504oQj6NQYhvZ2 durYyIg2NDTIkPTGtWs0G8CCIuQAAGZlhc+nR0Ihdb35puN4wDQZ4AlUuNSMG9MwtKO1NX2jQ5KO j4xoY2OjnluzZlZNBooxnBgg5AAA8rKtpUV7bK1hH161Sk/29WUM/ltXVyfDMHT6xg1NWRYtoYEK NJZIaGtvrzY1NurRUEivRKM6PDws6WajgT0XL87Y0CRbmCnGcGKAkAMAyMuu9naZhpG+IPGq4kjS y7GYVgcCenjVKr0ejerF6QsfAJUjte/u0OCgXolGVeNRaZmpyUC2MFNou3rACyEHAJD1jmquZSPd 4XBGFScl1U52RXX1Qv41ACyCw8PD2hIMZhyfqclAtjCTz3BiYCaEHABYInIFlmx3VHMtG8nn7urV ycmi/z0AlJ4aw9DjHR16drpBybaWlhmbDGQLM/kMJwZmQsgBgCWikMCS+jrXspENDQ2OCxQAS8cH /H69Y2spv7mpSbva27W7oyN9Q+W3z5zJ2TggW5jJZzgxMBNCDgAsEbkCS7Y7qu7jPx0e1urjx9VW W6uIa2YOgMq3srpaD69apT9etUpbz5zRqevXta6+Xo+GQunn5Ns4gDCD+UTIAYAKZl+iNu5q62xf 557tjurOtjZH16TRZFLn4nGdy7IXB0DlqPNoB//wqlXa1d6u7nA4/Xvh8PCw9vf1zVgZBhYSIQcA Kpj9jqokbQkGVWuaGevcs91RNQ1DtTmGe9q5l68AKG+ramsdzUW2BIOOGyJ2+VSGgYVEyAGACua+ EKk1TT3f1TXj6xKWpb0XL+ovL19WLJGY8fmrAwGd+fCH1XL0KHNxgAoRqq1N/3l7S4u+Pt1GXsod ZGgcgFJAyAGACjbbO6r7IhF9Ixx2HAuYpqYsS5OWlfH8K5OTqnvtNc/HAJSfasNIz8KRJMMwHM0D cgUZ9tqgFBByAKCC5XNH1au1tNca+oaqKknSex5toaneAJXFfcPC/TuBIINSR8gBgAqTax6OF69O SO4KkCStq6/XL+Jxz5ADoLSZkpIzPis79tWg3OS3mxQAUDZSoeXQ4KB2X7ignkgk5/OPxmKOr1+P RmVZlu4IBLTMNLXMMHR/c7Ne7OqSyXI0oCxlCzh1rsYiK3zO+9+rAwHt7exkXw3KDpUcAKgwuboe eVV5JlzB5Vw8rhenW8NK0rc7OmQahh586y1dpooDlAWfYWjK9dmuNgz9mt/v6Ji2uakp3Qpakr68 apUMw8i7EgyUKkIOAFSYXM0GvJam1bguYEZc3dQODgw4LooAlD53wJGkJp9P/75+vXoiER2NxTRh WarWzdbQNYahzU1NhBpUDEIOAFSYXM0GvKo8m5ua9MLQUPrYuvp6x53dS+Pj83zGABbCw7fdlm4Y 0B0OO2Zo7e3s1Nfa2tRTwH4+oJQRcgCgwuTqeuRV5XGHokdDIe3v69OB/n6djcczJp4DKC/LTFO7 29tnvOHhVemlgxrKFSEHAJYQryqPe1FLKiQdGxlhmRpQAT7W1JQRVrxueOTazweUG0IOACwB7oYD z61Zk16GYl+2krro+Vpbm8ap4KDCLDNNTWYZaGt3u9+vd8bGMm4AlIM601TANHXVNrvqN5qbM57n dcOjJxKZ1fBgoBQRcgBgCci1DMXdQvpoLKZ9kYhjXw5QKry6huXDlDRqC+6rAwFNJpP6hWvP2TLT 1Pmxsbme5qxVG8aMISyXVbW12t7SIkvS8WvXsg4B9lrWms/wYKBcEHIAYAnItQzF3UL62MiI3rx2 bUHOCyjUbAKO5D0nptrMHBc41232K6qr9Z/q6nQkGp3xuctM0xG8JOmjTU36WHOzjl+7po0NDemw 8h83buidLOFrSzCoyNiYzsbjOhuP67GLF7W3s1PPd3UVdO659vPZFTpwGFgMhBwAWAJytZWudl2c DNmWuQDlZoXPpy+vWqWEZekf3ntP0s0Oge4GGtn2m21qbMwroGSz3OdTrWnq/uZmRcbGZBiGtrW0 yLIs/cXly45lZJsbG9U3Pq6+8fF02Hk5GtWl8XG1+f3p7ofPrVmjpGXpk729+l/XrqnR51OVYciQ 9JmVK2Uahv7y+nXHeWTbT1OMgEKDApQDQg4ALAG5lqHMZWkMUGpu8fl0bGREE5al2wMBbW5q0s+G hx3BxauCIt3ci/M/1qzR2n/7t1kvWUtVU6SbbZntF/+7OzrSLZrHk8msS0Lt75Fq776rvV3/vG5d Ruvnfx0Z8XyfbPtpihFQaFCAckDIAYAlwL0MJWFZ6g6HdWxkRGE6qKGCnBsb0zlbQHlhaEj3NTVp hc+neDKpTY2NsnSzYuJ2fmxMXf/2b1mXhc1kRXW1rk5Opr9OXfy7qyf/7113qevNN/N+X3uIcAeK V11/j5XV1Xp41aqs+2mKEVByVYaBUkHIAYAlJmFZeuD0aRoLYMl42dZc495gUK/nWI42m4BTbRi6 p6lJH21q0p+Ew+njqYt/d/XklWg0Y7nciupqybIcy9nc75P6sz1guPfUPbxqVfqGhtfStGIEFBoU oBwQcgBgifHqnLY6ENDtgYDGkkmdun5dsakpTWZ5PVDOjo2MFPRvu9ow9CfToeGf+/rkb2zM+PxM WpaORKP6WHOz9nZ2Zlz8u6slp1z7ZySlK0BbgkHVGIYmLEs1hqHNTU2OEJH681OXLuk9W9XIq4Lj tTStGAEl3wYFwGIi5ADAEpG6q/vUpUsZj+1obXVctNx5/DiDQFHWbvf7tXrZMk1YliOUbGho0MGB AcdzV/h8nhUUSfpGe7t2d3RIkh4YHNR/XrtWHzpxwvPz8ca1a54dzdzVk3X19VkrqbWmmbMrmj1g 2Pfm2Cs4KV5L0wgoWCoIOQCwRNjv6tptCQYz7uZaNCNAGVvu82n1smXa3NSkR0Mh7e/rS1cukpaV EVAeXrVKpmHoQH+/47EtwaC+7goEpmFoR2ur52cp29Ivd/XEfk7uBgT5Lh/LpyLD3hksZYQcAFgi 3Hd17ctbUi1kE5alJ8LhRR2GCMzV4NSUXhga0gtDQzrQ368dra16bs0amYahrb29jueu8Pm0s61N PtPUzra2dPezXO2VU4HiaCyWdVmZnVf1JPV10rIyvmc+8qnIsHcGSxkhBwCWCPdd3YdXrdLXbBd1 Gxoa9Go0OqcZIUCpORuPp6suu9rbMz4HV6emtL+vT7va2/NeylXMJV/zuXyMpWlYygg5ALBEeN3V 7fHYmAxUolQlc2dbW8aytAP9/XMajgmg9BByAKBCebWPdc/KOdDfv4hnCCyc1H4Urz01qeGbhQ7H 9PqMFRqQivEeADIRcgCgQuWabJ6alUMHNVSy2/1+jSQSWldfr0dDofRxe1Xz7dFRx+egkOGYuT5j Un4BZqb3ADA75lxefO7cOW3ZskV///d/L0nq7+/X9u3btW3bNn3lK1/R5CRTFgBgsXi1j01YlrrD Yd114gTDQFHRbvf7dX5sTO9NTurw8LD29/WlH0vtVXm+q0s7WlsdryukA5nXZ8wuFWAODQ5q94UL 6olECn4PALMz65ATj8f1+OOPa9OmTeljTz31lLZv366DBw+qra1NP/7xj4tykgCAwrkv1jY0NOiB 06e1+8IFKjioaKkZOXbZwsPOtjbt7ezUp5Yv197OTkcHstRNga29veoOh5V0tVZ3f8bcX+cTYGZ6 DwCzM+vlarW1tfre976np59+On3sxIkT+tM//VNJ0r333qtnnnlGn/70p+d+lgCAgrkbDSRdQxGB SpWakfPC0FD6WLbwkKsDmXsp2f+oqtL7envTS89matGcz5wa2jwD82PWIcc0TdXU1DiOxeNxVVdX S5KWL1+uK1euzO3sAACz5r54c88HSVkdCGhbS4veGBnR0VhMw4nEQp0iMC82NDTIsiytDgQkSdta WmYVHtyVl+OJhDQ46Ng7k2v/TD4BhjbPwPyYt8YDTMsGgNLivqucsqO1Vbva29UdDjvufAPl6l9i Mce8J9MwZtWxLNtnRspv7wwBBlg8RQ05dXV1mpiYUE1NjQYGBrRy5coZX3Py5MlingIWGD+/8sbP r3zN5me3xbJ0uaZGp6emNGkYqpa0tqpKW65c0cmrV/VPo6NZX2tKSs7+dIEF9XPXQNufRCL6zatX C36f1GemN5HQhKYrOdParl3jd2gZ4me2dBQ15GzatEkvvfSStm7dqpdeekkf+chHZnzN3XffXcxT wAI6efIkP78yxs+vfM3lZ/fhHI8FTp2SsuzZIeCgnNwdDDr2n32irU13z7KikvrMJC1L/8+xY4o0 NDDPpkzx//fKW6EBddYh56233lJPT4/effdd+Xw+vfTSS/rOd76jnTt36kc/+pHe//7368EHH5zt 2wMAcpiPAYI1rtcvMwyNsvQYZabONPViV5d6IhEdHBiQdHMJfdKy5vQZMQ1Dv19bq7u7uop1qgDm 0axDzl133aVnn3024/gzzzwzpxMCAMzM3fUpdQFnDz3W9PO8gpA7JD0SCmnCFWiYdIZy1FpTk96D k2qV/tjFi3p2YEA7Wltn/GwAqAzz1ngAADB/3JueDw4MpC/o7Buls01Sd4ekV6LRjPbSk1RxUIbe GRtTz3SAsTsbj6f/zUvZPxsAKsOsh4ECABbPTAMDj8ZiOtDf7zhmv+hzXwCeun69eCcHLLJUhSbb Y/kM6QRQ3gg5AFBGEpalZ8bHdTQW05ZgUL91yy3a29mp7S0tjudNWFa6spNiv+hzXwCuq6+fv5MG FtiGhgbtbGvTlmAw47FNjY0Z//5numkAoPywXA0A5mA+GgDksi8S0V9PTEjT82z2dnZqV3u7kpYl w7Yn52gs5njd6kDAMYjQPaTw0VBIa958MyMYAeXo4MCAzOk26Xbuz0GuIZ0AyhshBwDmwGtvS61p zlvgybbMxj100D3Yc0drqyxJj1+8mO44tb2lRc+tWZM+xza/n5CDipDaf3O73+843ub3p/+9swcH qGyEHACYA3foSG3ez2czc7YqUK7qkHsCe7ZlNu5Kzc62NvVEItpz8WL6OY9dvChjOhwlLEuRsbHC /wMAJSw8Pu742t0mHUDlIuQAwBy4Q4fdTJuZ3VUg6WYoynZcuhleLl++7BhI6MVd2cl2Pqlj+yIR qjioOO4OgZubmhbpTAAsNEIOAMyBvWIynkw62jCPJ5Pa2tubdelatqVn7uMH+vvTr/caSJjvviCv QDaeTCppWXSXQsVz78cBUNkIOQAwB/aKSdKy0vM57IHn0OCgDvT3pwcRZlt6NpZIaO/Fi3p7dNTx Pc7G4+qJRLIufct3MKhlWbrD79eliQmNJpOSbi6v64lEclakgEqwo7WVgZ/AEkLIAYAisQeerb29 jsdSG6GT08tnDg4MyLIsfcDv1zvTe2GORKM6Eo16vrdXpSVVwXnq0iXHcfdg0FeiUd3T1KTHbPtx 3O/93Jo16T//dHg4HYKAcrfMNPW1UEhJy8pZWQVQWQg5ADAPslVGeiIR3ZhFgNjQ0KDucFhHYzFd HR3VitOnNWFZjuVxKYNTU46vDw8P63/mGPa5qbFRqZ0LlmXJcu1jAEqZIenbHR2y5Az4KaPJpP51 ZKSgpiAAyh8hB8CSNx+zblJr/w/09zsuugoJOCt8Pi2vrta2lhYZUnpJmqT0nBwvXiHl6uSk4+v7 m5vlr6pK/327w2FH5zWgXFRJ+np7u0zDSLdHdzvlCvnsQQMqHyEHwJLn1c3sa21teQWfbAEptXQt 1br5qUuX9J4raMzk6tSUrk5N6Qf9/eqfmMj7de5Kjpd7mpv1WEdH+u/gXvIGlIspKeeeNUlaV1/v qHpma70OoHIQcgAsee67uk9duqRXotG8lrfks+l/V3u74/0K9c48zK95w/Z33heJ6GoewQgoVakO hNtaWhwVyTv8fn3u1lv1x6tWaeuZMzp1/brW1dfr0VBo8U4WwIIg5ABYkuwVmHHXErL3JiczAkkq CCUsS0+Ew3q2v19DU1OKu1771KVL6cBgrwqFZ5hBE5C0kFNqxpPJ9N+lJxJZwO8MFN/ZeFwfOnFC 21pa9HhHh964ds1RWe0Oh9Of6cPDw9rf18eeHKDCEXIALEn2CowkbQkGdTQWy7pnZlNjoxKWpQdO n85ZkXFXRA709+tAf7/OzVCNqfP5FF/AasrRWGzGvwtQTs7G49pz8aL2dnbqedscKSn7TCoAlctc 7BMAgLlKWJa6w2Ft7e1VdzicbtOci/siJzI2plW1tY5jy0xTdwQCWlFdrQP9/frEqVMFh4Kz8XhG tycv0QVeLjaapTMbUO68Aox7Dw57coDKRyUHQNnzahzgXoribhCwsaHB0eL5bDyu+5ubHYFkNJnU uemvr05O5hVWZqtcdsSYkpigg1JSbRiatN3Y8AowqW6H9r1ybvPRZRHA4iHkACh7+SxFcQehb3d0 aHUg4AgutaaZcQxOBBwsptTyE/u/w482NupjwaCO2/bhZLzONqg3m3xulgAoHyxXA1D2si1FSS1j +61Tp7Q3HHY859n+fvWNjzuObW5q0raWlvk9WQCz9u3OTk3ec4/ub25OH3s5FpMkPd/VpV3T83Jm g307QGWhkgOg7KXu3B6NxTRhWToai6X35mQbcOluBPCB2tr0UEw3U5I1/T8AC291IKBtLS2yLEtb T5/Wq9PBJuWpS5cclZzZBJ1NjY2OJazs2wHKGyEHQMmbaa18ailKdzicXm7ywtCQVgcCnu9nKDOw RCYm9KETJ9Tn0QWNJVrA4ppMJPRKNKqXo1HPx69OTenQ4OCclpnls28HQPkg5AAoee618gf6+7Wj tTUj7Bx13d3NxufaqCxJk5bFXhygRP1iYkK/mJjI67mzXWaWz74dAOWDPTkASp77ouVsPK7dFy5k DLGccAWXUG2t9nZ26pPBoG7x/eqejjvgAChf9s+2xDIzADdRyQFQ8txr5VPs4SdhWQq7KjE101Ue 0zT1vupqDS3wLBoA86fGMNRWW6sP+v2aMgzVGIY2NzWxzAyAJEIOgBKXsCxZlqXVgYAGJyd11RZU NjU2pvfrHOjvz2gmMGFZ6WVuAMrbr9XW6he2joj3NDfr8PCwzk9/7vd2drLcDEAaIQdASdsXiegx W4e0LcGgak0zvTG4Oxz27KC2zDQV8WgiAKA83blsmb7w/venGwO49+DR8hmAHSEHQElzX7jUmqae 7+pKf31wYMDzdaPJpC7luVEZQOmblLNrWnc4rBeGhtJfjyeTSlrWrOfkAKgsNB4AUNKyDfrMx2iS 5s9ApYiMjWkymVR3OKytvb1KWpZjKOjh4eGMZiReUkOCt/b2pudpAag8VHIAlKyEZWkqmdQKn0/x ZFKbGhv1aCjkeM62lpasAz8BVI6z8bh+q7dXh4eHJd1sJ++ehZXPkjV3S3ppdnN1AJQ2Qg6AkrUv EtE3wuH010eiUXWHwzINI71M7baaGq3w+TSaSKjWMDRM9QaoWKeuX8/5eD6VXncQYi8PUJkIOQBK ltfFx19evuzosGYf4DnKshOgYgQMQ1NyzrVaV1+fruRI0vaWFhmGkW5GkE/7aHdLeubqAJWJkAOg JCUsS+MeVZk4lRpgSYhPhxt7R8VHQyHt7+tzhJpCGw2kglAhwQhA+SHkAJgXqfk1s70Y2ReJOO7Y pmxsbNTL0WgxTxVACVhmmp7NQtwdFee6f8Y0DPbgAEsAIQfAvJjr5l73DIyV1dV6eNUqTSQShByg gtQYhu5pbtahNWv0nUuXdKC/37EMNbWcbK43TgAsLYQcAHkp9AJjrpt7J1z7a9bV1+trbW1qef31 gt4HQGmpkpSwfT1hWTo8PKzbjh3T8upqfWblSlVN77OZsCwdjcXSrZ5TnRTpigZgJoQcAHkptDIz 1829Na4AFY7H1Xr0qAZtTQckyZBEuwGgdLk/o9k+r1enpnR1akrfCIe1t7NTm5ua0r9zXhga0gqf 85KFrmgAciHkAMhLIZWZhGXJsqz0DIttLS0Fbe5NWFZGJefc2Jjncwk4QGm7t6lJP7UtP/Vn2Xtj 5/X75arrBgdd0QDkQsgBkJdCKjP7IhE9ZhvQaRpGzqVt7qVw1vTyFQDlrXp6v4095AQMQ6MzvC71 +8X+O8dudSBAVzQAORFyAOSlkLarhVZ9PnHqlI5MNxM4NDioO1xTzAGUr//27ruOrwcTiSzPvOn+ 5mbH75enLl3Se5OTjufsaG2l6QCAnAg5APJSSNvVQqs+R1zd0i5kWZoGoLxMWlZGQPFSbRj6Nb9f 21patKu9PR1gUr9zUntzpJtzcwqt4tCZDVh6CDkAis6r6pPtIsOryjNpsdMGKHfVhpH3Z/nX/H79 7w0bPB/z+n1SaECZa0t7AOWHkAOg6LyqPt3hsOdFhrvqA6AyFHKzYntLS9bHijG8c64t7QGUH3Ox TwBA5UtYlg709zuOpS4ydra16fGODq2orl6MUwOwQO7w+1XtqsDUmab2dnbq6/NcVXEvmaUzG1D5 qOQAmHf7IhHHBHPpVxcZU5alV2MxjbjawwKoLJ+79VZZluXovPj1trYFWTZWSOMUAJWBkANg3rmX hqwOBPRIKKTHL17UE5HIjDMzAJSmgGEo7rEs7b6mJl2amNDg1JSW+3yOWVmGYehoLKYJy9KxkRF1 h8Pa2dYmS5q35gDFWPIGoLwQcgDMO/e+m1BtrR44dUov22ZnACg/mxobHTNwVgcC2tHaqqRlac90 xebq5KRjVtau9nbHHr0XhobSr6c5AIBiIeQAmHc729r0SjSaHvDpbhkNoDxdnpjQ3s7OjOrL1t5e x/Nm2vjv1QiA5gAA5oKQA2DemYahGmZSABXJq9oy06ysbI/nO18LAGZCyAEwr1Lzcd5gaRpQcVbV 1GgymdSTfX2Oak62jf6p3wdHYzFtCQZVYxja3NTkaARAcwAAxUDIATAvUhczB/r7MzqrAagML8di aj16VEPT3RHte2m8Kjz2oZyStLez0/E89uAAKBZCDoCiSQWbYyMjGksk2HsDLAFDrvbvufbSMJQT wEIh5AAoGvddWgBLT669NDPt1QGAYiHkAJizVAXnqUuXFvtUABTIkJQ56Sb34yuqq7Xc59N7ExMa TiTSxz/g9+fcS8NQTgALhZADYM6o4ACL75aqKr2vpkaSZFmWzo2N5fW6D/j9Op/juct9Pl21LUkz p4+Famsz9tt9rqUl5wBPhnICWCjmYp8AgPKVsCx1h8MZFZyV1dVaZmb+ermlqopfOsA8qDYMbWpq 0uTnBycAACAASURBVI7WVv37+vX63K235vW6W3w+nf71X9cKX+Y9z9WBgPZ2durhVascx5OSzsbj nnvuTly/PqvzB4Bio5IDICd7M4FNjY16JBRKt4sdTybTAz7t1tXXex4fsi1rATA7waoqxxIxSZq0 LL0wNKQXhoZ0oL9f21ta9O2ODh0cGMja3fB2v1//sX699vf1OSo1krQlGNRP1q6VaRhKWpZMw9BT ly7pvcnJnOfGHhsApYKQAyAn+1K0Q4ODeiUa9Qww0s0Kztq6Or2eZ1c1UzfvCgPlYplpypAUMM2M YLAQqg1D76up0XCOtuxn43E9dvGiHu/o0L+vX68ej1bu9hDj7nC2OhBIPyY5l5i5l6Xe39ysvvFx SdK2lhb22AAoGYQcADm5L4BO5ViOkrSsgtpGE3BQKqoNQ5PWr7bX3+73a3hiQqOSJpJJmdOPjyZv /qu9taZmUULOpGXpXJ5zp54dGNDujg7tam/XsZERR8ipNc10iHF3PNvR2irTMDKquI+GQrIsS88O DEi6GWp2tbfn3IMDAIuFkAMgJ/cFkHsp2u1+v345MaEbyeSiXPQBc3W736+3PvxhfefSJceyzH2R iA5OX9C7N/KfHxvTfU1N+peREUc4mo0VPp+WV1dnXVZmSqpyhbBCuT/HY4mEHr94UcevXdOGhgY9 3tGhN65dc3Q8c1dxJWl3R4d2d3TM+jwAYKEQcgDk5G75+mgopP3Te3IY+IlKcH5sTD2RiHy2ZhmP X7yoP41Ecr7ujWvXcgaP5VVVavL59Ivp5VzZ3OLzaXtLiyxJz/b3Z3RFC5imAlVVuppjP8wKVwc0 SQrV1qb30+xsa3MsNT0SjaY/u4cGB7W3s1PPd3U5Xs/gTgDljJADICevlq+pr+88fnwxTgkoum+H w0pFhEODg8pnAdaNpHPB5TLT1KqaGhmGkV7KJUk9kYj+++XLOj8x4fk+58bG9NjFi9rb2ak76uoy Qk5rTY3e8WjxvMw0dW9zszY3NenR6crTn1++nA5DR6JR9UQi6SVltR4dD1O8AgyDOwGUM7q5Aiia OtNUXY4LKaBUuRda5loYlu3u4Ggyqc/deqv+94YNeqyjQ6ZhpG8S3NnQMOM5pKqldrf7/VodCGT9 fpubmrSrvV0+09Tujg5tdL3+QH+/ktPVplwhxeuxnW1t2tvZqU8tX669nZ00FQBQVqjkAJiVhGVl DAP8elubXo3FHHt2AqaphGVpYo77FoBS0ejzaSjL/rNsS7rcVZFsz3EvD93Z1qaeSEQvZulo6P5+ 7u9zNh5PV3MeCYX0SjSqU9eva21dnT7S1KQ3r193fF87BncCKGeEHACzsi8ScezH2RIM6uvt7fqa Zen/OHEiPUE9nqSHGsqXocyqji9HNzF3RSTVoexoLKb7m5sVGRvTe2Nj8vl8usXnU5vfr1rT1Oam Ju1sa/MMFvbg494HN5ZIaGtvbzqo7Gxry2gXnQpCT/b1Ofbk3BsMZuzDAYBKwboSADklLEvd4bC2 9vaqOxxOL31x30GuMQz1RCL6nTNnFKXLGirACp9PEx/9qLYEg47j6+rrPZ+/JRh0VEQSlqUHTp/W 7gsX9MLQkI5Eo/rcrbfqSEODrvyX/6J/37BB9waDMmZowZwKPs93deme5mbHY0eiUR0aHNTuCxfU E4nINAztaG11PCcVvGgkAGApoZIDICevNrK72tszl8WMjuqFoaFFOUdgPjRVVenBt97SR5uadE9T U7rF8qOhkNa8+aajWpIaoGlJ6g6HdWxkROPJZMbg3GMjI/rN6T9n+2zlcvzatayPpUKL15I3iUYC AJYWQg6AnLLd/bVfSHldzAHl7p3xcb0zPq5Dg4N6vKPDsbRrR2trOqCkvjYNQ93hsOO426bGRunq VUmzq6zk2tuTCi3Z9tJkCz8AUIkIOQByynb3N3UhlbAs3XXixGKdHrAgnh0YcAzBzBYYcgWV1HK2 /zkdcmZTWbF/nw0NDTKkjCGe2dBIAMBSQsgBkNNMd3/3RSIZk9qXmaZGaTiAMpPapOr1L9ea3ptm /xx4BQZ3cNkSDKrWNNOvMW37b2ZTWSGoAEB+CDkAcprpoirbEMGXbR2ggHKQK5a3+f157Z/xCi5m lsYCBBYAmD9FDTknTpzQww8/rA9+8IOyLEurV6/WY489VsxvAaAEpNripvbjuPV5TGcHytWWYFA1 rqCSbVkawQUASkPRKznr16/XU089Vey3BVBC7F2hpJtT2c/bgs1QIrEYpwXMi9RyM3v3QDqTAUBp K3rIsZhqDlQ8913sOwIBdfj9OjYyokBVFb8HUFHcjQXoTAYApa/ow0Dfeecd/cEf/IE++9nP6ujR o8V+ewAlwH0X+1w8riPRqG4kk7o6OalBhoGiQmwJBvVoKJRehvb/rVkjSfrtM2ccw3EBAKWlqJWc 9vZ2/dEf/ZEeeOAB9fX1aceOHTp8+LB8PvobAOXMvgdnQ0ODpJvDDyUpVFurIzQZQIU6PDysNW++ qR2trdrZ1jarAZ4AgIVnWPO4ruT3fu/39Od//ue67bbbPB8/efLkfH1rAEX0zPi4/npiwvOxdsNQ mLvZWAL+oKZGvYmEXrPtOftIVZW+u2zZIp4VACwdd999d97PLWqJ5fnnn9eVK1f0+7//+7py5YoG BwfV0tKS8zWFnCxKy8mTJ/n5lbFcPz975WZTY6PCsZhk23Rt5/f7JducnGrD0CShBxUo0tCgTzQ2 6jVb0w1/Y6P+89q1WdtEe+F3Z/niZ1fe+PmVt0KLI0UNOR//+Mf1x3/8x3r55Zc1NTWlb33rWyxV A8qQe0nOlmAw63O3t7TIknRwYECSdFtNjX4aiy3EaQILakNDg5KWpRU+n65O7zs7PDysnkiEJWsA UGKKmkDq6ur0N3/zN8V8SwCz4K7E5BpI6MXdPa3GMLS3szO9J8eQ9Ma1a9rU2KhHQiF98vRpnZ2u 5py1VXWASlBjGLrn/2/v3oPjKu/7j3/O0eqyuq0kX6RgaSVxU1IsG8oEfEnCJXYSQjyZdoYOk2An nU6amSbEaSnG2BjI/LBsTKcZ/5LMtBlIqctkPIU0w89ACYYEwlQGUxNsQYtdXHslE2QjebWSZV13 z+8Pazd7zl60klfa3eP36y929+zqMUdrn895nuf7ralRxLL0UCCQ8HqqnjkAgNxhmgVwoYvdHH1j VVXsfdKFamrx748PUbd3dVF4AK42blnaHwyqO0WTW3rmAED+IeQALuS8s3yxd5qdO2yczUCBS1Gb 1xurugYAyC+EHMCFVlZXJ8zEzMSbQ0NpH08XmsoMQ6MUH0CBafN6dVV5uX4TDGo4Ekl4fX19vQzD mPUyUADA/CHkAC50sd3ZpwtJztfjXVFWpuMplvUA+cxfVqZnly7VFw8fti3B9Ei6pbZW9/n98piz 66Edv8TTPzam6yyLgAQAc4iQA7hQtDv7dFIVKLi3qUmvDgzo8LlzWl5ZqU1NTbb3xYeo/zl/3lZs oDdFPx0g3+0PBlXf2anlFRW25yeV2BR0pgHFucRzCRXZAGBOze6WFFDAwpaljkBA67q61BEIKHIR y6qy+Vm5GEP0wuu5/n5tPXFCO7u7JUmP9fRofzCoMxMT2h8MaldPj+190RC1r71dGxoabK+Ns0wN BaxvYkKvpCikcXRkxPY9mYls75MDAKTHTA4uORdbeWyuPmsm4mdgxiIR7Q8GY2N4dWBAL2bYnDDV hddMLsiiszp7ent1dGSERqBwvdkElIvdJwcAmBlCDi452byjmqu7szsCAW07eTLpazNpTui88BqL RLSuq0tjjk3X0QuysGVp+8mT+tGHH2okEtHK6mr9+7Jl2tLcrAODg/TIgess9HhU5/HoWNw+s9kE lPglnv6hISqyAcAcI+TgkpPNO6q5ujv71OnTaV+PD1vpGoPG772pLiqKzQhJ0traWpWapq1wwaPd 3bZmiC8PDOgTnZ3666YmfbqyMmUxAqBQ/XVTkzb7/drp+A7NVPw+uUOHDlF0AADmGCEHl5yLrTyW 7c9yhpB7m5r0WE/PRZWpjQ9b6ZbURffeSNKZiQnbZ5Sapva1t9ueSzZT1Tc5qa0nTmhNTc2Mxgjk qzU1NSorKtKNVVWyLEtfffddrayu1rNLl8qSEgIPgQUA8g8hB5ecTCuPZfuzUs2oOEPII4GARqaW izlDSfQzrBT7XhYXF2tjY2MsbIUtS3t6e23HxAeVdMvrxiIRTUQitsB1Y1VVytmaI8PDmfxvAPJa ncejXy1fLtMw1BEI2L6be3p75S8rs+2Bk+ZnHx4AYGYIOUCWRANIZyikcctSiWFolc8Xm5mJbsyX 7BdHzqAx4tgP0xkKxT47/jOSWVZRoQODg9rZ3a3Nfr8e7e5OOL4zFNLthw+reWxMo0VFKT9rfzCo 27u6bBd0V5eVqcY0NZCkUeKyigpbb5FkTEmJ7wTyQ53Ho49WrozNzDi/m0dHRhK+T1RJA4D8RMgB ssTZB0OSnj97Vq8ODNj2ukRFL47SNdaUpPeHh/UlR3PCVKLHPNffr98Eg+oeG0s45uzkpF6Ijmea njadoZDt8TFHk88ry8rUVl6uVT6fJiORacdIwEG++rzPp5euvVaWpI5AIFa5cDpUSQOA/ETIAbIk 1R3dw+fOJX0+enG02e/XP330kT5wBIio42NjOp4krEwnk1A0neFpLvLaysu1orpae3p7dWoWYwTy xWd8voQlatKF/TnvnDunvsnJ2HPJinIAAPILIQdwSFeNLJ1U+1Wqi4oSNvVfWVYWuzgyDUNt5eUp Q04+G4tEUpayBgrJT37/ez18+eUJNyt6xsYSAk6mfagAALlj5noAQL6JLjt7rr9/1t3N430wOirn 5dBgOGy7SFpRoEteugswmAHJhMJhRSxr2uVnpaZJwAGAAsBMDuAw2wafbw4NpXzNWQutemrDf3TW aLq+N/nqfwk5cIkJy4oV7JD+UBbesiw9EDdbyR4cACgMhBzAIVWDz3TL2MKWldEm5aj/HR1V5W9/ q4aSEh0v4KAwOf0hQME4MDiYUBY+YlkyDCMrfbUAAPOHkAM4pGrwmaqpZtiydNuRI0krqKUS0YVN /YUccIBCt8DjUX/cfpsbq6oSjsm0F9Zs9/IBAOYGIQeuNpsLj1QXNc5yytHHj3Z3zyjgAMi9YsPQ guJiW8i5mEiS6iYIACA3CDlwtUwvPDIJQ+OWfWfNgcFBfeXIEX2QpjnnpcxQ4l4kIF9MWJaOOb67 b6TZVzed2e7lAwDMDUIOXC3dhUd8sBmLRGKzMc/19+vVgQFbHwzTMFTiCD1nJyf1/Nmzc/+HKFAE HBSaiykqkGovHwAgNwg5cLV0Fx7xszxO8YFnT2+vvrZ4sd4/f35uBwsgJ9q8Xm1oaLioogKp9vIB AHKDkANXi7/wuLGqShHL0rquLq2srk7YY5PK0ZERPRQIzOUwAcyzhR6PVvh8WSsSkGmBAgDA/CDk wNXiLzw6AgHb/py1tbVJ37PQ47F1OAdQ2OqKijQQDiu+yPvGxkY90NKSqyEBAOaYmesBAPPFuT+n xDC0vbVVbV6v7flrKyvnc1gA5tjZuIDT5vVqe2srsy4A4HLM5MAVpquOlqxZ5yqfT/f5/YpYlv6l t1enxsdlSPqdo8JSsaSJefgzAJh7V5WX2wIO/W0AwJ0IOXCFdKWikzXrrPN4tPvUKf3TRx/pA0dD zmHHZ0cEwC2cVc/obwMA7kTIgSukKxW9IxBIaNZ5dmrPzZmJ6edowlkYH4DcWlxcrI2NjbFiJNEZ nN2nTtmOo78NALgDe3LgCs67s/GPnzp9er6HAyDPbGxs1Jbm5thStOgMjvNGB/1tAMAdmMmBK8yk R4Up+xK0Oo9Ho+GwJnRh/82IZdHIEihgV5SV6XjcMtS1tbUJfyc4Z2wWFxdreWWlOkMhdQQC7M0B gAJHyIErpOtRsb6+Xg+cPBl7HJF0ZVmZBsNhVRcV2fbkUGAAKGxFklpKS7Whvl5vnTuXspiAs1Hw 8srK2LLW58+elcTeHAAoZIQcuFJ8xaRPV1Zqgcej/rjeN5+sqNC+9nbdfvhwQuEBAIUrLOmVUEim aeql5ctTHuec/XU2B2ZvDgAUNkIOXCM+2IxFIrG7svF3a6Oi6+6PjozM6xgBzI9fB4N65ORJ3ef3 67GenoQS0c7Z345AIDaDI7E3BwAKHSEHBcvZ38KyLNuytFTqior0zx99pB+eOqX+DKqrAch/zr12 YUnbTp7Ub0OhhBseyZah3dvUpFcHBnT43Dktr6zUPY2N6ggE6J8DAAWKkIO8lq5Rn7O/RZvXm9Fn ng2HdTZMYWjATR5qbtaPfv979TluXGS6DO2xnp5YGNofDGrdu+9mFI4AAPmJkIOcSxVknE08nRca 062Zr/N4Yv1wALjXwuJiHRwa0nVxxQOihiP2dr6plqE5/z45fO5c2tcBAPmNkIOcS9Vx/NHu7oQL lvgLDWd1pLvq62UaRsKeHADu1jcxEdtPs6amRgcGB23hps3r1VXl5WnLy6erthZ9HQBQOAg5mHPp lpxJiXdIox3InctMJGk0HNa6ri6trK7W95cs0T999JG6x8bkLy3VPY2N+uGHH0qSuqmYBlySSk1T W5qbYzdOJGlDQ8O0S82c1dY2NTVpl6NgAQCgcBByMOdSzdREOe+gnpmY0NYTJ3RlWVnCZ708MBD7 nJ999FGs4d8Ho6NqfOMNlqcBl7hxy5pRc+CoZL222IMDAIWLkIM555ypcT6OXoDsPnVKZ+I2DU/X v+aE43UCDoCSJOWhAQCXHjPXA4D7OdeyOx9HL0g2NjbO6HOLKOcKwGGVz5frIQAA8gAzOZhzmS4d iT/OWTigzetVU2lpbLmaJBUbhiYsa9qf7zUMjWRwHID8U2eaGlNilbSoq8vK1Oz1qsQwtMrnY+8M AEASIQfzINOlI/HHTUQiur2rK9aY74X2dpmGoZ3d3drT26ujIyM6n+KiJ8qQZEkEHKAAOJt5Fkm6 tbZWL7S3a1dPj62QQLyrKyq0r719PoYIACggLFdDXoo25jszMaH9waB29fTEQtBV5eUZfQbRBigc tUVFtsdhKfbd3+z365GWFpUnWaJKaWcAQDKEHOSVsGWpIxCIlZGOcvbHAeAu/eFw0uc7QyHt7O7W G0NDuqy01PbalWVlLE8DACTFcjXklfhy0/FWVlfH+u10hkJaW1urwOiojo2M5GCUAObLuGWlXqpW Xq6daXpwAQAuXYQc5BVneekK09Rmv1+b/X7tdASgYi5mAFdaW1urUtPUyurqpE2Bo46dP68Xzp6V lLwHFwDg0kXIQV5xNgYdjkRkTvW9cF7sZFJZDUB+8UhK19FqbW2tXly2LDYj0xEI6PmpIOMUcvTG ct4kAQBcutiTg7yy2e9Xm9drey564TJOqAEKXl1xcdLn27xebW9t1fPt7drZ3a11XV3qCAS0qalJ 21tbE/5ekKRrq6psj9mvBwCIYiYHORXdZxO/pn5DQ4NtWVr0wqWE5WlAwasuKtKZiYnY4zavVxsa GmL7aToCgdj3P34J2oHBQR2N24PX5vXGyktP14MLAHDpIeQgp+ILDUQvaKIXKp2hkMYtS52hkDoC Aa2ork65bAVA/vKapkam+lp9MDpq23PjLBbgXHIWfexcyrqhoUEe02QPDgAgKUIOciI6g5OsVHS0 H078Hd3nz57VIy0t2t7aqh+cPMnSNaCAjDga95aaZsoGns4wE53Jjd78YNYGAJAJQg7mXdiydNuR I9ofDCa8dkNVlb5w+LAOnzuniOO1//vhh9rY2KjP+Xx6eWBgfgYLIOvS7Z1JFWaiNz8AAMgEIQfz 7tHu7oSAs7i4WBsbG/WbYDBlgDkzMaGtJ07o/7S0yLIsvZKmtCyA/LS2tjbtLAxhBgCQDYQczJlk RQVMw0ha5nVjY6O2NDcnLF+rME1VODYq7z51SqEU3dGBQmJIcsvCy6vLyhSR9NH4uIbjlqddXVam Zq9XJYahVT4fDTsBAPOCkIM5k6yowJbm5oQ19/F3dpdXVtpmeVb5fLq5psZWba1vMl2XDSB3iiSl i991Ho/Oxv3+egwjod9Tncej0UhE5yPOBZv56+qyMq1vaNC2kycTX6uoSNh/k+oGCAAA2ULIwZxJ VSXJueb+3qYm7Zy64PmczyfLsnRkeFjLKir0mamO52traxUYGdGx0dF5/3MAmZpufnFldbVW+Xz6 YU+P+iYnkza0XVFVpZU+n3Z0dycNOm1erxaNjeltKeF1Q9Ki4mK1V1RIlqVXQ6FpxzQTV5aVqa28 XOOWZbsZ8Y1PfCKhWW9Usv03qW6AAACQLYQczBnnjM2NVVXqCARi4ebZpUuT9sVo83q1sbFREcuy 3RkuN+ldi8I2blna7PcnLMuMd2xkRC8kKcoRtaGhQV/s69PXJydtfWOkCwFnY2Oj9vT2Jrw2W1eW lemTFRW2GZeIZcVuTESf/9KRI7b3LfR49NdNTUn336S6AQIAQLYQcjBnnDM2EctK2eQv3tGREW09 cSKhw3khLd/Bpa1MUtgwFLYslcb1iNkfDGpnd3dCQ8yohR6PPkgzW9nm9Wqz36/f9fVpfX29HnAs D5uMRGxLO6OKkyyLi39Nku31hcXFMnVh+egL7e3yOG4wJCsO4GzWe2N1dcrZmVRlogEAyBZCDuaM 80JoXVeX7fVUTf6i+tl7gwI1KklTocFfWmqbVTkwOKirvd7kYWaafSkbGhpie1fub27Wb4JBW5XB sykKcrSWlSliWQpNTmp5ZaVuqqnRm0NDsZsPzr0031+yRFtbWqb9c8Zb5fPZmvWu8vlSHkvPGwDA XCPkYN44w8xYJKJ1XV26sapKn6+p0SuO0tF9ExMqN02NRSJZ3VcAzKd+x4xNdNYifklam9erDQ0N 2tPbq74kMzwlhqGbamq0qakp9pxpGPJ60v8VvrC4WH0TEzoWF7JeHhjQLbW1sWIAzpsP0oXCAPFL SzMpDDCT4EKZaADAXCPkYN7EXwSNRSKxjcvP9fdrYYqLNZaoodCYkq2RrWVZ2t7amvTi3xkiks2q SIpt9N/V02MLB6lmQaULVQtLDMM2uxL/c9N9xs/PnInNPmVaGIDgAgDIJ4QczJv4iyDn3WP63qDQ FRuGqk1TA47f5dGpZWvRQhtRyQLBluZmmYahzlBI45alw+fO2fbu7OnttYWk+BsHK6qqZEmxZWib /X7t7O5OGnLi98Bs9vv16sBAQoPeeBQGAAAUGkIOcuLGqirb3eNUm6KBQjFhWepPEtaHp4oB7Ont 1YaGhrRLv5yzIfGVB6ULRTl2dnfriymOd4qGoGhoim/IGf8zX1y2zFYtzbIsW1EDCgMAAAoNIQcA 5kCJYWg8LrxHqwZKmfeE2ez3J5SDPjA4GAs508l0CZnzuIhlyTAMCgMAAAoWIQc58ebQUK6HAMyp m2pqki4Bm8nSL9MwtKGhwTabs7K6Wurry8oY0/3c+NAzm0IEAADkEiEHOeHc7LympkY9Y2Pqm5ig dDQKltcwVG6aWlBcrM9WV6t7dDShKedMl34lq1r2uzkOOU6Pdncn7XEFAEC+IuQgJ5I1Ck1WVQoo JCOWpZFwWP3hsB4MBHRlWZnt9bW1tTNe+pUPVcucs08UIgAA5DtCDnJiukahgBt8MDqqtbW1KjXN gl7m5Zx5pRABACDfEXKQF9L1+wAKWalpxhpvFqqZNPoEACAfZD3k7NixQ4cPH5ZhGNqyZYvaC/wf d8yPe5ua9JtgUAcGBzUSiYgWoHCLG6uqcj2Ei5YPS+YAAJiJrIact956S4FAQHv37tXx48e1detW 7d27N5s/Ai71WE+PXh4YyPUwgKzL1eK0sGXp0bjeN4W6VA4AgNnIasg5cOCA1qxZI0m64oorNDg4 qOHhYVVUVGTzxyDPzebiio3McKsDg4MZfyeyGUyoiAYAuJRlNeT09fVp6dKlsce1tbXq6+sj5Fxi ZnNxlWpPjimxdA0FbXwquGTynchmMKEiGgDgUjanhQesuG7fqRw6dGguh4A5luz8vXj+vP1xd7e+ OE1fj7WWpVMlJXpyfFzxXUUIOCh0I6GQXnQEjFTfiZl8d6b7u9M/NmZ/PDTE37d5hHNRuDh3hY3z d+nIashZvHix+uL+QT5z5owWLVqU9j3XX399NoeAeXTo0KGk5+9LgYBej+vQ/iW/X9dncDf605Ia AwFbd3eg0PWWlOgbDQ16Pa4PVKrvRKbfnVTfvXjXWZaWsCcnL2Vy/pCfOHeFjfNX2GYaULMaclav Xq0f//jH+rM/+zO99957qq+vV3l5eTZ/BArAxZSbjR7bGQrp6Pnz+mB0dE7GCMyXD0ZH9WowqO2t rdN+J7JZqpmKaACAS1lWQ851112na665RnfeeaeKior04IMPZvPjUSAu5uIq+t6OQEDPnz2b5ZEB uXFgcFAvX3fdtMcRTAAAyI6s78n5m7/5m2x/JArMbCpEOd/TGQrN02iBeZDi958yzwAAzI05LTyA S9NsKkQ531NXVDS3gwTmUWNpadLnKfMMAMDcMHM9ALjPbErXOo85Gw5ndUxALm2or1fYstQRCGhd V5c6AgFFLCvh935Pb68iGVSlBAAA6RFykHUrq6vTPs7kPYAbLPJ4tL21Vfc3N8dmbZ7r79fWEye0 s7s74ff+6MiIdnZ352i0AAC4B8vVkHWzqRAV/55fB4M6H6FDDgrfcCSi8NTvcrIZzmeXLtWe3l4d HRmxPQ8AAC4OIQdZN5sKUaZh6D6/X492d+vY8LCOUToaBapUUrQN5/lIRA8GAioyTa2sro7tu5Eu zF6ahqENDQ223lDMagIAcPEIOZgT6apGRV/rDIU0blkqMQytqK7WawMDenlgIMcjBy7ORJLndp86 pe9cdpnW1NToyPCwlldWalNTk8KWpYhlqc3rlSStr6+/qN44AADgAkIO5sSOQEDbpjq8P9ffK9VY QgAAGnJJREFUr4hl6YGWFkn2ilJR9MSBWxQZRkLxgDMTE3ooEIg93h8MaldPjyTFvieSZBgGJaQB AMgCCg9gTjx1+nTKx+w5gJt9zufL6LgDg4OzqkQIAACmR8hB1oUtS/2TkylfG6OoAFzIlFRhmpJl 6QfNzWrzerXQk3qyfGV19awqEQIAgOmxXA1Z92h3t/om7DsT1tfXx17bHwzGni83TRm6UIUKKGQR Xfg9fiUUUmBsTB/EFc9o83p1V329DElvDA0lVB2cSSVCAAAwPUIOss655KbN69X9U9XWnK8lKxW9 pqZGPWNj6p+cVP/EhGiNiELTPTZme3xVeXlsT5rTTCsRAgCA6bFcDVmXbMnNzu5uRSwr5XKcYsNQ m9erNTU1KjVN3VVfr+9ddtlcDxWYE5Wm/a/WsUgkoRgBAACYO8zkIOuiS26iTQ6PjozEqqlFX+sI BGxL1CYsK3asRLU1FLaz4bCuKC3V8akZnf3BoL505IhKp/rlxJdUj5eu9DoAAMgcIQdZF20GemBw MKGTe/S1iGXZSucCbtPr2JcW3YsWbQiabJlafHn1dMcBAID0WK6GOZOuctSW5mZtb22NNUEE3GY8 zfK0VKWiKSkNAEB2EHIwZzb7/dre2qqvLFig7a2ttspR0Rmd/7rhBq2trbW9b2Fxsa4uK5OXZToo YBNTIafN6034HU+1N42S0gAAZAfL1TBnokFmumNeXLZMO6f2IYxFItofDCaUoAbyXV1RkcYsS+OW FQs40oXKas8uXRr7HU9XKjr6PCWlAQC4OIQc5Fx8GFrX1ZXj0QCzs9Ln03PLlqkjEIjtq5EuzMZk EvilzG4MAACA6RFykFdWVlfHNlwDhWSVzyeJ2RgAAPIBIQc5k6xcbvSCsDMU0lgkos7BwaQNQ4Fc KzMMFRmGvEVF2rhkie5talJHIBD7fX526VLKPwMAkCOEHORMqnK58ct1nEt/gHwRtiwVGYaurajQ Zr9fu3p6KP8MAECeoLoaciaTcrn3NjVpYXFxwvPl3CFHjk1IGo5E9PLAgL505Ij29PbaXt/T26t1 XV3qCAQUmSpEELYsdQQCCc8DAIDsYiYHOePcf5OsXO5jPT1JK62trqmJNVcEcu23oZCtopokHR0Z 0dGREdusDs0+AQCYH4Qc5EwmG7SdszsVpqmV1dXyWJbqPB6dnZy0vW5KYgcP5lvYEXAqTFPDcXvJ or/HNPsEAGB+EHKQM5mUy3XO9qzy+VLO4CwoKlJ/OJzVMQKZcAZr5+9pdJYyk9lLAABw8Qg5yGvO 2Z7OUCjlsYNUYcM8W1xcrFqPR0dHRmLPtXm9eqG9Xbt6ehJmKSkvDQDA/CDkIK85t2WvqK7W82fP Jj12kk3cmGcbGxslKaEC4K6eHm32+xNKSNPsEwCA+UHIQV5zbtR+pKVF21tb1RkK6ej58/pgdDR2 LBEH8+UrCxYkzMTs6e2NFRuI/s4SaAAAyA1CDvKac2P2G0ND2tfeLkmKWJZ2TjUTfSMUUp+jCAEw F0wp9jsYtaW5WQcGB23L1igqAABA7tAnB3nNuTE7/nF06c++9nYtSNJLB5gLN/t8SZ9P97sKAADm FzM5yGvpNmqHLUuPTs3kNJWW2u6iA9lytdcrf2mpjgwPa3llpfYtXaqOQMD2O2kaBkUFAADII4Qc 5LV0G7Xj9+tI0kLPhV9nlq0hm5rLyvTS8uWxUL38P/8zFqjjG3pSVAAAgPxByEHBcu55INxgpjJp HlsyVSHNGaqj2HsDAED+YU8OChZ7HnCxMums9MHIiDoCgZQ9mlL9HoYtSx2BgNZ1dakjEFCEEucA AMwbZnKQ9+L33iTbAxEt3Qtk04KiIvWHw7GS0Gtra22vt3m92tDQkHLvjbP8uURJaQAA5gshB3kv 1cVidA/EZr9fXzpyRPuDwaTvX1xcrGUVFXp5YGDexozCN+qYeSkxDG1vbU0I26k4l7GxrA0AgPlD yEHem+5i0TQMlZqpV15+b8kSvTE0NCdjg3t5i4o0HPnDgrZVPt+MZmJWVlfHQnn0MQAAmB+EHOS9 TC4WncfEs6Z5HUhm45IlMg1j1iWhKSkNAEDuEHKQ9zK5WIw/5n/On7ft0XlzaEjPLl0qif07yMza 2trYksjZoqQ0AAC5Q8hB3svkYjH+mI5AwFbqd2V1tW3/zs6pIgY3VlXJkPTAyZNzOHrkWoVpakVV lToHBzUyTYWzhR6PFhQX6yafb55GBwAA5gIhB66TauYnbFnafvKkfvThhwqFwzoQCmnjkiUqNgxN UN7XtYYjEb0SCmlNTc20xSf6JifVNzmpB06elMFMDAAABYuQA9dwlpp+dunS2HKjsGXpNkcFtv7J ST0YCKjcNAk5l4BS09T21taMlyxSDQ0AgMJFM1C4RrTU9HP9/dp64oR2dncrbFl65ORJNfzHf6Qs Md1YUjLPI0UuRKuj/dcNN2h7a6vavF7b61eWldkeUw0NAIDCxUwOXCNZqelHu7u1bZo9N+sbGmQa hjpDIY1blkoMQ+OWlTIUofCsqalRxLK0rqsrtoQxfn/WyupqbWpq0q6eHqqhAQDgAoQcuEayUtPp lhx5TVP3NzUlraI1EYnojw4e1Aejo3M2XsyPBR6PbqqpiYXd+Iayzj037MEBAMAdCDlwjWQFB3Z2 d6fsj/P52lpta22VdGHPzo5AQE+dPi1JaiotJeC4hKELZcTjxYdf516uzX7/RZWOBgAAuUfIgWsk KzW92e+XZVn6l9On1T8xob7Jydhr8XsunMvanBvTy01TpYahYDg8N4NHVlxRWqoiw9CxuIA6Eolo LBKxHec899GS4/GzPAAAoHARcuBqpmFoa0uLtra0KGJZtj0Y8XsupqukdT4SUbmHr0u++1RlpVZU Vdl6Hw1HItofDGptba1KTXPac09VNQAACh9XbbhkpGsq6tzPI0kLi4vVNzERexw/C4T8FA0whmFo 96lTOhN3/kpNU/va25O+x7mXCwAAFDZCDiD7sjZJ+trixXo9FJq2eSTyw+LiYm1sbIztp4mG2egy NMkeXuL34ayoqtL/aWnRm0NDVFUDAMAlCDmA7MvaJKkjELAFnHLT1HnHvg7MnZn+/15eWZl0P5ak pMsTnftwtre2Jp3lAQAAhYmQAyTh3JeR7IK72DA0YVkJz1eYpixJo5GIiEUzV26autnn0wsz6FNU kqQaWrrliezDAQDA3cxcDwDIR6n2ZbR5vfrKggXa3tqqh1JcQK/y+TT8uc/pB1OzQpiZ+/1+ra6p mdF7Vvl8MzreeX7ZhwMAgLswkwMkEV3a9M8ffWQrR3xXfb0eaGmJ9dVp83p1amxMw3EzPdFZBTqt zNzCqQp2m5qaJEmdoZDGLUslhqFxy9L+uNmdVNXSMpFuKRsAACh8hBwgiehSJ8uybOWIo8HF2Vcn XnRW4Q1HA0q3uqK0VB9NTGRlz1Lf5KS2nTypp06f1oaGBv2/9vZYY85kJcBn27Qz3VI2AABQ+Ag5 QBrOoPLG0JDClqU9vb2259u8Xl1VXm6bFUhWljqd6NrRdFGhwjTVUFKi/x0dVeJuoMx/znRxxJAy /vzjY2MqnmXYSOXoyEisMMB9fn+sEtrK6mo9u3SpLClrgQcAALgPIQdII1kPlR2BgI6OjNiO85eV 6dmlS20X2pv9fkUsS09NlaVuLC3VK3EV2z7v8+nw8HCs/04m8yBbmpu1pblZ20+etM0wZSpVwPGa psbiCiXMNEA5CzA4izKkC01tXq8kJfw/lS4sJ3NWQotyPsfMDAAAiCLkAGkk27vxRwcPJhy3PxjU zu5u24W2aRh6oKVFD0wVIEi23Oqr776bdLZncXGxIpZla0C60OOJjef+5mYZhqHOUEhjkYjeOXfO duwVpaXqnZjQeCSiibjPTRWkmkpKbHuPZivar+Y3waCtBHetx6OzKZqp+svK9EJ7u3b19GhPb68t 7KyoqsqoEhrV0QAAQDxCDpDGTPZuTHehneyzUi1pW15ZqdXV1Xo4EIg9V+fxaGd3d0LDS+lCgOoI BGKzRk2lpTo+NpbRuCXJSLPUK1Wp7GQilqWIZen59nZd89Zb+mAqOJ2dnFS5acrQheBiWZZ+PfX/ KxoQH2hpUcSybHudLCWfTZOU9DkAAACJkAPM2F319UmLDmR6oR22rNgekxurqvRIS4sODA7q6Pnz sVCwPxjU2479QMdGR2NLtJxhyTQMmYYRmwVJtvQrXpvXq5rxcS30+bTK50sIF9KFmaO+yclYwFlQ VKT+cDjhs66IC1TRwgGmYeiTFRWxP4/0h15Dr4RCsSpqUbtPndKbQ0P6n/Pnbc+/OTSkZ5culZS8 EhrV0QAAQDKEHGCGtjQ3y5xaKhYtb7zK58v4Qtu5x2R7a6ueW7ZM67q6bKGgP8XyrlQzRpku2Wrz evVfN9yg3739tq5ftkzShRkYSbGZoPX19TowOKjnz56NvW9hSYn648JTm9erDQ0N6gyFEmaNOkMh rfL5UhZeGHFUYuubnEx67Mrq6pSzaezBAQAAqRBygBm62PLDqfaYZFqNLdWM0Y1VVRm9f0NDQ0Il Muf+IUnqCARsIcfpqvJybWluTnrcuGXFQl9HIGDrIxT9M8Tv2YmXrFIdAADATBBygHmWao9J9ILe ufm+zeuVv6xs2hmjTAoor62tzTg4OIsuOHsGxY/bOebD587F9g85l8KtqanRvy9bpl09PTowOKix SMTW5HNDQwOzNAAA4KIQcoB5lqxim/SHGaJ7m5p0e1eXDp87p+WVlXqhvV0e00z6WfH7e5z7WZIp Nc2M+8kkK25gGEbScW9oaIgtwZOkMxMTtv1DpuN98Z+drOocAADAxSDkAPPMGR7CU5XRohf5EcuK zWzsDwa1q6cn5cxG/P6eTCRb6ha2LO2Iq8x2V319LJikG3e8aDDZfeqUzkz8oWj1gcHBaZf3Xezy PwAAACdCDpBjzkIE0eaYUekKCjhfa/N6daXXGyuIsKK6WoakN4aGUs6SPNrdbVtOFq2ONpPgEX98 fOiitDMAAMgFQg6QY9NVRUsXFJIVK4ju28l0WVo2m2umWooHAAAwnwg5QI45g8r6+nrb3pd7m5ps y9niA4yzWMHRkZGUvXQy/fnR52aDpWcAACAfEHKAHEs2+xE/C9MRCNiWs0l/CDDRUHFgcNBW3Sw6 ExNfmCDZZ0d/vmVZ+pepPTlfW7xYlmVpXVdXyvcAAADkM0IOkGPTzX6k6qsTL1VZaud+n1cHBvTi smW20GIahra2tGjrVI+cdKEKAACgEGQt5Pzyl7/U7t275Z+6K7169Wp9+9vfztbHA5esVAEmXqq9 MM5AtD8Y1M7u7osOVQAAAPksqzM5X/7yl7Vp06ZsfiRwyUu3md+5HO3ZpUttszTJ9ttkUuhgulAF AACQz1iuBuS5dMvZnMvRJPvSss1+v14dGIj13ZGmDy1USAMAAIUuqyHn4MGD+ta3vqXJyUlt2rRJ n/rUp7L58QAcpltaZhqGXly2TDsdxQfSoUIaAAAodLMKOU8//bSeeeYZGYYhy7JkGIZuv/123X33 3brpppv0zjvvaNOmTdq3b1+2xwsgTiZLywgtAADgUmNYlmXNxQd/5jOf0euvvy4jTenZQ4cOzcWP Bi4ZEcvSk+Pj6gqH1V5UpG+WlFDuGQAAuNL111+f8bFZW672+OOP6xOf+IRuv/12HTt2THV1dWkD TtRMBov8cujQIc5fHvj0LN/H+StcnLvCxvkrXJy7wsb5K2wznRzJWshZt26d7r33Xu3du1fhcFjb t2/P1kcDAAAAQMayFnLq6+u1Z8+ebH0cAAAAAMyKmesBAAAAAEA2EXIAAAAAuAohBwAAAICrEHIA AAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICr EHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAA AICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAoh BwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAA uAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIA AAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICr EHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAA AICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAoh BwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrEHIAAAAAuAohBwAAAICrzDrkHDx4 UKtWrdJrr70We+7999/XnXfeqa997Wv6wQ9+kJUBAgAAAMBMzCrk9PT06Mknn9T1119ve76jo0Pb tm3Tz3/+cw0ODur111/PyiABAAAAIFOzCjmLFy/WT37yE1VWVsaem5iY0IcffqhrrrlGknTrrbeq s7MzO6MEAAAAgAx5ZvOm0tLShOeCwaB8Pl/scV1dnT7++OPZjwwAAAAAZmHakPP000/rmWeekWEY sixLhmHo7rvv1urVq+djfAAAAAAwI9OGnDvuuEN33HHHtB9UV1enYDAYe3z69GktXrx42vcdOnRo 2mOQvzh/hY3zV7g4d4WN81e4OHeFjfN36ZjVcrV4lmVd+CCPR5dffrnefvtt/fEf/7FeeuklrV+/ Pu17nYULAAAAAOBiGVY0pczAa6+9pscff1wnTpxQXV2dFi1apCeeeELHjx/Xgw8+KMuytHz5ct13 331zMWYAAAAASGlWIQcAAAAA8tWsm4ECAAAAQD4i5AAAAABwFUIOAAAAAFe56Opqs3Hw4EF9//vf 144dO3TTTTdJkt5//309/PDDMk1TbW1teuihh3IxNMzAL3/5S+3evVt+v1+StHr1an3729/O8agw nR07dujw4cMyDENbtmxRe3t7roeEDB08eFAbN27UVVddJcuy1NbWpgceeCDXw8I0jh07pu985zv6 5je/qa9//evq7e3VvffeK8uytGjRIu3atUvFxcW5HiaScJ67+++/X++++65qa2slSX/xF38Ru45B /tm1a5fefvtthcNh/eVf/qXa29v57hUI57n79a9/PePv3ryHnJ6eHj355JMJ5aM7Ojq0bds2XXPN Nbrnnnv0+uuv67Of/ex8Dw8z9OUvf1mbNm3K9TCQobfeekuBQEB79+7V8ePHtXXrVu3duzfXw8IM 3HDDDdq9e3euh4EMjYyM6JFHHtHKlStjz+3evVvr16/XF77wBf3whz/UL37xC9155505HCWSSXbu JOlv//ZvCTYF4M0339Tx48e1d+9eDQwM6E/+5E+0YsUK3XXXXfriF7/Idy+PpTp3M/3uzftytcWL F+snP/mJKisrY89NTEzoww8/1DXXXCNJuvXWW9XZ2TnfQwNc78CBA1qzZo0k6YorrtDg4KCGh4dz PCrMBAUxC0tpaakef/xxW3PsgwcP6pZbbpEk3XLLLfx7l6eSnTsUjvgbQtXV1Tp//rzeeust3Xrr rZL47uWzZOcuEonM+N+/eQ85paWlMgzD9lwwGJTP54s9rqur08cffzzfQ8MsHDx4UN/61rf053/+ 5/rv//7vXA8H0+jr61NdXV3scW1trfr6+nI4IszU8ePH9Vd/9Vf6+te/zj/QBcA0TZWUlNieGxkZ iS2RWbBgAf/e5alk506SnnrqKX3jG9/QPffco4GBgRyMDJkwDENlZWWSpGeeeUY333wz370CEX/u nn76ad18880yTXPG3705Xa729NNP65lnnpFhGLIsS4Zh6O6779bq1avn8sdiDiQ7l7fffrvuvvtu 3XTTTXrnnXe0adMm7du3L9dDxQwwK1BYmpub9d3vfle33Xabenp6tGHDBu3fv18eT062VyIL+A4W lq9+9auqqanRJz/5Sf30pz/Vj370I23bti3Xw0IaL7/8sn7xi1/oiSee0Be+8IXY83z38t/LL7+s f/u3f9MTTzyhd999d8bfvTn9l/GOO+7QHXfcMe1xdXV1CgaDscenT59mejjPTHcur732WgWDwVgA Qn5avHixbebmzJkzWrRoUQ5HhJmor6/XbbfdJklqamrSwoULdfr0aS1ZsiTHI8NMVFRUaHx8XCUl Jfx7V2BWrFgR++/Pf/7zevjhh3M3GEzr9ddf109/+lM98cQTqqys5LtXQJznbjbfvZyWkI6maI/H o8svv1xvv/22JOmll16i6EABePzxx/X8889LulCBpq6ujoCT51avXq1f/epXkqT33ntP9fX1Ki8v z/GokKl9+/bpZz/7mSTp448/Vn9/v+rr63M8KszUypUrY9/DX/3qV/x7V0C+973vqaenR9KFzdFX X311jkeEVM6dO6fHHntM//AP/6CqqipJfPcKRbJzN5vvnmHN83zda6+9pscff1wnTpxQXV2dFi1a pCeeeELHjx/Xgw8+KMuytHz5ct13333zOSzMwunTp2OlGMPhsO6//37KEReAv//7v9fBgwdVVFSk Bx98UG1tbbkeEjI0PDyse+65R0NDQ5qcnNR3v/td/pHOc++995527typ3//+9/J4PKqvr9ff/d3f afPmzRofH9dll12mHTt2qKioKNdDhUOyc7d+/Xr94z/+o7xeryoqKtTR0WHb54j88a//+q/68Y9/ rJaWltgqk0cffVRbt27lu5fnkp27P/3TP9VTTz01o+/evIccAAAAAJhLOV2uBgAAAADZRsgBAAAA 4CqEHAAAAACuQsgBAAAA4CqEHAAAAACuQsgBAAAA4CqEHAAAAACuQsgBAAAA4Cr/H/TAPQpOaPkq AAAAAElFTkSuQmCC ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAzkAAAJSCAYAAADgVgs0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81dX9x/HXzR6MkLD33ktwgIoDF7YOqEptkbpH1bpn RUWlivJrqa0VB+DALbgqVtyKoIBM2WFDCGTvfXN/f3xIbm7uTQiQdW/ez8fjPnK/8554g7nvnHM+ x+FyuVyIiIiIiIgEiKCGboCIiIiIiEhtUsgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiI iIgEFIUcEREREREJKCHHcvEzzzzDqlWrcDqd3HDDDXzzzTesX7+eVq1aAXDttddy+umn10pDRURE REREauKoQ86yZcvYvn0777zzDhkZGUyYMIFRo0Zxzz33KNiIiIiIiEiDOeqQc+KJJzJs2DAAWrRo QV5eHqWlpWhtURERERERaUgOVy2kknfffZdVq1YRFBREcnIyxcXFtG7dmocffpiYmJjaaKeIiIiI iEiNHHPI+eqrr3j55ZeZM2cO69evJyYmhv79+/PSSy9x8OBBHn744dpqq4iIiIiIyGEdU+GBxYsX 89JLLzFnzhyaNWvGqFGjyo+dddZZTJ06tdrrV65ceSwvLyIiIiIiTcTIkSNrfO5Rh5ycnBxmzJjB q6++SvPmzQG47bbbuPfee+nSpQvLli2jb9++tdpYaVxWrlyp98+P6f3zX3rv/JveP/+l986/6f3z b0faOXLUIeezzz4jIyODO+64A5fLhcPh4He/+x133nknkZGRREdH8+STTx7t7UVERERERI7KUYec iRMnMnHiRK/948ePP6YGiYiIiIiIHIughm6AiIiIiIhIbVLIERERERGRgKKQIyIiIiIiAUUhR0RE REREAopCjoiIiIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERER kYCikCMiIiIiIgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSg KOSIiIiIiEhAUcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5 IiIiIiISUBRyREREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiI iIiIBBSFHBERERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIi IgFFIUdERERERAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhA UcgREREREZGAopAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUBRy REREREQkoCjkiIiIiIhIQFHIERERERGRgKKQIyIiIiIiAUUhR0REREREAopCjoiIiIiIBBSFHBER ERERCSgKOSIiIiIiElAUckREREREJKAo5IiIiIiISEBRyBERERERkYCikCMiIiIiIgFFIUdERERE RAKKQo6IiIiIiAQUhRwREREREQkoCjkiIiIiIhJQFHJERERERCSgKOSIiIiIiEhAUcgREREREZGA opAjIiIiIiIBRSFHREREREQCikKOiIiIiIgEFIUcEREREREJKAo5IiIiIiISUEKO5eJnnnmGVatW 4XQ6ueGGGxgyZAj33nsvLpeLNm3a8MwzzxAaGlpbbRURERERETmsow45y5YtY/v27bzzzjtkZGQw YcIERo0axRVXXMF5553HzJkzWbBgAZdffnlttldERERERKRaRz1c7cQTT+TZZ58FoEWLFuTl5bFi xQrGjh0LwJlnnsnSpUtrp5UiIiIiIiI1dNQhx+FwEBERAcD8+fM544wzyM/PLx+eFhcXR3Jycu20 UkREREREpIaOufDAV199xYIFC3j44YdxuVzl+ys+FxEREWlQJSUwZw7MmAG7dzd0a0Skjh1T4YHF ixfz0ksvMWfOHJo1a0Z0dDRFRUWEhYVx8OBB2rZte9h7rFy58liaIA1M759/0/vnv/Te+Te9f/Wv x1//SuwXXwBQPH06m958k+I2bY74Pnrv/Jvev6bjqENOTk4OM2bM4NVXX6V58+YAjB49mkWLFnHh hReyaNEixowZc9j7jBw58mibIA1s5cqVev/8mN4//6X3zr/p/WsAxcXw5Zflm6FpaQw9cADGjbMd 775rvTzt2sEzz0CHDj5vo/fOv+n9829HGlCPOuR89tlnZGRkcMcdd+ByuXA4HDz99NM89NBDvPvu u3Ts2JEJEyYc7e1FREREakdoKLRvD4mJ7n1dutjXn36CP/wByobZb9tm+0TErx11yJk4cSITJ070 2j937txjapCIiIhIrfvgA7j6akhNhVtvhbPOsv0rV7oDTtm2iPi9Y5qTIyIiIuIXRo2CTZvc2wkJ EB8PAwdCSIgVJgCowVB7EWn8FHJERESkafn2W7jgAsjLgzZtYNYs+PprcDpt3x/+AE88Ab17N3RL 3TZtguXL4bjjYOjQhm6NSKOnkCMiIiJNyxNPWJgBSE628PDMM9ark5Nj+xcsgPHj4YUXIDa24doK FsrOPx8KC63X6YMP4MILG7ZNIo3cMa+TIyIiIuJXDi1c7rG9YYM74IBVZHv/fbj55mN/vf/+Fx57 DL777uiuf/FFCzhgw+qef/7Y2yQS4BRyRERE5Mhs3w7//jd88klDt8SbywW33AKRkdC9O/z8s+3f uhWGDYPoaAgOhrg429+rFzz4IAwZAoeWxPBQNo9n3Tqi162zIW1HYtYsuOgimDoVxo61wHOkWrXy 3G7oniURP6CQIyIiIjW3ZQuMHAm33QYXXwwPP9zQLfI0f771dBQUwO7d8Mc/2v7rroN162yY2v/+ Z/tXrbIenM6doVMnW0vnlFM871dcbAFo2DD6X3MN/Pa37iIFNfHOO+7nLhe89573OUlJcOONcOml cGjBUg+PPQYnnGDPhwyB6dPt+bJlMHeuBTgR8aCQIyIiIjU3fz5kZrq358xpuLb4cuCA5/bBg/Z1 /37P/f/+N0ycCBkZ7n0nnQQ//mhzXoYMgaAg68lZv959zqJF8M03Vb++ywWzZ8Mdd1ivTVClj1rd unlfc+GF8NJLNg/oggvg1189j7dta/OGCgosqHXpAq+/DqNHw7XXWjGC5curbpNIE6SQIyIiIjXX vr3ndrt2dfdaaWk28X/evJr3nowfD1FR7u3jj7eenbFjvc/dts2Gk1X2/vsWNEpLfb/GihVVv/5j j8H118Ozz9owtbJ5OGFhFqoeesjz/OJiz4BSXFz1/cPD3c//8x/3+j55efDKK1W3SaQJUnU1ERER qbmrrrLejnfega5d4bXXfJ/nckFRkecH84p27oTbb4dffrEP6YMGWZjp2dOOZ2XZ2jbx8ba9YAF8 9JHve+XkWO9Kq1buMtBlfvjBHg4HnHGG9+T/yj0tKSkWcqozZQpERMDdd3sf++AD39cUFVnAKSyE ++6znqVJk2xR0uHDYc0aOy8kBEaMqP71wT2nqKptkSZOIUdERERqLjjYeg2q6zlYuNA+wGdl2VwT X70lF1wAGze6t5cutQD1ww+2/f337oAD8PHHFkBat/a8T3a29daUzUs56yzfbXK5LJxV1KYN7Npl 6+JccQXs3WtD0yr3Gg0bZuHrww/d++bN8w4577zjObStIofDChtcfrkNeQN3IGrb1oasuVw25+f/ /g+aNYM777QguGePzSGaMsXmRC1dar1FO3fC5s3WS3X//b5fV6SJUsgRERGR2uNyWcApm7fzwguw eDE8+ihcdpntKy72DDhldu92P688DC462j74VzZpkufE+6+/rrptlYefRUa6w9q777qHf1UUFmYV 2p591jPkdO7sfe4NN/i+B8CMGdCjh3fQAis8sGWLzeEZPNj++4DNdyoLXA8/bO34+mubm+Nw2KKg 554Ljz/uuzKcSBOmOTkiIiJSe0pKrHelog0brLekbEhWaCicdpr3tb//vX3dtct6gIKCrOeoTRt4 +20bIlbRrl1HVpK5tNSCDcCZZ1oPSZmqwklRkU32v+MOUseNg5gYOPlkd+9UVhZMnmyBIze36tcu Cy4DB/o+vnWrDacrOw+8e5QWLrSAU9betWutGtu4cZCaWvVrizRBCjkiIiJSe0JDfS+g6XR6DuX6 5BObmzJ+vJV3njcPnn7ajt16qwWi0lK7buxYW5tnyxbvex6p/Hzo2NHmvtTUlVfCnDmUtGhhQaSk BPr1swDWujW88Ub1hQrA1snZscP7e6goMbHmbaooI8OGwFX3+kertNTafsYZcNdd7kVJRRo5DVcT ERGR2vXvf9vckr/8xSqYgVU8Gz3afU7Llu5QA1Y8ID7eSiyXlX0u8+679nj4YVsjJjHR1rM5/3wL Gkcadvbv9y4pXZ3Nm+GWW/BZR85XsGjRwnpciorc+woLba2brKwja2tVKn/fkybBP/9pQ9oqF1M4 FjNnWsU4sHlSAP/4R+3dX6SOKOSIiIhI7Rs3zharfPJJSE+3+Sq9ermPv/KK9eyMG2dV0cqGXPXp Y2u//PKL9z1zcqyXp8zJJ9vaNkuX2nZ0tH34r60gcbSqev20tJpdHx5uvUVOp80J6tTJiiJUHL52 ww32Om++6d63YoV7ns4119j8nmO1cmX12yKNlEKOiIiI1I3YWKsUVtljj9kQKLBegeHD3XNK4uNt kv/gwVYp7ZtvvBfHLFMWboYNs3Nyc604QVBQ3Qzdqi8Vh4QVFVmP1csve57z5Zeei7KW2bDBHnPm 2Jyd7t29z/n+e1i9Gk491SrTVeeMM2w+VMVtET+gkCMiIiL1IyXFhlO9+KLn/rVrPbcTE+2xfr2F nQ4dIDm56gVBK16fk1O7bT5WDod9raqwQU288IL39WXDAKuSlWWV3CqHnHnzbI6Ry2XzkhYutJ4f XwoKrMcI4Ntvbf0eX2sDiTRCCjkiIiJS93bvtjk5vibXVxcAqlp3xl8cS7gpczS9Ug4H9O3rvX/u XHebSkos9FQOOVu22Jyq7dvh9NOtgl1Z2BHxE6quJiIiIrVr40Y47zwLNQsW2L7//Ofw1cO6dq37 tjUFQUG2cOiJJ3ruT0iATZs893Xo4H39bbdZwAEb2jZjRt20U6QOKeSIiIhI7SkttSICX3xhQ9Mu v9x6Y+bNO/y1I0ZYoQI5NqWlVtY6OdmGpp1+Ojz0kM3tqVi5rl07q1hXWeUCCTUtmCDSiGi4moiI iNSejAyrBFampMSKAhw4cPhrP/7Yen/8vXBAY7BzJ5xzjnu+0g8/eJ9z8KCFnH/+04LMP/5h83B+ /3urouZyWSGHa66p37aL1AKFHBEREak9sbFWsausBHSLFp7r41TH5YL776+7tjU1lYem+fLcc7bI 50UXuQNRu3a2uGjZekQVS3/7UlQEW7dC+/a2OCrYe/nKK7bG0G9+o6psUu8UckRERKR2OJ22WGe7 dhZsXC6IiIAbb2zoljVNERGeC5L64nTChAmeFeoOHrSetD/96fCvkZ5uAWbdOoiMtDlY559vc4LK hh7+/e9W8nrs2KP+VkSOlEKOiIhIUxAfDw88YGvJ3H23DWWqTlGRDV1q0cK2CwvdRQQuucQWrKzs 0Ufhb3+r3XbL0avpoqirVkHz5pCdbduhoYfvvSkza5YFHID8fOsVOv98+PBD9zmlpfDeewo5Uq9U eEBERCTQOZ1WJviDD2wY0oUXVr/OyoIFEBMDLVvCVVdBcbFVS5s0yR6nnw5ffWXVusqUltqcmppy ONxryEj9Cario9+VV8LJJ0OPHtYz8/nnVc+L2rvX1u755BPvc8q2+/Tx3P/++1YIQaSeKOSIiIgE upQU2LXLvV1Y6Hv9mbw8+OYbmDzZ/ioP8Npr8PzzVkq4zLJl1hPUp48dLymx8HMka9q4XBAcfFTf jhyD0lLf4fK44+x937nThpb95S/wyCPe5+3aZVXw/vxnuPhiKyhRFmjCwuCpp+z5rFmer5OWZguP itQTDVcTEREJdG3awIAB7onozZrZB9WKMjLg1FNhwwbv66uqjJafbz09V111dO0qKTm66+TY+Fqg 9JVX4McfPfc9+SS0amXDG8t88IGF5jJvvGE9euvWQefO0KWL7e/Y0YpQpKa6z42Lq73vQeQw1JMj IiIS6IKCbHjZ2LE21+LPf3Z/GC3z5pu+A06/flonpSmoHHDAwtA991iwee892LHDikpUlJ9vayCN Hm2hZt06C8wAb79twSY4GG6+2YZJitQT9eSIiIg0Bd98Yw+wFeybN/dcCDIszPd1CxfCZZfVffuk 8brkEvsaGWlD2a67DubMsRBUVGShuVUruO8+2LPHnn/+uQ1pTEmxHrsQfeSU+qWeHBERkaZg0SLP 7S++8NyePBnGjPHc16kTrFkDq1fXbdvEP+TnW8CZNcv72KxZFnDAykpXDNAKONIAFHJERESagiFD PLcHD/bcjoiA776zCltlEhJsvRNpmnwVKNi8GV591cpEl4mOtoVAK3I667RpIoejaC0iItIUXHCB VUjbudNWsf+///M+JyjI1tOpKCnJ9/3Cw61KmwQuXwUKwMqPv/8+zJxpZaGvvNKKWfzwAyQm2tpK U6fWa1NFKlPIERERCXSLF9s6OQUFNnRo+nT767svHTt6rmfSsaMVK1ixwr3vtttg9uy6bbM0TsHB cNFFEBUFDz3keWzTJnv07Alt2zZM+0QOUcgREREJdC++aAEHbBL49Ok2z6ZjR7jmGvd6NTfeCGvX el67aZP30KPFi21NHWl6YmKspyY9HXJybOHYd96Bbt3gX/+CUaMauoUigEKOiIhI4Fq7FpYvh+Ji z/0rVsBPP9nzZcusV+bzz+Gll7zv4WtuxerVNl+jquFMErhSU23hUPBc52jZMisfvWGDDXsUaWD6 KRQREQlEixbB8cfDDTfYX9t797b9bdt6fjh9/337unix7/uU9fJUpoDTdJWU+F7IdfNmuPfemt9n yRL7GR02DObPr732iaCQIyIiEhg2boRp02zl+tJS65Up+yDqdNqinrm58Pzzntd162ZzcCpXxyqj KllyJJ59Fvr0ca/JVJWUFDjjDFi50nqA/vAH2L69XpooTYOGq4mIiPi7zZvhpJNsjgTY0KHWrT3P adPGJotfcolNGH/tNZtbsWeP9e5ERtZ/uyXwOJ1WfW3CBAvPVS0y+49/ePYGlZRY5b9eveqnnRLw 1JMjIiLi7z791B1wwCaCT5tmk8AdDjjhBHjqKffxadNg715bGycz0/bl59dvmyWwZWW5q/S9/z7c eivMnes+Xnm4Y3AwjBhRf+2TgKeeHBEREX+WlmbV0yrq1s16bn76yf6yXtW8mqysum+fNF033mil y2+/3b1v6VL429/g6qvhhRcgI8P2P/ooxMYe/p7JyTbUrU8fK4cuUgX15IiIiPizJ5+04UFlWraE t992b/sKOOnp1stT8TqR2rZwoWfAAZgzBwYOtIVk162DefMs+Dz88OHvN38+dOli1592ms0xE6mC Qo6IiIg/K/tLeJmhQ+1DYFXWr7f5O8uWufcNHGh/cQ8NrZs2ilSUlgYzZ1pgueIKGD26ZtfdfruF I7Beytdeq7s2it9TP5+IiIg/u/FGm4OTm2u9Nrfd5j62YgW8/DIcPGglpM88E667zrYr2rjRHiL1 pazQxaJFkJAA550HnTpVf03lstW+yliLHKKQIyIi4s9OOMGG/fz8MwwebD05YEPRzjzTc0jPzJla 30YaXkgIPPCADVGbNs32tWljobxbt6qvmz4drr/e5pkNHgx/+lP9tFf8kkKOiIiIv+vZ0x4VLV3q PWdBAUfqQ3Bw9esrlZTAlClWFbBMcrLN1zn1VBg0yHevztVXw+mnw4EDcNxxKnsu1dKcHBERkUA0 eDAE6de8NICaLCA7bx7ExXnumzHDhq0NGGBzbnzp2RNOPlkBRw5L//cTEREJRD16wNSpVlQgPNwW ZSwbyibS0Fq2tMIBnTpZz0/XrlBQYMeysy3wiBwDhRwREZFAs2ED9OsHjzwCmzZZRaqiItsvUl+C gqBXL9/H8vOtx2ffPvv5HDPG83h4eM1eY8sWWLLEXXVN5BCFHBERkUBx4IBVTps+3b3afMV5ODUZ RiRSW0pLYft238cKC+GyyyzsBAfDY4+5iw507QpPPHH4+//rXza07dRT4ZRTtG6OeFDIERERaewy M+Gee6ya1Hff+T7nvvugQwdo3x5Wr67X5okclQMH4Pnn7XmvXtYrs2MHbN1qJc+r43LBgw+6Q/zK lfDee3XbXvErqq4mIiLS2P3ud/DNN/b83Xet1G7F+TUbN3rOYdCwNPEXmZnu5+HhNpesJhwOK0Vd kRazlQrUkyMiItKYuVzw/ffu7aIi+PJLz3N8zUc43MKKIg2tdWu48sqjv/6552yoG8BJJ8HEibXT LgkICjkiIiKNmcMBw4Z57vvHPyA11b09fLj19lTc/ugjOPvs+mmjSFViYz23w8Jg4UJ45x1Yu7bq wgQ1sX27e57ZmjW2KK7IIQo5IiIijd0HH1jYKbN/P3zyiXvb4YD582HECNteswYmTPAMPiL1KTTU fgYrFwMoKoIbbrCf3+nTbV7O0Zo3z/28sBAWLDj6e0nAUcgRERFp7Lp18/6LeKtWnts//wyrVrm3 9+2z4UCjR9d9+0QqKy6Gb7/1PZQyIQHeegv+/W+rjlYWdFwuz2qAleXmWnCPiYEzzvBeTLS0tNaa L/5PIUdERMQfzJtnCyg6HHDNNXDxxZ7HZ870vqZNG7j++vppn0hlGRk1O+fhh2H2bGjWDKKirDS0 L08+CR9+aMUKvv/e+/4//njsbZaAoepqIiIijclPP8Edd9jq71OmwKBBtm/YMEhLs+E+ERHe1+Xl ee978EHr4RFpzGbPhjlz3L04t99uPZdXXOF5XkKC53bln3mtkyMVqCdHRESkscjPhwsugOXLbRL1 H/5gRQSuu86qR33wge+AAzB+vPc+BRzxF5WHqd10E+TkwFdfwf/9n/2b+MMf3NXUAG680XorwcpJ P/hg/bVXGj315IiIiDQWycnWW1PG6XRXjyothVmz4NJLva+bOtVWjBcJFLm5tlDo/ffbdnCwVWVb ssSGqg0fDueea0UMli+3xUMHDGjYNkujopAjIiLSWHTqZBXSKhYQqKhy8YHiYpuf88Ybdd82kbrm cLh7dE48ET791H3M6YQ334TXX7dezTLt2sGFF9ZvO8UvaLiaiIhIYxEcbMNzHnnE9we3yr01zz+v gCOBw+WydXTuvNMWvK28oK0WuJUjoJ4cERGRxqRVKwsziYk2pyY52fafdRYMHOh5buWJ2CL+rqgI NmyAFi2sYmBCAqxeDWPHwkMPNXTrxI8o5IiIiDRGHTpYVbXXX7cPfDffbH/pfuIJG8YzYIANVXv2 WftgKBIo1q+Hyy+HP/0JfvihoVsjfkohR0REpLHq1ctziNrLL8Ojj9rzFStsTs5HH1mp6S1bVEJX AsP+/fDuu/D++/bVV7ENkcPQnBwREZGG8s9/wtlnw623Wrnc6ixfDu+8473vssusUEF+ft21U6Q+ XHutZ4n00lKYNAnWrm24NonfUk+OiIhIQ5g3zyZYA3z9tYWcV1/1fe5bb8Hkyfahr6LISHfvTeVj Iv6mRw84/nj48Uf3vqIiq6o2bFjDtUv8knpyREREGsKKFdVvV/T8854hpm9fWyDxvPM8z3M4fD8X 8QdTpljBjbg4z/3p6Q3THvFrCjkiIiIN4bTTqt+uqPKHvjZtoH9/+Otf3WuG9OxpYWjUKAtBQfoV L35o+3b7ma748/vmmzZPx+mEBx+0NXSuv15z0KRaGq4mIiLSEC691IanLVxogaW68rgzZ8K2bbBx o20vWQIXXADTpllhgr59bVHE44+HTZvqpfkidaagwLPnMj8fdu+2OWnTp9u+FStsXakXXrDtlBQL SP37Q8uW9d9maXT0Zx4REZGGcuWV8N578PjjEB5e9Xk9e9raIRMneu6fMgXGjbPem08/VcCRwDB5 MvTp497u2hUGDYJ16zzP+/VX+/rTT9C7t/07GDAAtm6tv7ZKo6WQIyIi4i9Wr/a9PykJPvsMQjRA Q/xcRASceaatD3XPPXD33VaIoEULOOccz3PPPtu+Tp0KmZn2PDERnnmmXpssjdMx/d9w69at3HLL LVx11VVMmjSJBx98kPXr19OqVSsArr32Wk4//fRaaaiIiEiTtm8fxMdXfXzbNpuTc8MN9dcmkdrW p48NOSsosHlqn39uVQTBykk7HFaNcPhwuOUW21+5yIbmownHEHLy8/OZNm0ao0eP9th/zz33KNiI iIjUNper+uNLlnguHCrij7Zvt4AD8MMP1qNz443u43/8oz0qeuIJm6OTlgZdusADD9Rfe6XROuqo Gx4ezuzZs2nbtm1ttkdERER8adkSRoyo/pywMJWOFv8WHOy5XVR0+GtOOMHC0Zo1VpyjZ8+6aZv4 laMOOUFBQYSFhXntf+ONN7jyyiu5++67ycjIOKbGiYiINGYul4v42+P5sfWP/DLiF3I31WFJ2/79 YdUqe+5r7k2HDjB37uF7fEQas6Ag93CzTp1sLo7TefjrYmJswdBmzeq2feI3HC7Xsf3f8LnnnqNV q1ZMmjSJn3/+mZiYGPr3789LL73EwYMHefjhh6u8duXKlcfy0iIiIg2q+LNiCh4pKN8O6h9E9BvR tf46zX/+mb633uqxL+P442n5yy+U9dtkDxtGeEICYSkptf76IvXF5XCwac4cej34IOEHDwKQPnYs O1RMQICRI0fW+NxaLcMyatSo8udnnXUWU6dOPew1R9JYaVxWrlyp98+P6f3zX3rvGo/dX+xmJzvL t4NTg73em/zt+Wy/ZzslmSV0vr0zuzvvPvL3LzHRa1fMqafCL7+Ubzdft86GsynkiB9zTJjAwKef hkMBB6AUNpvGAAAgAElEQVTVN98wsnNnWwuqsl27ICvLSkxXHupWif7f6d+OtHOkVstP3Hbbbezd uxeAZcuW0bdv39q8vYiISKPS+uLWBEW7f5W2/aP3PNV149aR8lEKGd9msOHSDTi31WDoTUUJCfDW WzZsp8xZZ8Hll3tWkRo2TBOuxf81bw5btnjuCw+HaB89pDNn2vybYcPgt7+FkpL6aaP4haPuydmw YQPTp09n//79hISEsGjRIiZPnsydd95JZGQk0dHRPPnkk7XZVhERkUYlemA0I5ePJOWTFCK6RHiF nJKsEvK35Zdvu0pclG4vrXyb6p1/vnvRw+BgmD0brrrKtt9801Z8b9MG/v53ex4aCsXFx/BdiTSg Dz/03HY44NlnrXz6gAG2jg5YQYJ773XPQVu0CBYuhIsvrt/2SqN11CFn0KBBzJs3z2v/OZUXahIR EQlg0QOjiR7oex5OSIsQmo1oRs6qHACCooIIHlT9kBoPBQXugAM2ATshAX7+2SpKXX65PQC+/BKe esr7HrGxkJ6uggTiH7Ky3M+DguDWW+H226GwEAYPtrLSh9Zj9KKfcalAqyWJiIjUoaGfD6XTbZ1o d2U7hn09DMIhc0kmJZk1GFoTEWFV1co4HDBlCowebT08FYfnTJni+x5pafrwJ/7n3HOtHPRnn1nA AVi/Hl5+2Z6HhcH06e6S6WefbUPWRA5RyBEREalDYW3C6PNsHwa8OgBnlpPc8bmsPnU1KwavIH9X fvUXjx8Pmze7tyuGlS+/tAfAK6/A8uW133iRhjJwIPTr5x3QK27fcw9s22al1T//3IZqihyikCMi InIEXKUu8uLzKDpYg0UKK9n16C449Efpwn2FJDybUPXJn34KH39c/Q1DQmxuwl/+csRtEWm0hg93 90w+84z12oAFn+uv9zy3Z0847rjDVlaTpqdWS0iLiIgEstKSUtaPX0/awjQIhr7P96XjDR1rfoNK n8McIQ6vU/K25JG7Ppdma/cQWd29oqPhf/+z0rm5dbgIqUh9aN/e5pfdfDP06QOrV8PXX8Mpp8DO nVZGfdAgd+EBkcNQT46IiPi94tRi0r5IIy8+r05fJ/WTVAs4AE6Ivy0el7Pm8126PdINDtUoiOwT See7OuPMdZLzaw4lWSUkf5jM8kHL2XDpBlbMGEhW2NCqb5abayV0X38dTj3VvT84GO6+G7p3P/Jv UKShHDgAV1xhAee11+D44+H3v4ehQyE7G0aOVMCRI6KeHBER8Wv5u/JZffJqihKLcIQ4GPD2ANpe 6r1eTXVSPkmhYGcBseNiieoXVeV5ruJKgcYJLpcLB949MmAlpHPX5xLRI4LUhanE/zkeSiBufBwD 3x5IUUIRy09aTuHeQkLiQnDmOOHQMjqlBbB7zL8Zcsr/oGVLCzJjxni/yMaN1qPz3HOwdKlVpEpO 1qKg0rg5HN7zbUoPlVf/v/9zP09Ls7LpM2bUb/vE7ynkiIiIX9v/wn6KEm1+jKvExY4Hd7B3xl5K 0kvofHtnOt3Sqdrrdz22i11TdwEQ3CyY4346jmaDm/k8N+7iOFqc3IKspVbmtse0HgSF+B4Ukb8r nzVj1lC4r5CgqCBKC0vLA0zqR6ks67GMiN4RFO61STolqd7V1jLWOjhw3e20/1N7W/umb1/YutXz pORkWy+kRw/473+r/V5FGo3KAScoyHpvwHPhW4DFi+18h+8/Joj4ouFqIiLi14IiPH+VFe4uJHt5 Nvnx+cTfGk/m0sxqr0+cm1j+3JnjJPn9ZAD2PL2HVaesYtNVmyjOKGbv3/ey/sL1hLQKwRFuH7Yy FmdQWux7cc/dj++mcJ8FmNI8d8ApU3SgiKwlWT6udHNmOdl81WbSv0u3ylFffw033gijRpF79jUU N+9oVaVeeAEeeaTae4k0aqWl8Ne/2rC1f//bs1LasmU2LFPkCCjkiIhIo1OSXYM1ZA7pfHtnmh1n PS/BMcFeQ8ryt1dfpjmsQ5jHdsGeAn7u/TM7HthB1tIsDr52kOV9lrP9nu2kf5VO2sI0XIX2GmkL 00h6O8nz+r0FbPrTJpLnJx++8S4IbmnVCIKignz/VnZRvpgonTvDCy+Q9c9FrP/+bEKz97vPK1tL RMRfTZ9uC36uW+e94OfevQ3TJvFbGq4mIiKNRuGBQtaNW0fu2lyi+kcx9POhRHSrfrJxaKtQRq4Y SeG+QkLbhLLhkg2kfW7FAUJahRDSKoSVJ67Eme2ky31d6HB1B4/r+7/Sn40TN5K/I5+Y02M4+NpB qDSSpjiluMrXj78tntTPU+k3qx8AKwatwJntrPL8isK7hjP086GUpJcQ2TuSnLU5pC1KI/2LdHJ/ PVQxLRhantoSgANvHWD/czY8r6g4liJaEUa6nRcUZEUHiqtuq0ijEhwMzkr/VlJT4eqrrSx00qE/ IERF2ZpRIkdAIUdEROpd4YFC0r9KJ7xTOK3OdP/FdtfUXeSutQ/3eZvz2PHgDga+NfCw93MEO8rD 0KAPBpHwnwRK0ktoN6kda85cQ3GSffDfcu0Wmh3XjObDm5dfGz0gmhN+PYH8nfmsPWutV8A5HGem k+S3kylOLKbLvV1qHHBC4kJw5jtZMXAF4T3DcTgcFGwvAAcEtQgiemg0YR3CiLswjhYntiDtizQ2 T6qwMCjhrONpevIi4aTgGDSAqF8/P7LGizSk2Fho3hz27IGSSr23O3bAW2/B7t1w4YVWPlrkCCjk iIhInSnJLgEXhLRw/7op2FfAqhNWUXTAigV0n9qd7o92ByjfV359Rs2HrZUJjgym6z1dAShOKy4P OAC4YOtNWxn+3XCCIzwXrdl6w1YKdhZUf/MwoIo1QDN+yCDu4rgat7NioYHCHRWGmrmgNLOU3HW5 5K7LJX1ROrlrc8nZmON1jxx68ytPERqSTeSv+zgOhRzxI8nJ9rjsMli+3AJNmXbt4A9/8L6muBim TbN1dMaOhTvuqL/2il/RnBwREakTu5/azY8tf+THmB/Z9cSu8v3J7yd7hJl9/9oHgLPASfbKbI97 tL+2/VG//sG3D7LmjDUEN/cMM9nLstn3932UZJaw6/FdbL9/O/nb88uLBFQnpGUIYZ3Cqpw7k/a/ tKNub3USX04k+6dsH0ccuAilqCSWTIaSwPiypoj4j8xMePRR6FShEmJqqmfoKfPQQ/D441ZJ8M47 Ydas+mun+BWFHBERqXX5O/PZ+ded9mnbBbse2UXeNluoM6SV5yCCsu38+HyK9nl2k4R3Cj+q18/d lMumyZvI/TXX5/CxhBcSWHnySnY9uou9z+xl1cmrCO9x+NcqSS6hKKEISvH+DeqC9C/Sj6q9NeK7 iJuHeG7nRz5hMQspoer1fkQaleBguOYaSEhw70tNhXnzvM/96SfP7SVL6rZt4rcUckREpNY5c72D hTPH9rW7oh1tJrYBh1VD6zfHJuyHdw736HUJigzyWXSgtLCUooNFuCqvs3FIztocq3hWzdSYon1F 5G90V10rTiom/fMjDCg1CB2HVQfLfpTQnFKi2M0fKcXK8Lrq4oVEjlXr1nD99ZDjPRQT8F4vB2DU KM/t0aNrv10SEDQnR0REal30oGjiLo4j9eNUAOIuiKPZUCvz7Ah24CpygQucGU72zdxHzGkxhLYK Zch/h7D1pq04c510ub8L4R08e1cyfshg/cXrKckoIeaMGIYsHEJwlDsYJcxKIP6WeOtBCuLIgkhD jPGqw9fcyyQSuYBYVuAkisFMwaGBbNKYpKTAyy/bQraVnXsu3HCD9/4nn4TwcPecnJtvrvt2il9S yBERkVrncDgY/MFg0r9Kx1XqIvacWBxB1puQuz6XlI9Sys9N/TiV3HW5NBvWjNz1ueRttmFt2+/c TrMhzYg5Lab83K1/3lpejCDjuwz2v7if4qRiDr55kPCu4eRvy3cHh1KI6B1BwbbDFBMIYCW0JImz gVKWMY9RXNHQTRLxtnMnXHCBVVQ7/XSbc9O6te9zQ0Ot8IDIYSjkiIhInXAEOYg9N9Zrf8WelzJB 0TZ6+sCrB8r3uYpdHHzroEfIqTwMLvOnTFLet8BUuLfQ67dawbYCHGGHeo6Csef5TbM3o4BOFBJL OHVTHEHkmDz/PHTp0tCtkACiOTkiIlKvIntF0v3x7uXzUbo/1p2o3jZJPqxjmMe5ITEhpH2ZRtL8 JDIWZ9DtwW7ueSwhkP5lpXk0PipOu4oOhRonTTbglP26j+e2Bm6HiA9RUdaDM2kS5OY2dGskQKgn R0RE6l33h7vT6S9WLjY0JrR8f5/n+lCcVEzu+lyaj27Ovn/vY+/Te8uPt57QmqFfD+XXcb/iKnLh zKjZwptiUjmVDIYQw68N3RRpyu64w6qkLVtm23l5NmRt505o2xZmzmzY9klAUE+OiIjUm4J9Bex/ aT8pn6YQGhPqEXBcLhcp/00hJC6ETnd2ojChEFeeZ89LyocpJL2e5O6dOSRufFydVCoLNC6CWccM NnMHW7iTpbxDMic3dLOkKQkKsqICZQGnsm3b6rc9ErDUkyMiInUuY3EGmyZvonBPYXlhgC73diG8 SzgJ/0kgNC4UR5iDzO8yAUhbmFblb6iK83YAIvtG0uOJHmR8k4EzSz07h1NKOAe4uHx7I48whgsJ orgBWyUB7+yzrYraJZfAmDEQEgIlPsaXTphQ/22TgKSQIyIidSpzeSbrzl1HaYFnPeeE5xIozbd9 +eR7X+jj848vQc2DWHPGGgWco+QinFy60JwdDd0UCWQ//AB//SusWgWbNsHf/w533QVOJ5x5Jhx/ PJx8Mowf39AtlQChkCMiIrVi59SdHJh7gLAOYfSf25/oQdEkvZvExss3+jw/KDqoPORUpcXpLSje X0x+vI8QdEjuSk1UPlabeJhh3Es4KZQSQlBNE6ZITRUVweWXQ1KSbZ9wAiQmWm9Ohw4N2zYJSJqT IyIixyzlvynsfmw3hXsLyV6ezYaJGwBIeD7B5/lhHcLo+2JfHKHVT6TJ+iGLVue2qvX2iqc8uvMz b7OU+ezkqoZujgSqsoADsGIFJCcr4EidUU+OiIgcs4KdBT63Q+NCvc7t8tcu9PpbLwBS/5jKwdcO Vn1jl62FI3XPRQhFxOEkklKCSeJsnITTlm8JJbuhmyf+4rnn4OBB+OYbcLngl19sSNqoUVZsoGwe TkQEtGnTsG2VgKaeHBEROWax42IJbuZe5LPNZfbhpdsj3XBEHeqtcUDbP7alx2M9ys/rNaMX0cOi AQhtHer1pzdHhIPctRqOVn9cNGcz63mCzTxAPHeyiv9QQlRDN0z8QXAwDBkCjz8OTz4JS5faMDWn E5YsgT/+EUJD3RXWFHKkDqknR0RE2H7fdhLnJhLeMZwBbwyg2dBmR3R9VN8oRvw8guT5yYS1D6PD dR1I/TyVrTdsdZeBdtninkEh7r+vhbUJ4/hVx1OUVERoXChFyUXsfXovmT9lkr81H2emignULwdb uB9wB9Z8upDJEOKoouSvSBmnE66+GtLToUUL7+OffQbFh6r4ffIJvP8+XHZZ/bZRmgyFHBGRJi5p fhJ7Z9iCmyWpJWy8fCMnbjzR67ycX3NIejuJsHZhdPxzR4LCPAcDRA+KJnqQ9crkbsxl/cXrvdaz 2f/ifpLeTiJ2XCy9nu3Flqu2kPF9Bi6ni7C2YcT+JpbIPpHkzsrFVex5rdSXYK89IWRzgLOI4ydC yWuANonf2HGoSl96uvex7ErDHvfu9T5HpJYo5IiINHGFewur3QbIi89j9cmrceZYz0rmT5kMemdQ lffMWZPjFXAAcEJJeglJbyeR9HaSx6HCPYUkvpB4FN+B1K0SVvMfAIZwL3H80sDtkUYnMhLCwyEm Bnbt8n1OeDhMnAjz5tl2ixZw4YX11kRpejQnR0SkiYu7MI7glu6/3red1NbrnPQv08sDDkDKhynV 3rP58c1xhFVfOU38hfvvocmMbcB2SKM1cCDcdhvMnGnzcirr0QO+/hpee81CzvTpVl2tT5/6b6s0 GerJERFp4qJ6RzFy+UhSPkwhrGMY7Sa18zonslekx3Zws2CyV2fT/LjmPu8Z1jHM16gn8XMHOJ9Y VtCWbxu6KdKYrFxpj7POgvvug6ee8jzucsG4cbbQ59y5VnxApI6pJ0dERIjqG0XX+7vSfnJ7HEHe PTCx58XSc3pPgqLt10ZJWgmrT11N3hbv+RnOXCdbb9qKK19zagLRRh7he75kKe+RzrCGbo40Jl9/ Db/+6rkvKsqGsOXkwBtvwKxZDdI0aXoUckREpEZizomhNLe0fLs0r5T0b2xycdJ7SeyZsYfMnzNZ 1ncZSW8meV0f1DyIkFgNIAgEtqZOG9Yxg0JaoTjbBEVE+N7/3Xee22Fhntv799dJc0Qq028bERE5 rNKiUtactsZrf1TfKLbft728Opsj3IGr0PdH3tLsUkop9XlM/JOLUH7iAzrzPr15vqGbI/UlLg42 b4Z//hO++soW+SyTk2ND0zIzYeRIaN0apk61Y5GR8PvfN0iTpelRyBERkcPK357v0YsDVlyg1Vmt 2HD5hvJ9VQUcCWwHOIMMBtGaZXTiA0LIQWUnAlhqKuTnw7Rp9ujcGRIS3Mevuw4uucS9PWIExMfD eefBoKqrMpYrLYU1ayA6Gvr1q/32S5Og4WoiInJYYe3DoNJc4W6PdmPP03soSSnx2B8co4oDTU0J bchhILu4mhXMJYGLy48p9gagkBBo1cq9/e670K5CwZJLL4WbbnJvX3gh3HWXd8ApLITHHoMrr4SP P7Z9TidcdJH1AvXv7+4FEjlCCjkiInJYoa1CGfrfoYR1DiOkdQg9Z/Sk5Skt2fHgDq9zHaEOes/q Ta9/9vK+kcYPBLwi2rCNO9jM/ezh92zhvoZuktS28HDrYYmJgcsug/btLZxU9OKL8Omn1d/nppss xLz+OkyYYEPfvv4aFi50n/PYYzb0TeQI6deNiIhUKefXHDK+z6DZkGbEnhfLyXtPLj+WtSrL55/p S5JL2PbnbTQ7vpmPg3XYWGlUDjAOgCi8g7D4udxcewDMnw9ffAHZ2d7npaVVf5+vv3Y/d7ng22/h jDM8z3E47CFyhNSTIyLShBQlF5H1SxYlOZ5pI+PHDNaOW8u6C9aRvSa7fN/K41ey7S/bWHPGGhLn JHpcE39zfLWvlfNLTu02XvyOg2IG8NThTxT/lpUFJ5zgua9bN7jgguqvO+44z+3hw22tnQkT3Pv+ 9jdo0aJ22ilNinpyRESaiPRv01l/0XqcOU4iukcw/IfhRHSJoPBAIb/+5lec2TbcJHt5NidtP4mD rx/EVeTuqtn/8n46XNuhfDtvs/caOSIVuQgljZNozrYK+1BRgkD0yCOQkQFLlkCPHjb/Jj+/+mte eQXuuAN27LB5PJddZvsXLIBNm6zwQLdudd92CUgKOSIiTcTOKTtx5liQKdhVwL6Z++j9j97kx+eX BxyA4uRiCvcWEtbOc32LoqQiVo9ZTfMTmxMcHYyqQUtNHOQsOvEhIVgozmQQMWw4zFXSqI0da4UB Xn3VKqHdeiv89rd27NRT7bFvn5WM/vBDq6rmS2yszcepzOGAgQPrrPnSNCjkiIg0cdEDowltE0px cjEA4d3CiegRQZf7u5C9Kpu0z9OgFAp3FlK4s5DMHzUJWGoujx6s5EVasZJ8OpDBSIZzGy3Z2NBN k+qEh1v1s8r7pk6FW26ByZMhORlCQ6F3b/c5zz5rAQesJ+eRR6oOOSJ1SHNyREQCWFFKEet/t57l A5YT1jmM4OZW3jmiRwSd7+oMQGhcKMO/G077q9vT4foODP9uOMGRwYQ0C2HIf4cQHKWS0HJs8unM fi4mnRNxEcxa/k4ypzZ0s6Q6lQMOwH//Cw88AIsWuUs+FxfDjTda4QCw8tIVVd4WqSf6yRMRCWDx f44n5cMUwObQ9HiqB7HnxhLVL8qGnB0SPTCa/nP7e1ybuSyTPU/vKR/iVp3mJzWHEMhe4qPCkkgl pUSwjVuIYD+ZDMWBk0gSiGVVQzdNKoqNtQppQUHwr3/BOefY/oICz/OKimzYWnCwrYfz8cewdSu0 bAlPP13/7RZBIUdEJKBVLg5QlFBE8xHND3vd/lf2s/WarTV6jbBOYfT8W0/2z95PNgo5UjOlhLCO GRQTC4CDEk7gSqLY38AtE8CGppWVgI6OhvHj3ccmTIARI2DVoVA6daoFHLA1c9autWICnTpZ0BFp ABquJiISwOIuinNvOCD2t7E+zyvYV0DaF2kUJtoQlR33eK9t0vHWjj7LYhUlFLH27LUkv5NcK22W pqGY1uUBB8BFCFu4pwFbJB4qDlfLznYHGrDQ8+OPts7N6tXw0EOe10ZEWOEABRxpQOrJEREJYD2m 9SCiWwR5m/KIPT+W2HO9Q07G4gzWnb+O0txSglsGM/zr4T7v1eWuLuyftR8OP3pN5Khkchx5dCSK /bgAF0EEqYxf7QgOBudR/uMND/eudhYZaVXWRBop9eSIiAQQl9PF5qs380OzH1gxZAV5m/PoeENH es/s7TPgAOx5eg+lufZB0pnpZO/f99LtIc+1KTr8uQOF+woVcKSOucjFfvYSmMDPvEMhrRu4TQEi 1ve/f0JD3c8dlbpqw8PhzDPho4+gV6+6a5tIHVBPjohIAEmcnciBVw8AkLs+l81Xb2bkzyOrvaZw r2cVpcJ9hWQuziS0XSgxp8XQ8eaONB/RnB0Peg9hE6ldDnZxDQc4l1ROBxys5AXa8AM9mF2+1o4c heRkCyrbt3vuLy52P3e5YOhQWLfOAs4bb9ginSJ+SCFHRCSAFO73DCxF+4s8tvc9u4/UhalEDYii 51M9Sfk4hdx1ueXHHZEOsn7KwlVi5WBTPkmh2chmrD17rXpxpF7k0ptc3OuuFBFHAhNozbe04tcG bFkAWLkSJk6EL76w7ZYtrSpa9qGCIXFx8NVXVnAgLg5aqxdN/JdCjohIAGlzWRv2/WNfednn9le3 Lz924PUDbLtjGwDpX6bjzHESGhvqcX1oq1CPYOQqdLHzwZ3gqofGi1TBQTGRJDZ0M/xbixYWaj76 CJ5/HpYvhwULbJ5OcDCcdhrMnAlt2thDxM9pTo6ISABpNrgZI1aMoNc/ejH4o8H0eKxH+bGs5Vke 52YvzybmjBiPfa3OaUX04Ojy7aDIIAUcaXAuQvmZt8miDwc5g008SAIX60ezphwOCzdgBQPuvhvS 092FCJxOCzaPPw4dO8Ill0BWVtX3E/ED6skREQkw0f2jie4f7bU/ZkwM+//jXoOk5ZiWxP02joHv DSTl4xSi+kTR9YGuOPOcHHjlAAffOEjO6pz6bLpINYLJoi/bDpWZjmGNr4rm4ss338AZZ3juq1ze edMm+PXQcMAPPrA1bv71r3ppnkhdUE+OiEgT0fb3bek3px+tL2lNtynd6D3T5j3EnB5DSVoJiXMT ib8tnuBmwXS5qwshMfo7mDQmDnZyU/nWNm5hOa+QTY9qrglwYWGHP6dzZzjlFO/9zzwDffva8+OO gw4dPI/v2nXMzRNpSPoNJiLSBBSnFrPtrm0U7CygzcQ2dL61c/mx+FviSfufrWye+FIiEb0iKEku IXdLblW3E2kQTppVeB5NHtGs4kXGcD5Bh6uMERFhjxNOgAMH7JHsYwFbh8OqjPmDoiLvfc89B0FB 1hsTFQXTp3uWiS7Towds2WJFB5o3t0pqZQUJAC67rO7aLVIPFHJERJqATVduIm2hBZnMxZmEdw6n zfg2uFwuMr7P8Dh3/6z9FO4q9HUbkUbHRSi7+BM9eaX6EwsK7PHll/DHP8JLL8Gtt1rFMY8bNnDA adcODh6052efbcEsLg5ee+3w14aGWqh55BH7PmuieXP7esUVVk3tp59g9GgYN+7o2i/SSGi4mohI E1B5bk3ZdtLbSRQnF3scU8ARf7OHP7GRKaRygu2Iian+gkWL7IN85YAD1gtyLMaMsR4UsF6hESPg 2Wehd2/vcyvPk3E4bN/YsTBqFHTpAn//O8yda3Nkqnq9Cy+EkBBb82bfPrjpJtiwwff5JSXw3nvW c5Nbqbd23Dh47LHDB5z5822oW//+8Nln1Z8r0kDUkyMi0gTEnBlD0ptJtuGgvKpawZ6CBmyVSO1J 4iySGEP3m6Npd9cwcu9+jvD0LUS7dhC0+AfPk1NTfd/k+uut9+See2Dv3qNryOLF9jU01Cqa/eY3 tn3NNXD88TZEDGDIEOs1qcjlgnffdW///DN8/jls3mzX3XijhRiXy4bbjRgB27a5X7NMaSns2QOD Bnnff/x4WLjQtkeOhB9/tN6imtq713rCyhYRvfRSey2tqSONjEKOiEgT0G92PyJ7RlKwq4A2l7ah 5ZiW7HlmD1k/ZYEDlYmWABFGwnzY9cIvUDoKGEXsec0Z2uv3sH27nXLxxfDJJ76Hpb3xBqxbd/QB p6LiYgsmZSFnzRq46y6bB3TgAMybB4U16DVNTIStWy0gvfGGlXf+4AM7tnWr72u6dbOeqsp27XIH HLCerGXL4PTTa/597dvnDjgA+fn2/SjkSCOjkCMi0gQERwTT43GrQpW3LY/1E9aT9mlaA7dKpPYV J3kOv0xblM0vw9+m+UW59PjXMMJ2rYOPP/Z9cX6+feg/UtHRcPnlsGSJ9bqUGTjQvj7zDNx/vz2P iYGMDO97gO+iB61aQc+e7u3ly6tuR1AQTJliw9V8Ddlr0cJ6mCqGlNjYqu/ny9ChNlStLGANG+au 0ibSiGhOjohIE5LxYwa/DP3FK+BEDY4irHMNytGK+KGcNbkkfgJb/rKv5hPyK2rb1v3cV3jIy4M+ fWxo2W9+A8OH2zyc886z4zNnus/1FXBCQiA8HCZOtGt69LDg8Jvf2PyhikFkzBjfbQwNhZdftjk1 ZeWgV6+GCy6A88+3oXFxcTB7ts0ZKitSMGTIkf23iI62IW7TpsGTT8J339WslLVIPVNPjohIE5Gx OAWnbZAAACAASURBVIMt122hNL/U61inWzrR6aZOJM1PYs9Te8hZpUVAxf8FxwTjzHCXls5dnwsF lXpCOnWyqmu+5umEh8Mvv1iA+fRTtu3ZQ+9Jk2xdmf3uhXVxueCBB+B3v/McDlYmJsaGdPkSGWk9 SCUlNh9nwQK7T1Vmz7ZhbmVD1sB6gJKSPANYVhacey6kpNj20qUQHw9/+hNMnmzzdoKDq36d6rRp Aw89dHTXitQT9eSIiDQBmUszWTt2Lflb8z32h7YOpfvj3el4Y0cA2l7alq4Pdm2IJorUGkeIg65T ujLo/UE25+yQVidgPQ8VXXSR9Uy0b+99o4kTYfBgCzuXXELmaadZr8411/h+4aws3/tnz7ZgAFYJ 7frrLThddpmFjYrKykdXJSrKwtD557v3PfWUdw/Tnj3ugFPWtvh4e+5wHH3AEfET6skREWkCUj9L xVXiOdY/sk8kQ78YSmT3yPJ9pUWlpP63ispTIn7CVeJiz7Q9ZP2YRa9/9CJvYx6RvSPpnDnHcz5K ZKQFhJYtYeNGm9y/Y4cdGzTI1tLx5ZFHwOm042U9QGPH2vwUX045xcJLfr67vHSZW26B55+3523b Wgg6nJAQ+PRT+PVXW+em4pydMj17WgnqsiIKbdvCgAGHv7dIgFDIERFpAqL6eH6wanl6S4Z/O5yC XQUk/CeB8K7htL6wNet/t7580VARf5fxXQYZ32XQ8+medL2vK/zH5tY4CWMH15MbOozYlzLpem9L m+C/fLkNA2vRwnpZqlozJzTU5qM8/rgNTysttbkvIdV8rHI4vAMOwHPPwZlnWgi66CLo3Llm31xQ UNWhCuy1vvsO/vY3C2T333/kRQZE/JhCjohIE9D+yvbkxeeRPD+ZyJ6R9Hu5H/nb8ll14ipKMkoA iPtdnAKOBKTdT+62kHPDDbBkCdve7URi6W8hCzLu24Ej2EHHmzoSHBdnQ8lqKiTESlIfC4fD1pqp Cz17wpw5dXNvkUZOc3JERAJUSVYJCf9JIGFWAs5cJz2n9eSkzScx9LOhhHcKJ3FuYnnAAUj9QMPU JDAFNzs0/yQ0FN56i+zhv/c4vv3u7SyJW0LyguQju3FqKrzyii366WvdHRFpMAo5IiIByFngZM3p a4i/NZ74m+NZc9YaSovdE5wLDxSy/4X91dxBxM8d+oQT3CyYfrP7eRxqOaal1+mlBaVsvnaz1/4q paXBiSdaEYIJE3z3ACUnw//+557w70t+Ptx4o1Vsu/VWKCqqeRtEpEoariYiEoBy1+aSs8ZdBjp7 WTZ5W/LIWpJF6qepFKUUeZTWFQk0MWfGkL89n6LEIlI+SCH23FgcQVZqrdeMXoTGhpL6aSrZK7LL rynNL8VV6io/r1qff+4uUgAwd67Nr4mIsO34eDj1VCvtHBoK770H48d732fKFHeBgzVrbG7QE08c 7bctIoccU0/O1q1bOeecc3jzzTcBOHDgAJMnT+aKK67gzjvvpLi4+DB3EBGRuhDaLhQqVIh1hDlI /V8qW2/aah/sfs6u+mKRAJAfn0/hrkJchS4SX07k4Fvu0sxBoUF0f6Q7w74cRtQAdzGArg929Qw4 u3ZZJbWnn4bcXM8XaN3ac7tFC89FMZ9/3gIOWEW3adN8N3TDhuq3ReSoHHXIyc/PZ9q0aYwePbp8 37PPPsvkyZN544036Nq1KwsWLKiVRoqIyJGJ7B5Jv9n9CG0TSmi7UHr8P3v3HR1ltTVw+Dc9yaT3 QhJ6AgFCF6QIFhQRRRTLFQHLtaNXuZ/X7rU3bNfeERQbIFhBRFGQJoFAKKGFQHpvk0ymf38MTBjS KEkmCftZi7Xyvue8J3uMhNlzztnn2W4ceuyQp8MSok3EPhSLrdJ9ptJSUP+DV3WAmsEbB9Pv+34M Wj+Ibv/tVtdYWAgjRjhnVR54AC66yP3hCRPg3nudxQeCg+GLL9yrsXl7u/c//vqoY8+7gfrfRwhx Sk45ydHpdHz44YeEh4e77m3atInx48cDMH78eNatW3f6EQohhDglUbOiGFU4ilH5ozDuM2KvtTf/ kBAdnRIiroog6p9RrlvqYDWhU0Mb7K72UxN6SSgBI47bp7N+vfvBnGvXMnDMGOe5NB9+6Lz3yitQ W+ssQHB8sjJnTl2J59BQZ9+G3HOPc6nbrbfCggXOCnBCiNN2yntylEol2mOnZXHO7mg0GgBCQkIo KjrJKiVCCCFahVLb+Gda4deH4xXnRcnPJVRvqW60nxAdgdJLiaXUQu3BWrwTvPEb5Ef357vjFe91 cgN16+acmbHXfTigMhqdX9x2m3PGpUsXUKkafj4kBFJSIDcXwsLq9uo05IYbnH+EEC2m1aqrOaSU ohBCtBtxD8ThneBcLqPQHrPnQAnRt0QTfFGwJDiiU7DX2Nl51U6KFhVh3GOk8MtCavbUnPxAAwbA Bx9Ar16Q4F6dDZvNOXvTHJUKYmObTnCEEK2iRaur6fV6zGYzWq2WgoICt6VsjUlJSWnJEEQbk59f xyY/v47rVH52qk9V6PP1oAXzJ2YchQ7Uk9Qc8D6AdYu1+QGE6CCsZe7/P+/5cQ/aEG0jvZuQnOzc a2O1knDLLfhu3w6AITmZPbW1zpka0aHIv3tnjhZNckaOHMmKFSuYPHkyK1asYMyYMc0+M2TIkJYM QbShlJQU+fl1YPLz67ha5Gd33PaBsqoytrHt9MYUoh1Q+avwG+pH+W/lACjUCpKmJ+E/xP/0Bt6w gYMvvki3rl3xvfpqhsjsTIcj/+51bCeboJ5ykrNz506ef/55cnNzUavVrFixgrlz5/LAAw/w1Vdf ER0dzeWXX36qwwshhGjCwrSFvP332wR7B/Pqha8SXRFN1stZKBQKYv8di1e8F6Z8E9mvZoMdYu6O wSvW/U1ZVUoVlmILAaMDqFxX6aFXIkTLGvDLAHz7+7Lt/G1UbalCG6lFoTqBc2+a4+1N6SWX0E3e JAvRIZxykpOUlMSCBQvq3f/4449PKyAhhBBN21m+kxv+ugG7w7kh+nDuYd557R1M2SYAir8vZsjm IaSOTcW4z7lRuvCbQoalDUPt5/y1f+iZQxx85CAAuq46zNnHnbKuAGRrpeiAir8txpxnpnK9M3E3 HTKxZeQWwq8Np/dbvVHpVVhKLWQ8lIE510zE9RGET2t+eb0QomNp0eVqQgghWt+BqgOuBAfAlG5y JTjgfFOX+0GuK8E5eq96ZzUBIwJwOBxkPpVZ15ZZ96yLJDiigyr4vABdF53bPYfZQcGnBaj91PR6 oxe7rt1F2S9lAJT8UII2UkvgmEBPhCuEaCWtVl1NCCFE60gOSsZbXXewYHy/eFR+dWVslXolmY9k uj2j9FG6SugqFAqUXvLrX3ROKl8VIZNCUAfV/xy3Jt1ZZe3oLA8ADqjcIMs1hehs5F85IYQ4TSv2 r+Clv15ic+7mVv9eWRVZvLDjBUK8Q0iOSOb+s+/nq1u/ov8P/QkYG0DguECCzg+CY879VPoo6fdt P3RRdZ9uJ7yfgELn3KcQdGEQ3omNnMYuRAdjzjNjq7IR/3h8vbbgScEA+I88pgiBAvxHnGZRAiFE uyPL1YQQ4jS8/ffb3PnTnQColWp+mf4L47uNb7XvN3PpTDYVbwIguyqb+0beR4BXAIyFQX8MApz7 bUqW1Z3hEXRBEMETgin4soDy38uxVlrRReno/31/9El6dNE6qlKrSBkkpVVFx2ersLH94u0EXxTs dl/hoyD2X7EA9P2yLwcfPogpx0TE9RGyVE2ITkiSHCGEOA3zt813fW21W7n0i0vx1fny5Lgn+eeQ f57SmAu2LeD3zN8ZGDmQu4bfhVJRN+m+v3S/W999JfvqPR/771iqd1RTuqIUfZKe3m/1Jn9+Pukz 09365byZw6A1g9BF6yj6puiUYhWiPTLnmCldXup2T6WtW9KpCdLQ++3ebR2WEKINSZIjhBCnIdov 2u3aYDFgsBi47cfbGBM/hsTQxAafs9qt3PL9LSzZvYQewT348oov6RXSi09TP2XWslmufmXGMh4f 97jrekriFN7Y9AYAGqWGS3pfUm9spU5J3y/6ut0r/bm0Xj+HxUHp8lL8z/KncpPsSRCdiznHvWKg Ll7XSE8hRGcke3KEEOI0vDHxDUbFjsJX6+t23+6wk1me2ehz721+j09SP6HCVMGWvC3c9N1NAKzM WOnW74sdX7hdv3bRazzY/0HuP/t+/pj1B2d1OeuE4vRJ8mnwvneCN7ZqG1Wbqk5oHCE6quAJwc13 EkJ0GpLkCCHEaYjxj2HtjWsp/085o+NGu+77qH2Y+PlE4l+LJ60grd5zOVU59a7LjGVuVdMA9pTs 4e2/33ZdKxVKroi/ghcueIGRsSMBWLxrMePmjePyry4noyyjwTjj/hNH5D2RkARVwVVkh2Xz22W/ YZ9kpzarFlul7ZT/GwjREbgVGxBCdHqyXE0IIVqASqlixfQVfLL1E37a/xM/7fsJgMMVhzln3jmc 0/Ucnjn3GfqG9SUlN4Vg72C81d4Yrc6zbMqN5XR9vSuVpvrLxr7f+z13DLuj3v0V+1fw9c6vmbdt nuvcnN1Fu3n2vGe548c7MNlMPDnuSWafNZuVh1ZyVeRVVE5zH3/Pij0snLQQXawOU1YD5+UI0ZEp QaFTEP3PaAJGB+CwO1AoFZ6OSgjRBiTJEUKIFuKj8eHO4XdyuOKwK8kBKKstY2n6Un7N+JUB4QNY l70OAJWibiN0aW39PTNHJYQkuF3n1eTx1B9P8djqx+r13VOyh+uWXEettRaAu5ffTYWpgjc3vdlg ApVTmYPKW0W/pf3IeDgDa6lVlq6JDkcTqcGSb6nfYAeVTkXJ9yXk/C8Hrx5eJK9MxrublEwXorOT JEcIccbbVbSLtza9hY/Gh/+M/g+hPqGnNd7MgTN5L+U9KkwVbvcNZoMrwQGwORpfIuat9kaj0jA4 ajDPnPsMJTUlXLP4GtYeXovJasKBo8Hn9Bo91ZZqt3uP/v6oW4W2Y81InkHNvhrSJqVhzjfjUDpQ IJ90i44j/B/hJH6cSMHCAvbcuKdeu7XcirXcCkDtgVoOPnyQvgv71usnhOhcJMkRQpzR8g35jPlk DKVG50zKLxm/sOWWLQC89fdbZJRlMCVxCuO6jjvhMfuG9WXbbdv4bs93PPzbw1SZT25mRIECo9WI 0WpkdeZqXtv4Gp9t/4z04vRmnz0+wTnq6HI2cM443XvWvYztOpYJPSaw9469mPPNmNVmjGojAbUB JxWvEJ7ksDlQ6pT4DvBtvjNgq5L9Z0KcCSTJEUKc0TbnbnYlOADbC7azMmMlS3Yv4YMtHwDw5qY3 +X3m74yJH1Pv+Q+3fMh7Ke8RoY/gjYlvYLaZ2ZC9geTIZGafNZsx8WN4bs1zLNq9yC3RaIqPxsct WXnkt0dO81W6q7HUoFFpmNBjAgBZ2ixuuOsGskKziC2OZf6b85sZQYj2o3hJMVVbqvAb4odXdy9q M2rd2r26elGbVwsmUGgUxPwrxkORCiHakiQ5Qogz0g97f+Db3d8S4BWARqnBYq9bzz/x84kojyk+ aXPYWL5/OWPix2B32Hnkt0fYkreFWP9YPtz6oavftoJtFFUXYbKZUClULLpqEVMSp3BBjwv4etfX JxxbY7MxLSm1IJWDZQf5eOvHfBz+MbmWXACyQrP4bMxnTF8zvdVjEKIlOCwOtp2/jeF7hjNw9UB2 Tt1J9Z5qgicE0/357qCELcO2YDVZcVgcFH1VRPB5Uk5aiM5OkhwhxBlnVcYqLv3iUte+lgu6X0BO ZQ67ine5+thxn3VJDE2kvLacsR+PJa2ofklogOzKbNfXNoeNt/5+iymJU/gr669mY+oW0I2DFQdP 5eWckih9FMM/HE5xTXG9to/O+4hFIxYRXBHMB+9/gApVAyMI0X5Yy6ykXZpGj+d7MOTvIW5tOe/k YC21uq7zP80n4f2E44cQQnQyck6OEKJTKKouosZSc0J9Vx1c5bZxf2/JXiYnTK7XLz4gnr5hfXls 7GNM7DWRoe8PbTTBaUi5sZxRH41iXuq8JvspFUryDHknPG5LeCflnQYTnKMq9BUcjD7Iw9c+TLW2 utFCB0K0F1Ubqth+8XZqD7svV9NF69yutVHatgxLCOEhkuQIITo0m93GtG+mET43nNAXQ1m8a3Gj fdOL0/ki7Yt61dMKDAX4qH3q9ddr9GhVWl5a9xLxr8VzoOzAScW2OW+zWzW1xjgcDmpttc3284SN CRu55MFLuPzfl1PhVdH8A0J4kL3GTvUu9+WeoZeFEvvvWFT+Krx7eZP0dVKjzxu2GSj8upDa7Pb5 91EIceJkuZoQokNbvHsxi3YtAsBoNXLTdzdxRd8r6vVblbGKSQsnYbKZ0Kl0jI4dzdqstQDU2mpZ tHsRV/W9ym3vzLHL11pTu58lUUCFbwXvTHiHjMgMvCxeXLnhSsbuHuvpyIRA10WHKdt5kK0qQNVg lbUeL/Wgx0s9mhynYGEBu6/fDXZQB6oZtHYQ+iR9q8QshGh9kuQIITq0arP7p7ZGqxG7w45SocRm t5FTlUO4PpyX1r2EyeZ8I2SymThcftjtuRJjCTOSZ5xUgYAzzYrBK1xfp8WlMWr3KB5f9Dgau8aD UYkziTpMTcT1EZT9Vkbt3lpUvioCLwgEBzhMDrrc16Xe8rQTlfVyFke34lnLreR+kEuv13q1YPRC iLYky9WEEB3a1D5T6RtWd7DfZQmX8damt9iSu4VB7w0i/rV4/J/zZ8WBFW7PHa5yT3JmJs/k4l4X MzBiYJvE3dF1K+zG/d/dLwmOaDN+Z/kxImMEPef2xFZhw15jx1JooeCTAhx2B7FzYvEf6n/K46v9 1U1eCyE6FvkbLIRo9zZkb+DLHV8S7RfNv0b8C62qbuNwgFcAG2/eyB+ZfzB/+3y+3vk13+z6Bm+1 N0arEcCtPHRjonyjWJi2kGi/aFILUlvttXQWl2+6HP/aU39DKcSJ0sZo6ft5X5S+StIuTcOQasBW 5n6gZ+H8QgrnFxJzT8wpz770/F9Ptk/cjjnHjP9If2LnxLZE+EIID5EkRwjRrm3L38a4eeNcS83W Z6/n3UnvEuEb4erjq/VlUu9JXL3oate9ownOibp7+d0tE/AZolYjG7NF2zDnmEk9NxUc0Nz2tZzX c4h/KB5t+MlXUPPt78vIwyOxVlrRBMoMpRAdnSxXE0K0ayszVroSHICl6UuJfDmSB359wK1fgaGg 3oyNn9avTWI8E30x+gsywjMAKPcux6w0ezgi0anZaTbBAUABCrXilL+NQqmQBEeITkJmcoQQ7Vqf 0D4N3n/hrxeYmTyTPmHO9v/75f8w2+reaPcI6sG8y+bxcerHFNcU8/3e711tChTtv6JZO1fmW8Y/ b/snQYYgKnwq0Jv0jE4fjX+1Pzf/djNK+QxNtAGVvwq/EX6U/1IOCuj+Ync0wZKkCCEkyRFCtHND o4dyXf/rWJ25mpyqHLe2WqtzyZTBbGDR7kVubaHeoVz4+YUNHhAqCU7LsCvtlPiXAFChruDHIT+C AyZtmURMeYyHoxOdmhLUwWqsxVbKfykn7pE4uszuckrL1IQQnZN81CaEaLcOVxxm4HsD+Tztc3Kq chgYWVf5bGqfqfQJ7cPMpTOJfjm63h4cb413gwmOaGUKuP2W29kXsU+SSdFiwqaF0fO1nui66tAP 0hM7JxZrsdXVnvNajiQ4Qgg3MpMjhGi3Pt/+OfmGfNd1YXUha25Yg91hZ3TcaJ7+82nmb5vf4LN7 S/a2VZjiOFU+Vdxy+y088cUTjN0jB4aK01e1pYqkr5Pock8XAPI/zXdrV3rJZ7ZCCHfyW0EI0W4F eAW4X+sCGB03mrHxY1EqlOwr3dfos7mG3NYOTzRjXcI6T4cgOonaA7WU/loKQM2+GrSxWoIuCHI2 KiHgnADsFvsJjVW5uZJDzx6i6Nui1gpXCNEOSJIjhGi3bhx0I0lhSQD4aHx475L33Nqv7HOlJ8IS J2jVgFVUa6s9HYboJHJezyH3/Vw2JW5i+3nbMaQZnA12KF5czMFHDjY7RvnacraevZWDDx9k59Sd HH7hcLPPCCE6JklyhBDt1n9W/oedRTsBqLHU8Njvj7m1X5Z4GXcPl/Nt2iur2soj1z6CUePcL2XD 1swTQjSuOr2ajIcynOWkAUu+e8n4yg2VzY5R9HURDkvdXrGCzwtaNEYhRPshe3KEEO3W8RXTVh9a zfqs9dz9891sL9yOVqlFp9YBoESJnRNbriLaTmq3VK6ccyUhhhD+vezf9M/qj4JTP8dEnBkUGoVb MgKgT9RTtbmq0WcCRgU02naULk7nfh2ra6SnEKKjkyRHCNFudQ3oSm6V+96afyz+B5kVmQCYbWYM FueSFUlw2q8arxpqvGr416x/oTfqeWPeG4RWheJr8vV0aKKdclgc+A71RRutpfzXcvRJenq91YvK TZXsnr4bh8lBwJgAgi8JpvKvSvwG+xH3cFyz43a5pwvVadWU/FiCvo+e3u/2boNXI4TwBElyhBCt 4mDZQR5f/ThGq5H7RtzHyNiRJ/X83pK9GMyGevfzDHktFaJoYw6VA4OvgRvvuJEfnv/B0+GIds6w 2UDsv2MZsGyA655XnBdB44OwlFjw7uGNQnVys4JKjZI+nzZ8wLAQonORJEcI0eIsNgvnzT+Pg+XO jcDL9y9n1x27iA2IPeExpn0zje2F293uKVBgsplaNFbR9hxKB1+O+pIbf7/ReY3DbQmbHTtK2TJ6 xlAFqwi5JASFQkHBp+57ZKq21i1PK/6+mOJlxXj39CZ2TuxJJzhCiDOLJDlCiBZXUF3gSnAADGYD aYVpJ5zk5FTmkFaQ5nZvTNwYANYcXtNygQqPWXDOArZ220qwIZjQ8lDG7hmLUWPk4/EfE2oIZcbq GSTmJXo6TNEGbKU2bJU2VP4qfPr6ULOr7hBfr65eVKVWYSm0sOOyHRw9X9Z0yETvd2SpmRCicZLk CCFOyCdbP2FJ+hJ6BPXg6XOfxlfb+H6KCH0EXQO7klmeCYBeo6dfeL8T/l5/5/6NA/dNxw+PeZhr F197SrGL9mlH3A4AwsvCWXL2Etf9fexjfcJ6YopjeOHzF4gpi/FUiKKNlCwtcX2tjdEScHYAlZsq yf8on/yP8vHq6cWxvxJKV5Z6IEohREciSY4QollL05dy43c3uq4LqwtZeMXCRvtrVBp+vf5XHlv9 GDWWGv498t/EBTS/KfgonUrnVi0t1DuUGd/OoKy27NRfhGi3CgML0Zg1WLTuJYFzQnN466K3ePaL Zz0UmWgRWsB84t3NOWYCRgVQ9E3dYZ21+2vd+vj2l6IVQoimyaJnIUSzNmRvcLten72+yf5rDq3h nuX3YLKaeO685xgVN+qEvo/D4aCouoiZS2e6EhwfjQ/DY4ZTWFN4asGL9k9BvQTnqErv5s8+Ee2X NkaLUlP3VkMToWn2GaVeiSas8X4qfxUJHyW0SHxCiM5LZnKEEM0a2cW9MtrZsWc32je7MpuJn0+k 2uI86X5jzkb2z97vOs+mIZ+mfsqdP92J1W7luv7XUVRT9wlujaWGn/b/dJqvQHQoDkABSruSsbvG sidyDwn58qa2I7IUWXCY69aZWQqOJLNKQAXY4Pjq70mLkwg+P5iixUUULymuN6ZPog+a4OaTJSHE mU1mcoQQzbos8TI+uewTJveezL0j7uX9S95vtO+uol2uBAecSc/xZ90c64W1LzBr2SyqLdWYbCY+ Tv1YDos80ylAYVfgX+3POxe+w/LByz0dkThFxyY4buyABbcER+WvYsCvAwi5MASFSkHSoiRGZI5A P1Tv9mjsnBOv0nhUxboK9s3ex6HnDmE3yZlaQpwJZCZHCHFCZg2cxayBs5rt1z+8PwG6ACpMFQB0 D+pOjL9z4/hP+34iryqPi3tdTJRfFMvSl/HAqgfqjXF80QFx5nEoHZT7lQOQ0i0Fq8KK2qHGprRR ravG3+jv4QhFS4qcFUniJ+7V9BQKBV7xXvRf3J+9t+/FlGUiYnoE4VeFn9TYValVpI5PdSVchq0G kr5OarHYhRDtkyQ5QogWFeUXxW8zf2Puurl4qb147JzH0Kq03L/yfl5a9xIAkb6RbP7nZrbkbfFw tKIjyArLYsE5Cxh2YBgPX/swlT6VDM4YzLMLn0VnbXwZpPAgJfWWoTXFp59Po21ecV4M+HFAo+3N KV9V7jajVPqzVGYT4kwgSY4QosUNjhrsVn0tvTidVze86rrON+Tzbfq3jI0fiwKFzNyIZs0fN58f hvxApY+zEMGW7lv4buh3TNswzcORiQadRIITdGEQXWZ3abVQfPq6J1A+fRpPqIQQnYfsyRFCtKqi 6iLGfDIGq93qdj/UJ5Tzup/HkquX0Ce0j4eiEx1Jqa/7J/CF/lJxryNRhajq3evxWg+Slyej1Lbe 25GQiSH0fK0nvgN9Cb44mKRvZKmaEGcCSXKEEK0qNT+V4hr3CklX9rmSq5OuxmKz8O3ub9ldvNtD 0YkORYHrQEiNVcMvA36hVC9LjzoChVZB10e6olDXFRXx6eOD74C2Oe+myz1dGLp1KAN+HIBXvFeb fE8hhGdJkiOEaFW9Q3rjpa57UxHsHcz8y+ez9vBaQl4MYf72+R6MTnQ4R94jW9QWKvWV3HrLrWzo 6TzHqcynDIPO4MHgzizaWG2D9wPGB6D0P+ZsnEgNg9YNIvZfsQz8YyDRt0ej1Cup2V3DtnO3cfjF wwCYC8xsu3Ab62PXs+fWPditUgVNCHHqZE+OEKJVxQfGs2jaIqZ/O53y2nJKjaUkv5vMvtJ9ng5N dHQKKA4o5sHpD9KluAvZodko7Uru+vkuLv/7ck9H1+nZKmxu10EXBRH7r1hU/iq2nr3Vdd+Sb0Gp diY9AWcHULayDHt1XQKT81YOcffHsff2vZT9UgZA3vt5+PT2OaVy0UIIAZLkCCHagMlmory2Mt+M 9gAAIABJREFU3HUtCY5oadmh2QDYlXbenPgmF2y7AF9z2yyFOlPZKm1E3hSJrcKGd4I3XR/tilKn xJRnQumtxG50JjJKvRJtTN2sjzrE/a2HJsR5sKcxw+h2//hrIYQ4GbJcTQjR6palL/N0COIMYlfa kfNk24ZPbx96vdmLoHODsJRYANBF6UhanIQ+WY/vIF/6fdsPbWhdkhN9SzShU0NBAbpYHQkfJgAQ Pu2Y82+UEDY1rE1fixCic5GZHCFEq9hdtJul6UvZkLOBX/b/4ulwxBkk6XASXhbZXN4qVMAxq9QO v3SYzP9mYjfaUfmpGLB8AAFnBxAyMYSQiSFujzocDg7MOUDBZwXouugYsnUIfsl+rvb4h+Px6u5F za4agiYEETgmsI1elBCiM5IkRwjR4vYU72H4h8MxmGUTuGh7O+N28uaEN/nX8n95OpTOx30bDtbi utLwtiobh58/TP/v+jf4aOFXhWS/6lxWaCmykD4znWGpw9z6RFwb0bLxCiHOWLJcTQjRYlJyUxj4 7kDO+vAsSXCERy0bsYzf+/7eYNuZfPisQtu66/iaGt902NTktRBCtCSZyRFCnLbdRbtZl7WOh357 iMJqOaBRtA9PXvUkb1e+Tf9D/bl15a2sSF7B5p6b2RO9hzuW38GlKZeiOMM27zjMrZvgdXuqW6Nt IZeGcOipQ9gMzumgiOtk1kYI0XokyRFCnJa/Dv/F+QvOp9Za6+lQhKin2L+Y3/v/zu/9fncrRvBn 0p+ct+M8fE1Sge1keSd6E3VLFIZUA4Xz6z7U8OrthU9vn0af0yfqGbxpMMVLi9F10RExXZIcIUTr kSRHCHFa3kt574QTHAWKM3qpkPCg4yZsHvvmsc6V4Gih78K+YAfvHt6knp+KrczW/HNKnOWeqxs+ eFOhVdSb/TGmG8m4L6Ne39q9teS+m0vMnTGNfjt9Hz36Pvrm4xJCiNMke3KEECfF4XDwydZPuG/F fSS+mciC7Qvc2pMjkhkWPazhZyXBEe2AyqbCz+jndi8rOMtD0bQQM+y6aheWYgs+CT4MXDUQTYSm 2ce6Pd0N30H1k72AsQFE3hTJ4E2DCZ8eXu9sm8bUZsqMrhCifZAkRwjRpKXpSxny/hBGfTyKjdkb uW/Ffdz43Y28uuFV9pTscevbL6wf53U7j635WxsZTQjPs6ls/DzoZ9d1gX8B63qva/Y5pb6d/5Np h3137GON7xoyn8hkZNZIuszpUtd+zGyWJkZD4oJEAscFUrm20m2Yfj/0Y9Afg0j8MBG/ZD/6LujL sLT6H1xoIo9LotQQOiW0JV+REEKcMlmuJoRo1IHSA1z1zVVY7M5D/iYtnIRWpW2wb5/QPljtVl7Z 8MoJj69VaDE7zC0SqxAnY+6lc9nUaxN+Rj/+SviLOd/PafoBFfif7Y8hxYDSS4k5t33/f1uyrIT8 efn0nNuTyOsj2XnVTox7ja72+PvjiZweSemK0nrP+g/1d31dm12LcY8RfX89EddHULCgAACVn4rB 6wdjKbZQ+mMpdpud0Emh+J/lX288IYTwBElyhBCNOlB2wJXgAJQYSxgaPZQ8Q55bPwUKdhfvPunx JcERHqOAjf03EmwP5oY9NzB672hXU9CFQej76VH5qjDuN6LSq7CUWCheXOzqowpSgRLnvpeGt7N4 nLXCeYaNb7IvdpN7kNYyZ1vAOQH4DfejalMVABEzItBGOD/IKFtdRtqkNOw1dtTBagb+MZCom6Kw GW0EnRuEUqvEu6u3W1IkhBDtRTufexdCeNKQqCFE+ka6rgdEDGDh1IWMiRtDrH8sZ0WfhY/GR/ba iA7JZDOR58hjw7kbGLRmEF3u60LP13vS/4f+zLt4HomKREbGjGTZb8so+7XM7VlbmQ2/QX4tkuCE /yOc8OvCG29vos2lgUrYIZNCXF+HTnZfRlb0bRFrAtewddRWEj5KIOnbJAasGEDivERXn8PPHMZe 43yB1lIr2a9kE3hOICEXhaDUytsHIUT7Jr+lhBCNCvEJYe0Na7l3xL08OPpBfpvxG71CevHnDX/y /bXfszF3IzWWGk+HKcRpWZ+9nh/9f+TuwXfT39if6NeieWbNM5gxU+lTyUPXPoTRYMSsdJ95LP+1 vMHxNFEaBm0YRNwDcSe0j6f4+2KCJwQT91BcvTaVnwrjPmMDTwEK8B/lz/CM4Q0+u/v63djNziTF 4XD/IKJ6WzW2ChuGLQb23b6PsClhBE8IRqGoy5YUOvfMSamTtwxCiI5DlqsJIZrUI7gHr1xYf5/N O5vfqXdPq9RitssSNNHxXLfkukbbbCobS4ctJaV7Co8seQS/Wr8G+3l196LHaz0IvTgUhUpBwFkB xD0QR9HSIvbctAcaqehsr7Kz5+Y99PuuX722Xu/1Iv0f6Q0/qIF+i/uhjdDS/enuqPxVHPzPQVez IcVA9c5q/Ab5oYvWNfr6TDmmBu93f7Y7VZursBRY8Orh1WAiJYQQ7ZV8LCOEOCV2h/s6HV+NL/3D +7vdU6FiQvcJ9Aur/+ZNiHbtuBWY71z0Dpt6bWL+efMbfaQ2oxZHjQOFqm4GRB2gJvCcwEYTHNe3 szjwivOi6xNdUWgUqPxU9P2yL0HjglCoG1iLBmCGqi1VrsvI6yLr9c19OxeALvd1IXhSMEovJV49 vdxmaSJmNHwop+8AX0ZkjGD4vuEM3zkcr1ivpl+EEEK0I5LkCCFOiVLh/uvjnhH3cN/Z97ndU6vU xAfGk1+d35ahCXH6FDgTHYf7vZ+G/ASqxh9z2OvvT6v4owJtdMNVCY8KGBOAT4IPXR/ryljjWEZX jCb86nB0UTp6f9AblZ8KhY/CbfmbQqvAu5e361oXoyPh4wS3/Tl5H+ZR+mspNek1VKypwF5rp/Zg Ld2e7Ub3l7qTtDiJbv/t1mhcKh8VPj19ZKmaEKLDkeVqQoiT9vO+n3kv5T3XddfArjwx7gleWvcS kb6R5BucSY3JZuKDLR94KkwhTku4Phy9Rs/BirolYP7+/gRPDKb0h/qll336+hA2Ncx1bau2seu6 XZQsK3HeUEDQhCBqkmvoMbgHfsP8KPisAIfVQex/Yl0zQMfOBAFEzYoialYUAIeeP8TBRw6CHQLP CyR9Rjq2GhvxD8UTflU4YVeEkT7DfXmbtdRK0aIibJVHppNsULyomMHrBp/2fyMhhGiv5KMZIUST cqtymfj5RHq/0ZsHfn0Ah8NRr1x0UXURN313Ew+uetCV4AjR0b158Zt8POVjBkUOAkCn0vH2xW/T 48Ue9fqGTw9naOpQlDolhjQDefPy2HL2lroEB8ABXnFeaK/SEn51OPnz88l8PJNDTx1i17Rd2K1N l2qzVljJ/G+mc+mbA8p+LqNyfSXV26rZfd1uavbUoPJREXlTXUVE797eBF8YjNrf/TNNlX8T01FC CNEJyEyOEKJJNy67kRUHVgDwwl8v0DukN+d3Px+dSofJ5tyw3CukF59u+9STYQrRojRKDVcvuhoH DgZHDibllhTiA+IJ8QnBUmKp1z/qxiiUGiXF3xWz84qdOKwNl1X37uWNAQPWSiuHnjjkul/6cyll v5YRclFIg88BWKusOEwNj+uwOjAeMOKT4EPCBwmEXhaKtcJKyCUhqAPUxD0QR/nv5VRtrkIXq6Pn Kz1P8r+IEEJ0LDKTI4Ro0t6SvW7X+0r2MSBiAKtnrWb28Nk8d95zlBnLGnlaiI7JYre4zn/akr+F lNwUQnycCYgmREPcw3WVxkKnhDqLCwA5b+Y0muBEXB9Bl3u7OC8U1DvbRqFspMDAEboYHSGT65Ig pXfdP+GacA1+w5xV3xQKBaGTQ4mcHokmUONsD9Yw5O8hjCobxYjMEej76pv5LyCEEB2bzOQIIZo0 JXEKr254FQCVQsWk3pMAGNFlBCO6jGDBtgUcqjjU1BBCdHjH/z/e/enuRF4fic1owzfZ13W+jDrQ /Z9VhU6BykdFj1d6uPbVAKj91HR/vjsZD2SAA0KnhhJ0flCTMSgUCpKWJFG0qAi70U7QeUHkfZSH vcZO9G3RaMOaLm4AuJIeIYTo7CTJEUI0ae6EuSSEJLC/dD+XJlzK6LjRbu33LL/H7TrGL4ZQn1C2 FWxryzCFaFXRftHMXDqTvSV7ubT3pTw45kF8Enzq9ev+Yneq06qpSa/Bd4gvA34e0GjyEXd/HOHX hGOrtuGT6ON2EGdjlGolEdfUlXzu9kTjldGEEOJMJkmOEKJJSoWSW4feWu9+mbGMQK9A176co0qN pVSZq+r1F6KjCvIK4ud9P/PDvh8A2JC9wZn0DJxZr693V2+G7x6OrdqGSt/85n6vODl7RgghWkOL 7snZtGkTI0eOZMaMGVx//fU8/fTTLTm8EKIdKKwuZOC7Awl+MZieb/RkQvcJbu12h51KU6WHohOi ZXXx78KGmzewt9R9b1pzM5UnkuAIIYRoPS0+kzN8+HBef/31lh5WCNFOPPnHk643eBllGSSFJZEc kcy2gm0oUHBB9wtcn3gL0dElRyQ7Kwp2O9+tCMf53c/3YFRCCCGa0+JJjsPRcFUZIUTncPwsTaWp kkt6X0JmeSYVpgpJcESnoVFoeGD0AwC8PvF1YgNi2Za/Db1WT1F1EVa7FbVSVn0LIUR71OIlpA8c OMAdd9zBddddx7p161p6eCGEB1jtVtKL0ympKeHOYXei1zjLz2qUGg6UHeCZNc9QYarwcJRCtCyL w8JFn13EPT/fQ74hn1uG3ML67PV8tPUjZi2bxVXfXOXpEIUQQjSiRT+Cio+P56677mLixIlkZWUx Y8YMVq5ciVotn3QJ0VFVmao4f8H5bMrZhE6lY2j0UBQKBb2De3PdgOt4fPXjng5RiFZTbanmf5v+ x7fp3/LU+KfcSkl/m/4tFbUVBHgFeDBCIYQQDVE4WnF92bRp03jttdeIiYlpsD0lJaW1vrUQooV8 kfEFL+96ucG25KBktpVJqWhxZpiTNIeXd9b9XVAr1Pyn33+4PP5yD0YlhBBnjiFDhpxw3xadYvn+ ++8pKirixhtvpKioiJKSEiIiIpp85mSCFe1LSkqK/Pw6sMZ+fgazgZlLZ7Lm0BqGxQxjRMwI2NXw GGovNQ+OfpAX/3oRjUrDqNhRrDq4qpUjF6LtqRQqknok0aegD3tK9mB32LE6rDyT9gyJPROZPmD6 CY8lvzs7LvnZdWzy8+vYTnZypEWTnHPPPZc5c+awatUqrFYrTzzxhCxVE8KDLHY7GuXJbb17YvUT LNm9BICf9v1EsFcwiaGJpBeno0SJQqHA5rABMCN5BgG6AKYkTGFd9jrWZ69HpVC52oXo6LQqLV0D u3LToJu47cfbMNvM9fr8kfnHSSU5QgghWl+LZiB6vZ533323JYcUQpyCNeXlXLlzJ0UWC9MjIpiX mIjyBE5TB9z2HAAcrjxMyi0pbM3bSrRfNKXGUn7N+JUQnxAqaiuYtWxWK7wCIdoHrVKL0WJk8e7F DSY4AEOjh7ZxVEIIIZoj0yxCdEIz0tMptFgAWFBQwIXBwVzXzNLRo67pdw2Ldi3CgXO73qacTewq 2sWouFEAhPiEcNuPt7E5dzMqhRx4KDo3g8WAwWIgqzILpUKJ3WEHIMQ7hOTIZCZ0n8AtQ27xcJRC CCGOJ0mOEJ1QyZEEp7HrpkztM5WRsSNZl+UsAV9rrWXuurl8eeWXALzz9ztszt0MIMvSRKehVWox 281olBos9ob/vgyPHk6EbwRB3kE8c+4zRPtFt3GUQgghTpQkOUJ0QrNjYnj28GEAIrVarggLO6nn Y/zcKyJ6qb1cXx+/ZMdL5UWtrdZ1rVaqsdqtJxuyEB5ltptZe8NaVh9czSOrH2mwz+3DbmdG8oxT /h4FhgLSi9OxmE78QwchhBCnpsUPAxVCeN4z3buzYsAAPklIYOuQIcTodCf1/FPjnyLWPxaAboHd ePycurNw/jnkn3QL7AY4K06ZbCZXm0qhkgRHdFjnfnoufcL6MDp2dL226/pdd1oJzsbsjfR+szfj Ph3HFauvIDU/9XRCFUII0QxJcsQZZ31FBdfv3s1de/dSaG54I/HJsrXecVPNsjscHKqtpdLqnlxM CA5mVlQUkY0kOA6Hg6czMxmzdSt37N1Lta1u6dnHFWoKBy8g7Lw/eeu6DXQL6uZqi/SNJPW2VH6b 8RsfXvqha+8OyPI10bGZ7WamLZrm9v/0UZ/v+Jyol6NYvn/5KY393NrnqDRVAlBpqeSFv144rViF EEI0TZIccUY5YDRy/rZtfFZQwFu5uVy4fftpjZdhNJK0aROaP/7g/NRUqqxtO4thtNk4b9s2um7Y QNS6dfxQXHzCzy6yWHg0M5O1FRW8k5vLv/bvB2BlaSkvZmVhcjgostqYnr6X488M9tf5M77beK7o cwW9gnu16GsSwpPsDjvrs9c32JZvyGfaN9OotdY22N4UtdJ9dbhGqTml+IQQQpwYSXLEGeXvykpq 7HbXdarBQMVpJCZ379vHrpoaHMCq8nJeOLIPpjU5HA7u2bePgDVriFq3jtXl5QDU2O1cumMHt++t n5Q0ZM8x/x0AtlZVAVBw3OxWmdWK+Zjxvisq4rpdu3ji4EEUKm/W37SeqYlTT/dlCdFuHK2g1hCD 2eCakTkZT45/kijfKAAivCJ4dOyjpxyfEEKI5kmSI84o/X190RxzXkxPb28CTuPA2uLjqpYVnUQV s1P1aX4+/8vJodJmo8LmvjzMAbybm8vCwkLXPYPVytOZmczZv5+d1dWu+0NV7uWfbQ4Hgzdv5ruS Erocs8RtRkQEuiMHir6WlcVlO3eysLCQ/x46ROz69ZhUvkzsNbEVXqkQnvffsf8l0jfSdX1xr4sJ 14ef9Dh9w/qy/+797L5zN4vHL6ZXiMyACiFEa5LqauKMkqTXszgpif/l5OCvUvFSjx6nNd7tMTFs Sk/HAXgrldwYFdUygTbhkMnUbJ/cY/pctmMHvx2Z7fkoL49tw4YR7+XFhWo187y82F/rXHqTeiQB 2mowMC0sjPOCgghSq7nymMpsL2VluX2fcpuNIZs3c3VQMiqFSvbkiE7lrJizSAxL5JbBt2CxW+gR 1IPrk68/5fF8ND4khiaSciilBaMUQgjREElyxBlncmgok0NDW2SsmZGR9Pb2Zmd1NaMDAkjU65vs v7GyEpvDwUh/fxRHZpS2GQw8fegQCuDmyEgeOniQzNpaxgQGMi8xsd5M0yUhITyZmUljC2oC1Wou P/L6Ss1mV4IDUGGzsaa8nPjISEodDleCc7wMo5Gvk5IA3Ja+NfQ98y0WXi+0QOg5UPRbk69fiPZO o9Bw11l3EegVSElNCdcsvgYAX60vG2/eyKvrX2X+9vnE+MXw3iXvuRXlEEII0X5IkiPEaRoZEMDI gAAAdlVXMy8/n0KzmTGBgdwUFcW+mhrWVVayqKiIH0pKALgiNJRvkpIot1o5LzWVkiP7gr4pKnKN u7S4mJvT0/mmXz8AisxmJqelsbGqih46HRkmk1sNqLP9/LgwJISrw8Lo6eNDnsnEOanuZWoVQIxO R5XVir9CgbdCgbGB/Tt7jUaWFBbyak4O6ysqiPfyoo+PD8l6PfmNVaTz7S5Jjujw5pw9h+fOfw6A yLl1y9QMZgPj5o2jqMb5d3RX0S6uWXwNG2/e6JE4hRBCNE2SHCFayA/FxVy+cyfWI0nDpwUFbKys 5POCArdiBwCLi4tJqarCDq4EpyFLi4uxORysKivj0rQ0TEfGPtDAkrWd1dWsq6riw7w8ViYn81Fe HvuMxnr9zt22DQAfoH6rU5XNxrW7d7sKDmTU1pJxZNZHr1RSfdzrUQKq6gPIEYeio1Ki5L/j/svD Yx923Yvxj6GgusB1fTTBOWpP8Z42i08IIcTJkSRHiBbyWna2K8E5amlxcb0E5yitUkmsTtdg0nCU FRiRksK26moszVRMqzgyRpbJxMgtWwg4rrAA4DbzU9PkaLhVVDvW0Vi1wH1xcRSbzeSbzfzQ+34o WgsOSXVEx6JT6kifnU7XwK78vO9nXtnwCn5aP54e/zQ3LLvBLdE51uSEyW0cqRBCiBMlSY4Qx6m2 2ZiblUWxxcLMiAiG+vuf0HMNVWkL12garLh2T0wMA3x9ARgfGMgPpaWNjrvZYDjByOuUWa2UtfKZ PWZgdVkZG6qqUACovCD5FcicB2FjoXIXFKxo1RiEaAkmu4mVB1YyNn4sU76agtnmXJK5NX8r1w+4 nrnr57r6Tk2cStfArsT4xzB7+GxPhSyEEKIZkuQIcZwrduxgRVkZAB/n5bFl6FASfHyafW6wry8/ l5ZitNtR4Jw1qbHZCFSpKD+u1PPtMTGur0cEBDSZ5LRXCmDDkbN1XHM+Af0g+cgbwuhLQd8NMt71 RHhCnJSsiix2FO5wJTgAmeWZbgmOr9aXr6Z9Ve9gTyGEEO2PnJMjxDFsDge/HElwwHnA5p/HVCdr zLLiYh7JzMR4ZCnX0Tf9B02megkO1J2vs/DIvp1wTd3p5wpAfcxZPu1V88eNAmHjWjkKIVrG4crD DI0eiq/W13Uv1j/WrY/BbMBoaWwnmxBCiPZEPo4S4hgqhYIEHx/Sa+p2rPQ5MouzvqKCvyoqGOLn x/igILfn/q48uRPQb0pPZ6CvL18VFdVrU0K9vT0dlsoLetwBfv1ApQFzFaTd5+mohKhnffZ64gPj WTVjFW9uehM/rR+3Db2NCZ9NIN+QD8BFPS/CT+fn4UiFEEKcCElyhDjOd/36cde+fRRbLNweHc3o wEC+Ly5myo4drnNi5icmcn2ks7xskcnEV4WFJ/U99hiN7Gmg8hlApzpOUxMAXaa534u5Ekr+AnM5 2OVTcdE+hPo4z5YaHjOc+ZfPd93fcNMGPtv+Gf46f24ZckuTY1SaKtGpdOjUulaNVQghRPNkuZro 9LZWVfFlQQFZjRx8ebxePj6sSE4mZehQbo6OBuCzggK3gzDn5Ts/2S21WEjavLnRQzVFA3reCWct hMQHIWiYp6MRZyi9Rk/v4N6u643ZG1mxv36hjPjAeB4e+zCzz5rdZPJy6/e3EvB8AAHPB7AwbWGr xCyEEOLESZIjOrX5+fkMTUnh2t27GbB5MzurqxvsZ7HbWVpUxLLiYqwNlHOO1rm/uVlbUcErhw8z Y/fuBquniRMQNgYGvAjdb/N0JOIMNCR6CNlV2a5rm8PG/O3zm3iicSsPrOT9Le8DYLKZuHHZjVhs 8ntBCCE8SZIc0am9kpXlmoEpt1r5KC/P1VZhtbKitJTtBgMXp6Vx+c6dTNmxg8t27MBit2M4pgTz E127EnlMcQCzw8GcjAx+7IBV0dqdmKng27v5fkK0oD8P/UmNxf20qGjf6FMaq9LkvifPZDO5VWkT QgjR9mRPjujUjj+75uh1odnMyC1byKitdZV7Puqn0lJC//qLSpuNqaGhfNW3L/5qNUP8/CSpaQ1K DQx6A9ZdDrbmjigVouWplWou6H4Bj57z6Ck9f1HPixgYOZDU/FQA7hx2J3qtviVDFEIIcZIkyRGd 2hu9ejEpLY1sk4nRAQGc5efHOzk5ZBiNZBzZR9NQHbPKI2WflxQXE75uHVNCQ/n1mNLSooU4HKBQ gFILI76GdVMh5jLw6QYl66BkracjFJ2cRqlh7Y1rGR4z/JTH0Gv1rL1hLSszVhKgC2B8t/EtGKEQ QohTIUmO6NQG+PpyeMQIDDYbXxUWMjEtDWj6HBqtQoH5mBLOZVYrnxwpNCBa2LE/B7Ueet0NUZOc 1749JMkRp02FClsDNQsfHfso1eZqpvaZeloJzlF6rZ4piVNOexwhhBAtQ5Ic0ekpFAr81GreP2Y/ jtXhIEqrJc/svm7eV6Xi6rAwPpKkxjPCz6/7unyL5+IQnYYNG3qNHrvDjgIFwd7BvHrRq1zZ90pP hyaEEKIVSZIjOgWr3c7crCzSa2qYHBrKFWFhbu0Gq5Xi46qg/TMyEl+1mqXFxeSYTMR6eXFPTAz3 HjjQlqGLY6mOqWKnDfZcHKJTqbY4qyomRySTeltqvfYteVuoqK1gVNwotCptW4cnhBCiFUiSIzqF ew8c4M2cHAA+LSjg+379uCTUebhfldXKlB07OHjMWTY+SiULCgo4aDK57h0ymVhbUVFv7OOXr4k2 YKt1zupUpEHBStCFgX8SFNQ/x0SIE5VTlVPv3sOrHubZtc8CMLLLSH6b+Rteaq+2Dk0IIUQLkxLS olM4vijA0etDtbUk/f03v5WXu7XX2O1uCU5TJMHxBIWzIkTvOTBmOQxfAAn3g0I+lxGnbsaAGW7X NZYanlv7nOt6ffZ6ft73c1uHJYQQohVIkiM6hWS9e7nWgb6+ALyWnU3WCSYzoh1R6UB5/K8nBTjq byAXojkKFMy7bB4vX/iy615KbgoXfXZRvb46ta7ePSGEEB2PfCwqOoX3EhLwVqnYU1PD5JAQZkVF AWA/gVmYoX5+7DAYqJUZm/ZNoQCfeKjJ9HQkop1TK9RYHXWH+U4fMJ2ZA2e6ro0WIxM/n0hRTZHb c1cnXc1FPesnPkIIIToemckRnUKAWs0niYmsGzyYB+PjXfdnx8TU6ztQr8dPpcJfpeLSkBC2VFVR 63CgATRtGLM4BX2f8XQEop0bED6Af/T/h+vaV+PLo2PdD/ksqC6ol+DMvWAuGWUZRM6NZPZPs3HI hx5CCNGhSZIjOqUqq5VVZWXYgH+Eh7u1pVZXc2jECEpGjeKnkhLsR+5bjvwR7Zg+GnrdC0rdkT+y QVy42164nUMVh3jvkvd4YtwTbPrnJnqF9HLr08W/C/3C+7muw3zC+GLHF/yd+zdFNUW8+febfLrt 07YOXQghRAuS5WqiUzloNLK+spKHDx4ks7YWJXCWn1+9fjaHgzSDAWv9IUR7F30pRE0GhwOyFkLm R56OSLQzfxz6gxDvEP438X/E+Mdgd9ix2W1oVM65WrVSzaoZq5i7bi5Gi5HZZ81m/KdOYWodAAAg AElEQVTj3cY4VH7IE6ELIYRoIZLkiA7L4XDwS1kZtXY7FwUH82d5OZfu2EGt3e7qYwfWV1W5PXd1 WBgrS0v547iKa6IDUSicf+Kng39fqC1w3t/3CjgkdRWwJH0JG7I38OjYR5mzcg4mq4mHxjzEk+Of BCBcH86LF7zo6v+Pfv9g7vq5AHipvJiSOIXl+5dTaark4l4X46v19cjrEEIIcWokyRHtWqXVyobK SrrodPQ9roLa9bt383lhIQCj/P3xUirdEpzGfF1UxFdFRc32Ex1E0OC6rw17IXep52IRHhGuDydS H8n2wu1u93MNucxePhur3Zn4PvXnU1zS+xKGxwyvN8bAyIGoFCpsDhshPiHMXT+Xz7Z/BkC/8H6s v2m9JDpCCNGByJ4c4XF/VVTwYEYGH+XluW32LTSbGbx5Mxdu307/v//mg9xcV1t2ba0rwQH4q7IS 4wkkOOA8fkV0Uj3vhq43eToK0cbenfQu629aj1JR/5+0ownOUWXGsnp9AB5f/Ti2IyXKc6pyXAkO wI7CHaw8sLIFIxZCCNHaJMkRHrW2vJxxqak8f/gwN+/Zw/0ZGa62/2Vnc6C2FnAuO3s8M9PV5qNS oTpurH/FxNBF5zzjwkehaOXIRbt0dAlbxERPRyLa0K0/3MqsZbOYe8HcBhOdowZGDmRM/JgG27Qq rdu1Wum+0CHAK+D0AxVCCNFmJMkRHvV9SQnWY2Zvvj1mGdmXx8zUANjsdmwOB8VmM0FqNXfHxHA0 lbk/NpZpERFknHUW2SNHIinOGS5hjrM4gVc0+A/wdDSilRXVFPHNrm/YlLOJvDl5JIYmurVf3PNi Fk5dyNob1uKj8WlwjNcues21HG1o9FA+mPwB3mpvAGYPn8253c5t3RchhBCiRcmeHNGq7A4Hzx8+ zJqKCob5+fFYfDzqY06y7+Ht7da/ymYj8q+/ODsggGKLe0Fns8NB4Jo1GOx2orVacs1mV9vmqiqe zMxkRWkp/fR6QjQaqo9pF2cYhQp63+f82pgHm/7RdH/RKXy962vuPutubhp0E/+38v8A0Cg1PDTm IUbFjWry2Qk9JpB9bzZFNUV0DeyKWqlm+oDpWGwWvDXeTT4rhBCi/ZEkR7SqV7KyePjgQQCWl5Zi dzh4unt3V/vNUVHsqanh2+JirA4HWSYTAN8WF6M7bslZuc3m+jr3uATmt/JyfjtSLW1dZaXM5Ig6 5amAAtmN1fnZHXY+2/4Zb016i4SQBHYV7eKCHhcwOGpw8w/jXJJ27LI0tVJdb9maEEKIjkF+e4tW tfG48s3HXysVCl7u2ZOXe/bkku3bXUkOgOk0ThyXt7PCJWgoJD4C5hKoSIOSNZ6OSLSiCN8IACYn TGZywmQPRyOEEMJTZE+OaFWj/P2bvD7WNeHhjbapgCitttF2IRrlFQYR50LsNOj3JPS6z9MRiZPg p/VrtJhA37C+9A7pTax/LDqVjssSLuP/zv6/No5QCCFEeyQzOaJV3dOlC3bgz/Jyhvn780BcXKN9 p0dGEqbVsq6igoUFBew/UlktVKNh+9ChqBUKrt+9m7TqaorMZiyNjlRHr1BQfRozQqITip4MdguU bgCNv3Omp2QjFK/2dGTiOJN7T2bJ1UsYN28cf2X9Va89zCeM1bNWt31gQggh2j1JckSrUigU3Bcb y32xsSfU/8LgYMYHBrKxspL9tbV4K5W80bMnUUdKQy9PTub81NR6e3IaIwmOaFCXqc4/RwUNkyTH g9QKNVaHtd79sfFjUSvVfHXlV0z8fCJphWlu7ftK97VViEIIIToYWa4m2hWD1crktDRWlDkP7DPa 7Tx16JBbH7WcgSNami7EWXIaBShlWWRbayjBAfh468cARPlFkXpbKmd3OdutfUTMiFaPTQghRMck SY5oV67ZtYtfytxPJK+w1r0BKrNYeCAujgDV8UeBCnGaet8HY5ZDn/96OhJxRJRfFK9veB3vZ7zR P6un1lbr1t49uDtrDq1hfdZ6D0UohBCivZLlaqJdOVoG+lj3Hlnq9p8DB3gxKwsF0F+vZ3t1dRtH Jzo9pRYOfuDpKM5oRw/g7B3Sm4dGP8QFCy7AcaRe4pa8LW59v9zxJXPXzQVgZvJM5k2Z16axCiGE aL9kJke0KwN9fd2ub4yMZE5sLKlVVbyYlQU4y0NLgiNahcPmPEhUeMz/t3ff8VVX9x/HX9+7k9zs PYCQEAKEFQLKcta6cFsVt9a6V1tarHW0dmjraqlbwVprlSqtraNWa/nVYkFANmEEIiAjOyF73fH7 I+GaG5IwTHKTy/v5ePh45Dtz4jeXm/c953zOz075GQ33NbD2lrWE28N9Aacre2r2+L7+w7o/sL1y e380UUREBgGFHBlQnsvK8vulfK2khL3NzWxqaAhYm+QYYphh1D1gORC2zRA5ARLPhOG3QHhOQJsX rAwMJiVN4vlZzzN9yHRufOdG7v34XkZEj2DGkBm+88yHCKB2s72vmyoiIoOEhqtJQNW73Ty5ezcV ra1cl5QEgKfD8Ravl6LmZnY0NgamgXLscY6AKX+Auu0QOhQcSV8dG3oZbPgRVC4PXPuCiMPiIMoR xdNnPc3FYy5mU9km8l7Mo8nVNvfm86LP+fiaj3lx1YvM/ddcmt1fLRZsNsxcPOZi3sx/E4CHTn6I IZGHV8VRRESCn0KOBNSFGzfyr/ZCAwuKi1k+aRLjwsLY0D4cLc1mY0dTE6n27j+htQBd12YSOUq2 GIg5ru1rrwc6LkaZ/SPY+hhULg1M2wahVGcqTe4mTIaJCHsELo+L6UOm8+K5L+K0fTVE9dMvP/UF HIDFOxZjM9vIisnyCzgAiy5dxAWjLuA3Z/wGs2Em0ZnYbz+PiIgMfBquJgHT6vH4Ag5AndvN8poa Ppk4kV8OH0663c6elhYu3bSJv5eXc2tyMuFdVFVTwJG+1WlOiC0KMr4DJg2NOlx76/ZS0VhBWUMZ hVWFXDvhWl6/+HW/gAMwLmEcBl+ViB+bMBaTYWJ84njCbeG+/RnRGczKmgVASniKAo6IiBxEIUcC 4qV9+5i6ejUO01e/ggaQHRpKUXMzTW43O5u/+uT2bxUVzBk6lI2TJwegtXJMM8zgaoCO5YvDhkPK eYFr0yC3varrAgHThkzjlQteYVraNM7LPo+/z/47AKkRqfz7mn9zWc5lXDfxOv59zb+xmq392WQR ERlkNFxN+pXX6+Xi/HzeLi/37TMDo8PCuCs1lX9XVfHgzp1dXntZfj5PjhjBd5KSmF9c3D8NFgGw hILH/VX1tca9UPIxhKaDuxGaSwLdwkHl/Ozzuz12zYRruGbCNQftn5I6hYXfWtiXzRIRkSCikCN9 qqi5mZKWFsaEhWEzmfi8ttYv4AC4gTdGj2as04njk0+6vdequjrO3bCBTZMn8+fSUmo9nm7PFel1 pg5DJb0eyJ4LsVPB64X6HbD1kbZiBcc4EyY8HcqHOG1O6lrqAIgPjee5Wc9x8ZiLA9U8ERE5Rijk SJ9ZVFrKlZs30+L1kut08p+JEzuMtv/KULudzJC2BQDdnY6NDw1lfYfy0TVuN2nLVdlKAix0SNt/ AIYBzgyY+Cym5bPxtFZ2e5nFZMHlcXW7PVg5rU5OHHYi/9j+D7+AA3DV+KuYlTWLupY6zhl5zkHz cERERPqC5uRIn5lTWEiLt23S9pq6Ol4uKmJyRISvVDRAntPJP8aN4/XSUhaWlHBbcrLvmNUwmDdi BCk2W7+3XeSIma14Er/Z4ylXjbvKb7urgHNO1jlfuykWU998fmVg+BUAOGDpDUvZVLapy2ty4nM4 Z+Q5zB472xdwfrf8d3zj1W9wy3u3UNtc2ydtFRGRY5t6cqTPdF6n/MDnu78fNYp7hgzBYhgk2mwc t3o1W9p7a0aHhnJ1QgITnE4yHQ7Oz8+nxu0m1mKhwjX4P/GWIBeVB3v+3OWhUXGjeOHcFyhvKOe9 be91e4t/bPtHt8cMDJrvb+aKP17Bol2LDjr++Dcf57zs81i0aRELNy6koKKApo4FE45CuDUcDJg+ ZDr3n3g/ecl5TH95OmuL1wJwwagLKK4rZlf1Lr/rkp3JXDvhWm6bcpvf/jc2vMHd/7wbaCsRXdNc w+sXv/612igiItKZQo70mUczMrhmyxZavV7GhYWxr7mZEZ99RrrDwYJRoxjmcPBeebkv4ABsbmhg c0MDn1RX4zSbqXG3DWBTwJFBIWJUt4e+qPyC9wre45yR5/QYcjoO9zIw8Hb4uOCMzDOwmq2EWcK6 vHZH1Q5yns2h1dN6FI1vE2mPpLq5GoBT0k9h8bWLDzpnyfVLeHvz24RYQ7hw1IVc9/fr/NoZYY+g 4M6CLoemfb7v8x63RUREeoNCjvSZ2YmJzIyMpLilhQ319Xx761YACpuauGbzZj7JzSW+m6FoXzY3 k6phajLYWJyQNIsQXJjcDYQ27qCsbg8ALZ4W7vrgLhZfc3Bo6I63U3/o/SfeD8Dlwy/nH0X/oKyh zHfMYXbwzOfPdHkfh9nh69GJD42nrKEMEyZmDp3Jvrp9bK/8qmDCzXk3c87IczAZJmYMndHl/Zw2 J1dPuNq3nexM9js+K2tWt3NvTko/iSc/e/Kr7WEndXmeiIjI16GQI30qzeEgzeHg/Ur/ydhbGxpY Wl3NiJAQfpaezs937aLV6/8HXZTFQlFLC6qhJoOGYUD2D2hs3zQVvQ0Fv/MddnlcRIdEd3lpiCWE Rldjl8cAUsNTGZc4DoA4RxyzsmbxyrpXfMd7GpZmt9ixmq2kR6Wz6JJFNLgaSHImUdlYSc6zOX7n ZsVmcXza8Wwt30pZfRnxYfGH+KHhgRMfIL8sn//s/A+5Sbk8cfoT3Z57XvZ5/OmiP/HO1ncYGTuS +06475D3FxEROVIqPCD9YlZMDDbjq9pqNW43M9asIWv5ciY6nXi9nWfwQH5DgwKODGq18d9kdHxb iDAbZh75xiPEh8Xz+Dcfx2ivNTg6bjSzx87mjxf+scd7ZURnYDN/1bu5v3l/j+fbzXbf19XN1dS2 1LKhdAO3/uNWJiZNJMmZRJPr4GB063u3Mv658Yx/fjxDfzuUd7e+e8ifM9wezvtXvE/9j+v59Nuf khye3OP5V4y7goXfWsjPTvkZdou9x3NFRESOhkKO9IvJERF8MnEi9wwZwvHh4TS2r3FT43Zz+7Zt aMaNDHYmINps9t9pcfLuNUv49PpPKbizgOtzrwdgzvQ5lP6wlH3f38em2zfxxsVvcP6o85mUPKnb +y/5cgnzPpvn275x0o2+KmoWk4UJiROAth6h35z+G+6YckeX99lRtcP3dW5SLmdnne133OV1sbWi bWhpk6uJOR/NObz/ASIiIgOIhqtJv5kaGcnUyEi+vWULy2u/KhvbrEU9JQh4gCq3/0pPZuCE9ZuZ ERnF71OG+h2LC43z27aYLCy+ZjHPrnyWZncz04dM58q/Xkl5w1eL57624TXumXkPAGdnnc2K76xg 5b6VTE6ZTG5SLntr9xLliMJpc7KhZAMvrH7BtxDnAZfmXOr72jAM3pn9DiOeGsHO/TsBsJqsfoUL PF69PkVEZPBRyJF+d21SEn8sKcHl9WIC3Ao5EmQchkGo2Uyly0VRSwuLysr4qLKSl7KzuTQhodvr Ih2R3HvCvb7tKSlT+GD7B77t4rpiv/Nzk3PJTc71badFpPm+Hpc4jtU3rebjLz7G7XFT3lhOZnQm V433X6vHbDKz9NtLeeiTh6hpruGq8Vcx56M5bCnfgs1s41en/eqo/z+IiIgEikKO9LsFRUW42ufg eICKTp9+iwx20yMjsZtMfNCh4EaN283sTZvICQsjJ6zrEtCd3TjpRr+Qk5ecd0TtyIrNIis265Dn JYcn8/w5z/u2T04/mQ0lG0iNSCUtIo3tlduZv3o+EfYI7jr+rm4rp4mIiAwUCjnS7+o7hZpEq5WS 1qNf10NkIDEBOWFhTHI6/UIOtC2Qu7Wh4bBDzoWjL+S3Z/yWP+f/mfSodOadOe/QF/WCUGsox6cd D0BRbRHTFkzzDZv75/Z/8t/r/9sv7RARETlaKjwg/e57aWmEmtp+9UJNJl4bPZrvpaX5VV8TGaw8 wFN79/KvqirOj431O2Y3DI6PiDii+9099W6W3rCU1y9+/bDKOfe2pbuX+s0LWvLlEiobK3u4QkRE JPAUcqTfzYyKIn/KFP42diwbp0zhtJgYNjc00NJFGWmRwer10lJGhIRwdWIiCVYr48LC+GzSJFLt g6tkcmZMJibjq7eKhLAEIu2RAWyRiIjIoWm4mgREekgI6SEhvu3OQ9hEgsHLxcVUzpwZ6GZ8LROT JrLgvAU8+r9HCbeH88zZz2A2mQ99oYiISAAp5MiAMHfIEJbX1Kg3R4JKsAzBvG7idVw38bpAN0NE ROSw9fpwtUceeYTZs2dz+eWXs2HDht6+vQSpRo+HBKuV4PiTUKRNg8dDQ4B6KVvcLSzcuJA3NrxB s6s5IG0QEREJlF7tyVm5ciW7du1i4cKFFBYWct9997Fw4cLe/BYShHY2NnLl5s20qhdHgkyt282O piZGhYays6mJOKuVSEv3/+yWtbTwUlERFsPg5pSUHs/tidvj5qw/ncXiHYsBOGHoCSy+djEWkzrv RUTk2NCr73jLli3jtNNOAyAzM5Oamhrq6+sJO8xyqRIcChoamFNYSI3LxffS0rggvueKUF82Nyvg SFAyAQZw4po1LK2pIdRk4s2cHGZ1qroGbfPSZq5ZQ0FjIwALS0tZPmkSVtORd7jnl+X7Ag60VURb X7KeScmTjvZHERERGVR6dbhaeXk5MTExvu3o6GjKy8t7uEKCjdfr5cz163mvooL/VldzyaZN5NfX 93hNrtPJcIfjoP2a2iyDnQeYs307S2tqgLbha3ds29bluWvr6nwBB2BNXR3bO2wfiWhHtF9FNAOD aEf0Ud1LRERkMOrTsQvew/h0ftWqVX3ZBOljnZ9frdfLjqYm37bL6+XdDRtoslp7vM9zZjPzLBY+ cLl8+zy921SRgCivrvbbrmtu7vLfvSqPBwtw4BXgAPZt3kxDN8ULDvVv59ycuTy56Um8eLl79N1U flFJJVrfZqDQe9/gpWc3uOn5HTt6NeQkJCT49dyUlpYSf4ihSnl5eb3ZBOlHq1at6vL5Tfr8c1bX 1QHgNJuZPWGCX7no7pwB/G7PHn5fXEyIYbCstra3myzS70otFjJNJgqbmjABvx45krzk5C7Pfa20 lB9/8QUWw+A3I0bwjS6GtUH3r72O8vLy+OVFv8Tr9ark8wBzOM9PBiY9u8FNz29wO9KA2qshZ8aM GTz99NNceuml5Ofnk5iYSGhoaG9+CxkEPhw/nl9++SU1Lhe3pqQcVsA54K60NO5MTeXu7dtZWVeH S3N1ZJD7sqWFO1JSuCg+nhS7newe/k28LCGByxISeu17mwwTKlkoIiLHol4NObm5ueTk5DB79mzM ZjMPPvhgb95eBokQs5kkm41ws5m4QwxTO6DW5WJjfT3pDgfvVVTw1N69fdxKkd5nM4wu13r6X3U1 T40cGYAWiYiIHJt6fU7O97///d6+pQwiXq+Xs9avZ0n7PISXiopYP3ky8TZbt9fsbmrihDVr2NXc TIjJxAmRkf3VXJFe1d1itgnd/P6/XVbGgqIiEm02HsnI6PY8EREROTJaNEF6VVlrqy/gABS3tLCs pobz4uK6veapvXvZ1dy2WGGjx8NHVVV93k6R/nRraupB+5bX1PCt/HxfgY2CxkaW5Ob2b8NERESC VK+WkBaJsliI7bCAoQlI76I8dEf6JZRg9u2kJM6Pi+P9igrGrFjB6BUr+Ht5OStravwqCP6vupp/ K+CLiIj0Cv19Kb3KZjLxzrhxTHQ6GRESwkvZ2Yx3Onu85rtpaYxsL06gGlASLI53OvlOcjJnxcRQ 2tLCJfn5bG5oYEtDA5fl55MZEuL3D7AXOGfDBrY3NASqySIiIkFDw9Wk102PjGTN5MmHfX6S3c66 yZNZWVvL30pLeXLfvj5snUjfiTabibBY2NXczPK6OpbX1TG/qIgHhw2j0fNVv02z10u81cqro0Zx 1ZYtvv1NHg/r6usZoaqUIiIiX4tCjvSZTfX1bKivZ0p4OBndlJF2eTyUtbZiNQyu27KFLzosJCoy 2FS53VS53QftX1lby8iQEAoaGwHICglhTFgYo0NDSbfb2dk+Jy3UZCL3ED2fIiIicmgKOdIn3isv 56L8fFq9XkJNJv49YQJT26um7W9t5XuFhayvq+OLxkb2u90kWq2UtLYGuNUifeP/qqoIN381GDPK bKbW5eKktWvZ2dyMCZgaEcGjmZndfiAgIiIih08hR/rEDwoLaW0vp9vg8fDcvn2+kHNTQQFvlZX5 na+AI8GsyeulyeXyba+sq+Px3bvZ2t6z4wHKW1uZofLpIiIivUKFB6TXraiu9v3xdoDN1Par1uR2 s6xDiWmRYGE3DGZGRHBeTMwhz400mwk1+5fZMBlGXzVNRETkmKOeHOlVJS0tnLdx40H7b0xOpt7t 5sQ1a9jT0hKAlon0rWavl09raggxdf3Z0VWJiSytribEZOKprCwmOJ38tbycjfX1hJhMPJaR0c8t FhERCV4KOdKr/lRSctDQs5MiI5kcHs4bpaWsrqvzOxZmGDR6vX7rhRi0ldMVGYw6VlEDSLPZ+OvY sUyJiDjo3M/z8tja0ECyzUa8zdZfTRQREQl6Gq4mvSq006fYsRYL/xw/HpNhYO9iOE59e8A5cFWu 08nfc3K4IiGBiG4+ERcZTFLsdkZ2UxLabjIx3ulUwBEREell+itSetX1ycmcFh0NgMNkYqjDwV3b t7O/tZUL4+M5Pza2y+s8tHUrrqmr4/z8fFbV1lLT6RNxkcHABNyUlERk+5ybFbW1zFyzhoYuSkt3 paSlhc319bi96s8UERE5Wgo50qvsJhMfjR/P77OzafJ4WFNXx0tFRVy/dStmw+DtsWPZNXUqqV18 cn2g9pQXDipcIDJYeIA/lJRQ3SHUbKyv57wNGxi1fDk3b91KczcB/tXiYtKWLWPMypWctm5dt+eJ iIhIzxRypNcZhkFhp0U9V9bU+I4NdTi4IzX1iO9rPvQpIgNCs9d70ITHf+/fz9bGRl4sKuKRXbu6 vO6ubdtwtffg/Gf/fv5cWtrHLRUREQlOCjnSJ07otN7HiVFRftv3DB3KbzMzibdaD7o2zGTiivj4 g/Yf3mAfkYHhQM9kiMlEVqcFPrvrqXR1GqLWeVtEREQOj0KO9InTY2J4c8wYLomP554hQ5ifne13 3DAM7h4yhN3TpvF2Tg4nR0aSarNxZnQ0Z8bEsLDTYqEig9X5cXHcmpLit++cbuam/TozkwPlOSaH h3NZQkIft05ERCQ4qYS09JlLEhK45BB/pNlNJi6Ij+eC9p6bqatW8c+qqv5onkivGhkSwqXx8RQ0 NvJmh5AeY7HwvSFDiLdaWVVXx0mRkb7f985uT03l9OhoyltbmRQejl0VBkVERI6KQo4MGF6vl5W1 tYFuhshROT0mhp9nZLC7qYktDQ2sr6/nuPBwfpqeDsBVSUlcdRj3yQoNJatPWyoiIhL8FHIkYJrc bp7Ys4e9zc3MTkjgxKgopkdG8ml1daCbJnJIHRetHRcWxv3DhlHc3Eyly8XKvDy8oJ4YERGRAFHI kYC5bssW/tw+rGd+URFLc3P529ixPLBjB6UtLdyQnMycwkI2NzQEuKUiB3th5EiGORxkhYQwzOHg L2VlXLV5My1eL7lOJ/+ZOFEhR0REJEAUciRg/llZ6fu61etl8f79zI2I4NmRI337E6xWpq9ZQ4uq TMkAc1NBAQBpNhsbpkzhe9u3+35P19TV8e0tW7gkIYFL4+MxDMN3ndfr9dsWERGR3qePGSVgcsLC /LbHdtpu9nj4fmGhAo4MaHtaWsj9/HP2trT47f9LeTmzN23ixq1bAah3uzl7/Xqsn3zCuJUrKdSC tyIiIn1GIUcC5s9jxnBebCx5Tie/HTGCszuV1X2/ooL/djE/x24YhHYxDMipoUESIDubm7s99oeS EjxeL499+SUfVFbiBjbW13PXtm3910AREZFjjIarScCkORz8fdy4bo9bOg3pMQFWw6DZ64VOvTsW w+DWlBQe27OnL5oqctjSbDb2dOjVibdaMRkGZa2tfueVdtoWERGR3qOPvmXAmhUby/ntvTsm4LzY 2LaA0wWX16uAI/3qQATv/EnR7IQE5qSlEWoyMcxu589jxgBwTVISjg69jTclJ/dPQ0VERI5B6smR ActsGDyemUl2aChpdjuxFgt/q6gIdLNEABjucPC/3FzSli3z25/ucHB7WhqPjxjht//4iAhW5+Xx 3+pqxoSGckJUVH82V0RE5JiikCMD1heNjRy3ejVVLhfQ9sn3nLQ0Xi0uZr/bTasKEkgATY+MJMlu 55qkJH5fXOzbf9f27bR6vXx3yJCDrhkdFsboTgU2REREpPdpuJoMWO9XVPgCDsAfS0p4fMQISmfO ZOfUqZymT8IlAIba7Xw/LY3n20udz8/O5lfDh/uOe4DvFxayr4diBCIiItK3FHJkwEqz27vdTrHb +WD8eB5KT2eiPhmXfvTGmDE8MWIEYWYzACbD4OToaL9zvECd2x2A1omIiAgo5MgAdmF8PD8cMoRY i4Wc0FDfBO4DLCYTD6ans2ryZIZ1CkQivaXjmN6zYmKYHhmJy+PxOyfP6eQbHXoWL4iLIyskpJ9a KCIiIp1pTo4MaI9mZvJoZmaXx7Y3NHDexo1sbWhgdGhoP7dMjhXXJiVxVkwMaXY7+9oX/lxXV0eM xcIbY8bwzZgYLCYTH4wfzz8rKzEbBmfGxGB0KoEuIiIi/Uc9OTJo3b5tG5sbGvAA+Q0NRJrNRLYP IRLpLYk2GxcnJJDf0MBF+fmsravDC1S4XFy+aZPvPKvJxLlxcZwdG4tJAUdERAxU8wIAABwrSURB VCSg1JMjg1bnxRWrNQdC+sAJkZEAvF1eftCx/S4Xbq8Xcxeh5j9VVbxUVESs1cpP0tOJtVr7vK0i IiLSRiFHBrzylhY+rKoi0WrltJgY3/5bUlK4uaAggC2TYGXQVjwg0+Hgx198wcdVVWQ4HAedd2tq apcBJ7++njPWr6elvcz5qtpa/jdpUh+3WkRERA5QyJEBrbSlhSmrVvFleznee4YM4Vftc3RuSklh dGgod2/fzpq6um7vYaKtrK/I4Yo0mzkvNpZXS0sBWFNfz8/S07kiIYH/VVeTbLMxZ8gQvpWQ0OX1 n9XU+AIOwNKaGlweDxaTRgiLiIj0B73jyoD2t/JyX8ABmLd3r9/xE6KiWJqby9BuqqudExvrW89E 5HA1e70UNjX57dvW2Mifxoxh57RpLMvL6zbgAEx0Ouk4O2x8WJgCjoiISD/Su64MaFEWS4/bAA6z mRHdlOutam0lt9MfnCKHMsnp5IwOQyOBg7Z7khcezps5OXwzOprZCQm8N25cbzdRREREeqDhajKg fSs+nmsSE/ljSQlRFguvjhrV5XmPZ2Zy5vr1lHYqRvC/mhqcZjNvjx3Li0VF/KuykuYOw4hEunJt YiLfSUkhzmplbV0dp0ZHc1kPPTdduSg+novi4/uohSIiItIThRwZ0EyGwR9Gj+aFkSOxm0zdrj2S Gx7OrqlTWVFbyylr1/rm4FgNgxirlXPDwjg3Lo6f79zJgzt3+q5zAE1d3VCCQohhMNHpZEN9PXWe 7mdmHSg0ABBvsXBOXByGYXBramq/tFNERER6l4aryaDgMJsPubiiw2zmxKgons7KItxsJtpi4fej RpFgswFQ1tJCis3GqJAQwk0mjgsP5/j28sASnNxeL182N5PazZytA7xAqs2G02SizOXitm3baO0h FImIiMjApp4cCRoer5c9zc1cnZh40Cfw5e1V2nZ1KGKworZWc3WCXAuwt6UFAKfZTF0PaykVt7Rw 4Ojfyst5ubiYm1NS+r6RIiIi0uvUkyNBocHt5pS1axn22WckLV3KPysqfMee27uXqatX+wWcA7R8 6LHj24mJfJqby93dDEGzdap+VtVpfpeIiIgMHgo5EhQWFBXx3+pqAOo9Hm7ftg2Am7du5bZt2w4q B3yACbglORl7h6Fwtj5vrfQ3M7CjqYn/7t/PY5mZbJg8meuTkhgfGspEp5OHhw/ngWHDfOcnWq1c npgYuAaLiIjI16LhahIUmjrNn2j0eKh1uXipqKjba6zA66NH863ERJ7Lzgag3u3G5fFw3OrVFDQ2 9mWTpZ/EWixUuFy8W1nJu5WV7Ghq4sXsbF7uolLfzMhIvmxu5tSoKJIPMY9HREREBi6FHAkK1yYl 8fy+fXzR1IQJ+Gl6Oi6vl56KRb+Zk8MFHUr8rqut5aWiIuIsFmZGRrK7uZlGTT4f9LJCQqiorfVt /6uqyu/4vD17+HdVFROcTh4YNowTtGiniIjIoKeQI0EhwWZj9eTJLK+pIdVuJycsDIAfDBnC47t3 A/5lggG/T+qf2rOHu7Zv78cWS3+JtVr9tse1/24AvLBvH99tf+7vVlTQ4HbzxIgR/do+ERER6X0K ORI0Ii0WTu+0Kv1jmZlcnpBAvdtNtcvFTQUF1Lrd3Dt0KMdHRADg8niYU1jY473jrVbKNBF9wJsW Hs6yDr02AB9WVTE+LAy7YZAVGsrvsrJ8x5a1z+M6YGlNTb+0U0RERPqWQo4EvUnh4b6v98XFHXTc Q9t6Kj0pa23F1H6uDFwXxMdT7/Gwvr7et8/l9bK+vp6ns7K4vVNltakREfyhpMS3Pa09+IqIiMjg psHncsyzmUz8JD3dtx1qMvFERgbDOk08V8AZuMLNZr6TnMz309L4NDeX10aPJqHTMLWS9vVyOrol NZXfZGYyKyaGHw8dyq8yMvqrySIiItKH1JMjAjyYns4FcXHsd7mYGhHB3MJCv3V11IvTv8aFhlLQ 2EjzIXrYDjgtOpqX2ivkhZtMXJmYyJdNTfx4x462fWYzsxMSAPB6vfzoiy94q6yM4Q4Hvx81iu8O GdI3P4iIiIgEhEKOSLvxTicA/1dVxby9e337TUCk2UyVW0uH9ocTIiNp9ngOO+BA18MN7x02jFyn ky+amjg9OpoRoaEAvFpSwqPtxSh2NDVx7ZYt/N/Eib3TeBERERkQNFxNpJP9Lpfftgf8Ao4BnBwZ 2eW1ZuDaxESmdKjgJUfm8oQE9nUxtKwnx3czl+bM2FhuS031BRyAwk7rH23XekgiIiJBRyFHpJPT oqPJ6fBHcUeXxsdTPH06/544kYu7KGIQb7XyyujRvDZmjF5cR+G0qChuSE7mhqSkHs8z09a7BnB8 eDh3dCoo0JNzYmOxGoZv+6IunqOIiIgMbhquJtJJuMXCskmT+EdlJa8VF/NeZaXv2OnR0STYbCyv qWHx/v0HXRtvswHQ4PFoDs9R+LS6mvt37GCI3c7L2dnUuN3EWSw0ejw4TCYe3b2bZo+Hn6Snc1Fc HJUuF0k2G6YOoeVQjouIYEluLn8vL2e4w8ENycl9+BOJiIhIICjkiHQh3GLhsoQEFpaW+u3f3tSE 2+vle9u3U9VpWFu0xcKz7WuwxFmtmIFjYRZPut3Ozg5FGr6OJq+Xx9rnyyTZbKzJyyPJbmdvczN1 bjfrJk/GMAyKm5t5r6KCjJAQUjpVwTscx0dEdDvETURERAY/hRyRHpR2mhuyu6mJ41atYnVdnd/+ 6xITeSE7G5upbZBamsPB/Oxs7tq2jSavl1iLheJeWEz0rpQUatxuXumwtkug9VbA6ay4pYUPKiup drn4fmEhXuDCuDh+nZHBjDVrKGttxQBeGDmSG1NS+qQNIiIiMjhp2oBID25KSeHAQCi7YWAzmQ4K OFbD4IyYGF/AOeC65GRqTjyRlpNOYve0ab45PBFmM++MHcvi8eP95oYcyuTwcOaNHMkjGRmktA+L 6y3hR9CO7jhNJkJMJhyd/j9YDnHvn6enM8Lh6PJYjMXCnPaAA/B2eTkP7NhBWXtg9AKPt/f8iIiI iBygnhyRHlyblESmw8H6+npOiIzkF7t2HXROq9fLLQUFnBMbi9PS9UvKYjKxaOxY6lwuQs1mTIaB 1+vFZhi0dlH++MLYWD6qqqLe89XMnsvi4wFIstv5PC+PdysqKGxspKChgfLWVj6vraXJ6+XkqCia 3W6W1dYe/g9qMsHXLJEda7Xyi+HDSbHZ+Ob69b45SS6vl1Sbjb3tvWInRkTwv5oa31A+E7BuyhQ2 1Nfzz4oKHtq1Cy9toTLOZqPz/53OISqim//nIiIicuxST47IIcyMiuK21FTGOZ3dzuOodrspPYzh aE6LxTdJ3jAMns7K8vV0dOzv2Fxfz+nR0cRYLESazSRarTy3dy/Ptq/fk2y3c1NKCr/OzOTtceNY MmkSl7Uvdvmf/fsPGXDMHb4eERLCaVFRXZ53oE2xZjOH6uvZ1dzM1Vu2sLWxkRfa5yYdsLelBYdh MCY0lIsTEvzmKt2/cyfXbdnCC/v28X/79/tCTbPXy/P79vGT9HTfud+IiuK3I0Zwcnt7E6xW3zwo ERERkQP0EajIEbg6MZEndu8+aB2XCWFhDD3MCfB7m5u5fssWtjc2cmFcHLunTuXDqiqu27LFd86W pia2NDX5tqvbe1lu37aNvPDwg8LW+ro6/nCY83TeHD2aM2Jj+cOqVcSmp3NWTAwWw2DfunUsbw9H YSYTLR4PB2JbhdtNdkgIWzutKWOibchYx96WhSUlPDVyJCbwqzDX5PWyqaGB3+7Z43cPL/BWWRkA TrPZ71iIycRP0tO5ND6eGrebyeHhmA2D/5s4kf2trUR0CI0iIiIiByjkiByBeJuN1ZMn87fycjxe L7uamnCYTNyVlobFdHgdo9/esoV/VVUB8OSePYwKDeWEyMiDQkF3djQ2HhRyjuTP/OMjI4mwWJhu sZCXmOjb/1leHkv27+fL5mamRkQwYvlyv+s6BpxQk4kfpKUxxOHgxoICv/OW1dQA8FJ2NvcUFlLe qQpdRWtrtz9rndtNss1GUUsLWSEhPDBsGACju1hcNcpqPYKfWkRERI4lCjkiRyjRZuPmr1HNq7BT b8j2xkZuTEnhxexsfrJjB0UtLd2GnViLhRO7GFqWGRJCtNlM1SHm1VwcF8fQbib5A5zQ4d63paTw 7L59AH5zagCaPB7uT0+n2ePhl19+yc4OvU6twNWbN/Pf3FxfZbSOTo6KIt5qZUFx8UHfP8PhYOOU KZS1tpJss2E9zOAoIiIi0pFCjkg/uzA+3lcRzGIYnNdede2G5GRuSE7m3fJyLt20iSaPh1SbjW8n JeG0WKh1u7k2MfGgdWG2NTTwVmnpIQMOwNmxsYfdzmdGjuSCuDiqXS6mhIdz6rp1fNEeZm5OScFq MmE1mViam8uMNWvY0SHorK+v59L8fF4bPZqn9uxhR3uZ6ekRESzKycFsGJwcFUVJayvJViuvl5bi NJt5OCODELOZoZ2GrYmIiIgcCYUckX72aEYGo0JD2d7YyDmxscRYLPyxuJhcp5OxTicfVVXR1F5V LcZqZe7QoV1WbfN6vVy9eTN/Ki097OFqCT0M8VpXV0dxSwszIiJ83++bMTG+4yvz8ni/ooIYq5VZ HcJSst3OO2PHMnPNGt/cIWgrgBBvs7F2yhSW1dSQarMx1un0Hb8qKcn39RUdvhYRERH5uhRyRPqZ YRjckJwMwOKqKiZ+/jktXi9Ww+DPY8bwdHsFNaCtrHJlJd9qr5zW0ZLqav5UWgr4T/w3gOPDw6lx uxkREsJnNTVUuVzckpLCOe29Rh3Vu92ctX49S6qrARgVGsrS3FyiOwWiGKuVq7sJI2OdTv42diyn rlvna8uk8HCgrcTzGR3CkoiIiEhfU8gRCaBn9+6lpX2dnFavlwVFRYSYTDR2WB+nu3VgXF2sr/NE RgbnxsWRFRrqt9/j9XZbhez2ggJfwAHY0tDAwtJSbk1NPaKf5eToaF4dNYqXi4tJtNl4IjPziK4X ERER6S2a1SsSQF31lvx+1Cjfgpc3JSdzclQUW+rrqelUpeykqChmdeoh+cEXX/gqt3XUU5nl5V2s qRNylBP+r0pKYvHEibwxZsxBc4dERERE+otCjkgA/Tw9ndz2eSrjwsJ4ePhwLktIoHrmTGpmzuRn w4cz4fPPGb1yJcM++4ylHXpczIbBO+PGcUOHIWRe4In2ogYAH1RUcPHGjdyydStlndb2OWBmZKTf 9oSwMCY4nextLxYgIiIiMthouJpIACXZ7ayePJlGt5uQDhXFbCYTNpOJnxcWsqWhAYD9LhdzCwv5 dNIk33kmw2BMpzVkDgxvW1Nby3kbN/qGtb1bUcGqvDySOvWwPDViBHFWK/n19cyIiOCjqiomrVqF GXhu5Ehu/BrlskVEREQCQT05IgNASDclk1s7zbvpvA1wa0oK34yOBtqqpz0/ciQAK2pr/ebt7Gtp 4aQ1a2jx+K/C4zCbeSQjg3fGjWOIw8Hi/fsBcAN3b9+Ot4vvKSIiIjKQ9VpPzttvv828efMYOnQo ADNmzODmm2/urduLHJPuSk3lzdJS9rW04DCZ+Gl6ut9xl8fD8/v2MSo0lLtTUzkrNtY3/ybP6cQE fguLFjQ1sbOpiZGdChMc4OkUaBRvREREZDDq1eFqZ599NnPnzu3NW4oc04aHhJA/ZQrr6+sZ7nAw xOHwO377tm28WFQEtFVq+yQ3lxntc2wmR0Tw4siR3FRQ4As60RYLyTZbt9/v4vh4ntu3j6U1NRi0 relj9FC0QERERGQg0pwckQEuymrlxKioLo+9X1Hh+9oNfFhZ6Qs5ADekpJBqt/PQrl1YDYNHMzII 76YkNbQNm/vPxImsrasj1molIySk134OERERkf7SqyFnxYoV3HjjjbhcLubOncvo0aN78/Yi0sno sDD2dqiaNrqLYWhnxsZyZmzsYd/TajIxJSKiV9onIiIiEghHFXLeeustFi1ahGEYeL1eDMNg1qxZ 3HnnnZx00kmsXbuWuXPn8u677/Z2e0Wkg1dHjeKWggK+aGri0vh4Lk9MDHSTRERERALO8PZR6aSZ M2eyZMmSHsfzr1q1qi++tYiIiIiIBJm8vLzDPrfXhqvNnz+f5ORkZs2aRUFBATExMYc1YflIGisD y6pVq/T8BjE9v8FLz25w0/MbvPTsBjc9v8HtSDtHei3knHvuufzwhz9k4cKFuN1ufvnLX/bWrUVE RERERA5br4WcxMREXn311d66nYiIiIiIyFExBboBIiIiIiIivUkhR0REREREgopCjoiIiIiIBBWF HBERERERCSoKOSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdE RERERIKKQo6IiIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgRERER EZGgopAjIiIiIiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQk qCjkiIiIiIhIUFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoK OSIiIiIiElQUckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6I iIiIiAQVhRwREREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIi IiJBRSFHRERERESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhI UFHIERERERGRoKKQIyIiIiIiQUUhR0REREREgopCjoiIiIiIBBWFHBERERERCSoKOSIiIiIiElQU ckREREREJKgo5IiIiIiISFBRyBERERERkaCikCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwR EREREQkqCjkiIiIiIhJUFHJERERERCSoKOSIiIiIiEhQUcgREREREZGgopAjIiIiIiJBRSFHRERE RESCikKOiIiIiIgEFYUcEREREREJKgo5IiIiIiISVBRyREREREQkqCjkiIiIiIhIUDnqkLNixQqm T5/OJ5984tu3ZcsWZs+ezRVXXMFDDz3UKw0UERERERE5EkcVcnbv3s0rr7xCXl6e3/6HH36YBx54 gNdff52amhqWLFnSK40UERERERE5XEcVchISEnjmmWdwOp2+fa2trezdu5ecnBwATj31VJYuXdo7 rRQRERERETlMlqO5yG63H7SvqqqKyMhI33ZMTAxlZWVH3zIREREREZGjcMiQ89Zbb7Fo0SIMw8Dr 9WIYBnfeeSczZszoj/aJiIiIiIgckUOGnEsuuYRLLrnkkDeKiYmhqqrKt11SUkJCQsIhr1u1atUh z5GBS89vcNPzG7z07AY3Pb/BS89ucNPzO3Yc1XC1jrxeb9uNLBYyMjJYvXo1kyZN4qOPPuLqq6/u 8drOhQtERERERES+LsN7IKUcgU8++YT58+ezY8cOYmJiiI+PZ8GCBRQWFvLggw/i9XqZMGEC99xz T1+0WUREREREpFtHFXJEREREREQGqqNeDFRERERERGQgUsgREREREZGgopAjIiIiIiJB5WtXVzsa K1as4Lvf/S6PPPIIJ510EgBbtmzhpz/9KSaTiezsbH7yk58EomlyBN5++23mzZvH0KFDAZgxYwY3 33xzgFslh/LII4+wbt06DMPgxz/+MePGjQt0k+QwrVixgrvvvpusrCy8Xi/Z2dncf//9gW6WHEJB QQG333471113HVdeeSXFxcX88Ic/xOv1Eh8fz6OPPorVag10M6ULnZ/dvffey8aNG4mOjgbghhtu 8P0dIwPPo48+yurVq3G73dx0002MGzdOr71BovOzW7x48RG/9vo95OzevZtXXnnloPLRDz/8MA88 8AA5OTnMmTOHJUuWcMIJJ/R38+QInX322cydOzfQzZDDtHLlSnbt2sXChQspLCzkvvvuY+HChYFu lhyB4447jnnz5gW6GXKYGhsb+cUvfsG0adN8++bNm8fVV1/N6aefzm9+8xv+8pe/MHv27AC2UrrS 1bMD+MEPfqBgMwgsX76cwsJCFi5cyP79+7nwwguZOnUqV111FWeccYZeewNYd8/uSF97/T5cLSEh gWeeeQan0+nb19rayt69e8nJyQHg1FNPZenSpf3dNJGgt2zZMk477TQAMjMzqampob6+PsCtkiOh gpiDi91uZ/78+X6LY69YsYJTTjkFgFNOOUXvdwNUV89OBo+OHwhFRETQ0NDAypUrOfXUUwG99gay rp6dx+M54ve/fg85drsdwzD89lVVVREZGenbjomJoaysrL+bJkdhxYoV3HjjjVx//fVs3rw50M2R QygvLycmJsa3HR0dTXl5eQBbJEeqsLCQ2267jSuvvFJv0IOAyWTCZrP57WtsbPQNkYmNjdX73QDV 1bMDeO2117j22muZM2cO+/fvD0DL5HAYhoHD4QBg0aJFnHzyyXrtDRIdn91bb73FySefjMlkOuLX Xp8OV3vrrbdYtGgRhmHg9XoxDIM777yTGTNm9OW3lT7Q1bOcNWsWd955JyeddBJr165l7ty5vPvu u4FuqhwB9QoMLsOGDeOOO+7grLPOYvfu3VxzzTX861//wmIJyPRK6QV6DQ4u559/PlFRUYwaNYoX X3yRp556igceeCDQzZIefPzxx/zlL39hwYIFnH766b79eu0NfB9//DF//etfWbBgARs3bjzi116f vjNecsklXHLJJYc8LyYmhqqqKt92SUmJuocHmEM9y4kTJ1JVVeULQDIwJSQk+PXclJaWEh8fH8AW yZFITEzkrLPOAmDIkCHExcVRUlJCampqgFsmRyIsLIyWlhZsNpve7waZqVOn+r7+xje+wU9/+tPA NUYOacmSJbz44ossWLAAp9Op194g0vnZHc1rL6AlpA+kaIvFQkZGBqtXrwbgo48+UtGBQWD+/Pm8 //77QFsFmpiYGAWcAW7GjBl8+OGHAOTn55OYmEhoaGiAWyWH69133+Xll18GoKysjIqKChITEwPc KjlS06ZN870OP/zwQ73fDSJ33XUXu3fvBtomR48cOTLALZLu1NXV8dhjj/H8888THh4O6LU3WHT1 7I7mtWd4+7m/7pNPPmH+/Pns2LGDmJgY4uPjWbBgAYWFhTz44IN4vV4mTJjAPffc05/NkqNQUlLi K8Xodru59957VY54EHjyySdZsWIFZrOZBx98kOzs7EA3SQ5TfX09c+bMoba2FpfLxR133KE36QEu Pz+fX/3qV+zbtw+LxUJiYiKPP/44P/rRj2hpaSElJYVHHnkEs9kc6KZKJ109u6uvvpoXXniBkJAQ wsLCePjhh/3mOcrA8eabb/L000+Tnp7uG2Xy61//mvvuu0+vvQGuq2d30UUX8dprrx3Ra6/fQ46I iIiIiEhfCuhwNRERERERkd6mkCMiIiIiIkFFIUdERERERIKKQo6IiIiIiAQVhRwREREREQkqCjki IiIiIhJUFHJERERERCSoKOSIiIiIiEhQ+X/G7NKjMfT3SwAAAABJRU5ErkJggg== ", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7602226,"math_prob":0.9901977,"size":40496,"snap":"2020-10-2020-16","text_gpt3_token_len":11106,"char_repetition_ratio":0.15778425,"word_repetition_ratio":0.3454517,"special_character_ratio":0.2838305,"punctuation_ratio":0.16982456,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998585,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"im_url_duplicate_count":[null,2,null,2,null,4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-02T04:38:51Z\",\"WARC-Record-ID\":\"<urn:uuid:debebe5b-89c1-45c4-b2ee-359243007120>\",\"Content-Length\":\"1048971\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8c822415-f203-43ce-a3ce-819e0fd4e27e>\",\"WARC-Concurrent-To\":\"<urn:uuid:271467de-fa41-4304-8215-c8cd1d1e6d87>\",\"WARC-IP-Address\":\"128.208.3.226\",\"WARC-Target-URI\":\"https://homes.cs.washington.edu/~jmschr/lectures/Parallel_Processing_in_Python.html\",\"WARC-Payload-Digest\":\"sha1:4O75M7PJTIV4RVJH5PNRKDW2JWVS2H7F\",\"WARC-Block-Digest\":\"sha1:BCQ6ZRX4UJWU2L4YWJUVGVWIWPOWLL5C\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370506580.20_warc_CC-MAIN-20200402014600-20200402044600-00378.warc.gz\"}"}
https://sci2s.ugr.es/covariate-shift-cross-validation
[ "# A Study on the Impact of Partition-Induced Dataset Shift on k-fold Cross-Validation - Complementary Material\n\nThis Website contains additional material to the SCI2S research paper: A Study on the Impact of Partition-Induced Dataset Shift on k-fold Cross-Validation\n\nJ.G. Moreno-Torres, J.A. Sáez, and F. Herrera, A Study on the Impact of Partition-Induced Dataset Shift on k-fold Cross-Validation. IEEE Transactions on Neural Networks 23(8): 1304-1312 (2012)", null, "Summary:\n\n## Abstract\n\nJ.G. Moreno-Torres, J.A. Sáez, and F. Herrera, A Study on the Impact of Partition-Induced Dataset Shift on k-fold Cross-Validation.\n\nCross-validation is a very commonly employed technique to evaluate classifier performance. However, it can potentially introduce dataset shift, a harmful factor that is often not taken into account, and which can result in inaccurate performance estimation. This works analyzes both the prevalence and impact of partition-induced covariate shift on different k-fold cross-validation schemes.\n\nFrom the experimental results obtained we conclude that the degree of partition-induced covariate shift depends on the cross-validation scheme considered. In this way, worse schemes may harm the correctness of a single classifier performance estimation and also increase the needed number of repetitions of cross-validation to reach a stable performance estimation.\n\n## Single-experiment classifier performance analysis results\n\nThis section includes the results for the single-experiment classifier performance analysis experiment. There are 4 files, one for each type of partitioning studied (DOB-SCV, DB-SCV, SCV and MS-SCV). Inside each file, you can find the results divided in sheets. Each sheet corresponds to a different partition granularity: 10x1, 5x2 and 2x5. On each sheet, you can then find the test AUC obtained by each method on each dataset.\n\nWe also include here the results of the partitions created to obtain \"true\" classifier estimations. These are presented in a single file, since we use the same data as a reference when studiying all 4 methods. Remember the presented results are classifier performance measured as ROC AUC in the test set." ]
[ null, "https://sci2s.ugr.es/sites/default/files/icons/pdf_download.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8391216,"math_prob":0.61970556,"size":3440,"snap":"2022-27-2022-33","text_gpt3_token_len":765,"char_repetition_ratio":0.15599534,"word_repetition_ratio":0.32520324,"special_character_ratio":0.19912791,"punctuation_ratio":0.110367894,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95483,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-29T06:48:50Z\",\"WARC-Record-ID\":\"<urn:uuid:ab3d5c44-713c-43b8-9df7-f1ce0bef4e69>\",\"Content-Length\":\"33023\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:81bb0d85-31f5-465c-9e31-a80bd56d4f2a>\",\"WARC-Concurrent-To\":\"<urn:uuid:f8b9a14b-0719-4607-8e9b-c1647f6c62fe>\",\"WARC-IP-Address\":\"150.214.190.154\",\"WARC-Target-URI\":\"https://sci2s.ugr.es/covariate-shift-cross-validation\",\"WARC-Payload-Digest\":\"sha1:GHPNDV7OMZUNNDTRRCBZYHZR5NNBH7QP\",\"WARC-Block-Digest\":\"sha1:JK543BYIKXTRX3N5G5HGMCJLVGRH55XU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103624904.34_warc_CC-MAIN-20220629054527-20220629084527-00521.warc.gz\"}"}
http://www.weddslist.com/rmdb/pages/relations/cant.php
[ "# Cantellation\n\nCantellation is a non-symmetric relationship between some pairs of regular maps of the same genus. Any self-dual regular map can be cantellated.\n\nIf a self-dual regular map is described by\nM:{p,p}   V   V   E\n(meaning, it is in manifold M, each face has p edges, each vertex has p edges, it has V vertices, V faces and E edges), then it can be cantellated. This yields a regular map described by\nM:{p,4}   E   2V   2E.\n\nThis relationship is never symmetric: the cantellated regular map has twice as many edges as the original.\n\nFor example, if we cantellate the tetrahedron we get the octahedron.\n\nIf you have a regular map and want to cantellate it,\n\n• replace each edge by a vertex\n• retain each face as a face\n• replace each vertex by a face\n\nThe same procedure can be applied to a regular map which is not self-dual. However the result is not a regular map, it is semiregular. For example, if we cantellate the cube, we get the cuboctahedron.\n\nIf a regular map has Petrie polygons of size r, and we cantellate it, the result has holes of size r.\n\n### The name \"cantellation\"\n\nThe term \"cantellation\" was coined by Coxeter. It is further defined in the Wikipedia entry cantellation.\n\n### Halving\n\nThe book \"Abstract Regular Polytopes\"ARM, page 197, uses the term \"halving\" for an operation closely related to what we call \"cantellation\". Halving converts\nM:{4,p}   2V   E   2E\nto\nM:{p,p}   V   V   E\nand is the same as taking the dual and un-cantellating it.\n\nARM denotes halving by η." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.922447,"math_prob":0.9220573,"size":799,"snap":"2020-34-2020-40","text_gpt3_token_len":194,"char_repetition_ratio":0.19874214,"word_repetition_ratio":0.030075189,"special_character_ratio":0.19649562,"punctuation_ratio":0.10759494,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9556532,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-24T05:45:47Z\",\"WARC-Record-ID\":\"<urn:uuid:d0af5992-d517-40ca-a8b4-2ce95bf72659>\",\"Content-Length\":\"3296\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5fa7534-9bd5-49f4-92c4-0ab067d5f1d0>\",\"WARC-Concurrent-To\":\"<urn:uuid:1438372c-4437-4229-beeb-5bf59d5c375a>\",\"WARC-IP-Address\":\"209.68.18.39\",\"WARC-Target-URI\":\"http://www.weddslist.com/rmdb/pages/relations/cant.php\",\"WARC-Payload-Digest\":\"sha1:K7MDBX6W7YS2R55ZB6TVF2P6B3RCLTJN\",\"WARC-Block-Digest\":\"sha1:WRU3QZVFND26MR4YGF5PFGJXGXCMHAU6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400213454.52_warc_CC-MAIN-20200924034208-20200924064208-00614.warc.gz\"}"}
https://calculator-converter.com/grams-to-grains.htm
[ "", null, "", null, "", null, "# Grams to Grains\n\nThis calculator provides conversion of grams to grains and backwards grains to grams (gr to g).\n\nEnter grams or grains for conversion:\n\nSelect conversion type:\n\nRounding options:\n\n## Conversion Table\n\n gram to grains Conversion Table: g to gr 1.0 = 15.43236 2.0 = 30.86472 3.0 = 46.29708 4.0 = 61.72943 5.0 = 77.16179 gram to grains 6.0 = 92.59415 7.0 = 108.02651 8.0 = 123.45887 9.0 = 138.89123 10  = 154.32358\n grains to grams Conversion Table: gr to g 1.0 = 0.06480 2.0 = 0.12960 3.0 = 0.19440 4.0 = 0.25920 5.0 = 0.32399 grains to grams 6.0 = 0.38879 7.0 = 0.45359 8.0 = 0.51839 9.0 = 0.58319 10  = 0.64799\n\nThe gram (British spelling: gramme, abbreviation: g) is a unit of mass in the SI system (metric system). One gram is equal to one thousandth of the kilogram (kg), which is the current SI (Metric system) base unit of mass. 1 gram (g) = 15.4323584 grains or \"troy grains\" (gr) = 1000000 microgram (mcg or µg) = 1000 milligram (mg) = 0.001 kilogram (kg) = 0.0352739619 ounces (oz) = 0.00220462262 pounds (lb). The grain or \"troy grain\" (gr) is the non-metric unit of mass used in the Imperial and U.S. customary units. Since 1958, 1 grain (gr) = 0.06479891 grams (g) = 64.79891 milligrams (mg) = 0.00006479891 kilogram (kg) = 0.00228571429 ounces (oz).\n\n## Weight Conversion\n\nOunces to grams (oz to gr)\nGrams to ounces (gr to oz)\nPounds to kilograms (lb to kg)\nKilograms to pounds (kg to lb)\nGrams to kilograms (g to kg)\nKilograms to grams (kg to g)\nKilograms to ounces (kg to oz)\nOunces to kilograms (oz to kg)\nKilograms to newtons (kg to N)\nNewtons to kilograms (N to kg)\nNewtons to pounds (N to lb)\nPounds to newtons (lb to N)\nMilligrams to kilograms (mg to kg)\nKilograms to milligrams (kg to mg)\nKilograms to tonnes (kg to t)\nTonnes to kilograms (t to kg)\nShort tons to kilograms (t to kg)\nKilograms to short tons (kg to t)\nMetric tons to short tons (t to ST)\nShort tons to tons [metric] (ST to t)\nKilograms to stones (kg to st)\nStones to kilograms (st to kg)\nMilligrams to grams (mg to g)\nGrams to milligrams (g to mg)\nMilligrams to micrograms (mg to mcg)\nMicrograms to milligrams (mcg to mg)\nMicrograms to grams (mcg to g)\nGrams to micrograms (g to mcg)\nGrains to grams (gr to g)\nGrams to grains (g to gr)\nOunces to grains (oz to gr)\nGrains to ounces (gr to oz)\nCarats to grams (ct to g)\nGrams to carats (g to ct)\nKarats to gold hallmarks (kt to hallmark)\nGold hallmarks to karats (hallmark to kt)\nCarats to ounces (ct to oz)\nOunces to carats (oz to ct)\nMilligrams to ounces (mg to oz)\nOunces to milligrams (oz to mg)\nMilligrams to pounds (mg to lb)\nPounds to milligrams (lb to mg)\nKilonewtons to tons (metric ton-force) (kN to t)\nTon-forces to kilonewtons (t to kN)\nNewtons to kilonewtons (N to kN)\nKilonewtons to newtons (kN to N)\nKilonewtons to pounds-force (kN to lb)\nPounds-force to kilonewtons (lbf to kN)\nTonnes to pounds (t to lb)\nPounds to tonnes (metric tons) (lb to t)\nShort tons to pounds (t to lb)\nPounds to short tons (US) (lb to t)\nPounds to grams (lb to g)\nGrams to pounds (g to lb)\nPounds to ounces (lb to oz)\nOunces to pounds (oz to lb)\nStones to pounds (st to lb)\nPounds to stones (lb to st)\nCups to fluid ounces (c to fl oz)\nFluid ounces to cups (fl oz to c)\nTroy ounces to ounces (ozt to oz)\nOunces to troy ounces (oz to ozt)\nTroy ounces to grams (ozt to g)\nGrams to troy ounces (g to ozt)" ]
[ null, "https://calculator-converter.com/pics/calculator-converter.gif", null, "https://calculator-converter.com/pics/calculator-converter_sm.gif", null, "https://calculator-converter.com/pics/calculator-converter_sm.gif", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6977617,"math_prob":0.9922835,"size":1082,"snap":"2020-24-2020-29","text_gpt3_token_len":460,"char_repetition_ratio":0.15213358,"word_repetition_ratio":0.0,"special_character_ratio":0.55637705,"punctuation_ratio":0.21818182,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.994557,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-05T20:08:04Z\",\"WARC-Record-ID\":\"<urn:uuid:a4007f88-a894-4310-be99-73dab72ab03d>\",\"Content-Length\":\"28912\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e8ae4f31-434c-4394-bc6b-343b8b63d4e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:1f8aaf49-b720-43c3-a24c-07b29ffd2472>\",\"WARC-IP-Address\":\"67.222.24.105\",\"WARC-Target-URI\":\"https://calculator-converter.com/grams-to-grains.htm\",\"WARC-Payload-Digest\":\"sha1:KED4JQQG3YV7CTHAQPMS23OTMXZ2QUEG\",\"WARC-Block-Digest\":\"sha1:DWOWSAR7IYBBCN5ASC7CBCQUJUEH4SEQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348502204.93_warc_CC-MAIN-20200605174158-20200605204158-00309.warc.gz\"}"}
https://stats.stackexchange.com/questions/127394/r-forecasting-flat-forecast
[ "# R forecasting, flat forecast\n\nI’m trying to produce a hourly, daily forecast for revenue in R. I set seasonal periods to 24, for 24 hours, and 365.25 for days in a year. I attached the fit vs actual plot and the forecast produced by R.\n\nI then fit the time series with the tbats model due to the high seasonal periods. I then try and forecast 8112 periods or just under 1 year.\n\nMy problem is that I keep getting a flat model\\$mean. However, the fitted vs actuals looks like its catching the seasonality.\n\nrev_ts <- msts(revenue_data, seasonal.periods=c(24,365.25))\nrev_fit <- tbats(rev_ts)\nrev_forecast <- forecast(rev_fit,h=8112)\nplot(rev_forecast )", null, "", null, "UPDATE:\n\nTrying to reference your write-up here Rob:\n\nhttp://robjhyndman.com/hyndsight/longseasonality/\n\nSo m=365.25? And n= # of observations? Sorry I'm a current student and new to R (and modeling for that matter). Where does this take into account hourly seasonality\n\nTrying to implement your code from post using these lines of code:\n\nm=365.25 (Where does this take into account hourly seasonality)\n\nn= 25656 (number of observations, historical data)\n\nrev_fit <- Arima(rev_ts, order=c(2,0,1), xreg=fourier(1:n,4,m))\n\nplot(forecast(rev_fit, h=2*m, xreg=fourier(n+1:(2*m),4,m)))\n\nAny explanation on the theory and what this is actually doing? Sorry for all the questions, but I'd love to understand this more fully.\n\nThanks!" ]
[ null, "https://i.stack.imgur.com/4g46E.png", null, "https://i.stack.imgur.com/2o3tk.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9152671,"math_prob":0.7102422,"size":1334,"snap":"2022-27-2022-33","text_gpt3_token_len":362,"char_repetition_ratio":0.124060154,"word_repetition_ratio":0.020304568,"special_character_ratio":0.27361318,"punctuation_ratio":0.15547703,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98638487,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-05T10:58:08Z\",\"WARC-Record-ID\":\"<urn:uuid:ff0f4efa-6494-4037-ac43-a56ebf9e2bb7>\",\"Content-Length\":\"220210\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:29b94065-57cd-4320-a910-81c0833e39d8>\",\"WARC-Concurrent-To\":\"<urn:uuid:2f013424-d582-4e2e-b037-6ee35980aa0c>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://stats.stackexchange.com/questions/127394/r-forecasting-flat-forecast\",\"WARC-Payload-Digest\":\"sha1:IF6YK3AVUFER2POVEAJVHGVSMX5I4GLJ\",\"WARC-Block-Digest\":\"sha1:4Z47B5KDDVVOWUPC5JGSYTV5CJDCY2NI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104542759.82_warc_CC-MAIN-20220705083545-20220705113545-00617.warc.gz\"}"}
https://qanda.ai/en/search/%5Cdfrac%7B%202%20%20%7D%7B%203%20%20%7D%20%20x%20%3D%20%20-2?search_mode=expression
[ "", null, "", null, "Calculator search results\n\nFormula\nSolve the equation", null, "", null, "", null, "", null, "Graph\n$y = \\dfrac { 2 } { 3 } x$\n$y = - 2$\n$x$Intercept\n$\\left ( 0 , 0 \\right )$\n$y$Intercept\n$\\left ( 0 , 0 \\right )$\n$\\dfrac{ 2 }{ 3 } x = -2$\n$x = - 3$\n Solve a solution to $x$\n$\\color{#FF6800}{ \\dfrac { 2 } { 3 } } \\color{#FF6800}{ x } = - 2$\n Calculate the multiplication expression \n$\\color{#FF6800}{ \\dfrac { 2 x } { 3 } } = - 2$\n$\\color{#FF6800}{ \\dfrac { 2 x } { 3 } } = \\color{#FF6800}{ - } \\color{#FF6800}{ 2 }$\n Multiply both sides by the least common multiple for the denominators to eliminate the fraction \n$\\color{#FF6800}{ 2 } \\color{#FF6800}{ x } = \\color{#FF6800}{ - } \\color{#FF6800}{ 6 }$\n$\\color{#FF6800}{ 2 } \\color{#FF6800}{ x } = \\color{#FF6800}{ - } \\color{#FF6800}{ 6 }$\n Divide both sides by the same number \n$\\color{#FF6800}{ x } = \\color{#FF6800}{ - } \\color{#FF6800}{ 3 }$\n 그래프 보기 \nGraph\nHave you found the solution you wanted?\nTry again" ]
[ null, "https://qanda.ai/_next/static/media/qanda-logo-logotype.c0ac75e1.svg", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.52647203,"math_prob":1.0000015,"size":1242,"snap":"2022-05-2022-21","text_gpt3_token_len":463,"char_repetition_ratio":0.24394184,"word_repetition_ratio":0.21794872,"special_character_ratio":0.4404187,"punctuation_ratio":0.026737968,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99977344,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T14:36:45Z\",\"WARC-Record-ID\":\"<urn:uuid:2b209b89-f1e7-463a-8b87-81a53cb234eb>\",\"Content-Length\":\"111257\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f114ffb1-b95d-4270-baf6-b461d3a9c75c>\",\"WARC-Concurrent-To\":\"<urn:uuid:733b42df-8f6a-4abf-8a68-4523eb39b4c9>\",\"WARC-IP-Address\":\"13.32.204.123\",\"WARC-Target-URI\":\"https://qanda.ai/en/search/%5Cdfrac%7B%202%20%20%7D%7B%203%20%20%7D%20%20x%20%3D%20%20-2?search_mode=expression\",\"WARC-Payload-Digest\":\"sha1:A43WU2MCPC6DXMVKINDJ3VPVKDI2PG7G\",\"WARC-Block-Digest\":\"sha1:VDRQMV3TVGN5F7KG2D2RHT2BTHO6YLSP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305266.34_warc_CC-MAIN-20220127133107-20220127163107-00563.warc.gz\"}"}
https://www.research.lancs.ac.uk/portal/en/publications/measurement-of-the-cjet-mistagging-efficiency-in-tbart-events-using-pp-collision-data-at-sqrts13-text-tev-collected-with-the-atlas-detector(ca07f6bc-80c1-478e-ad10-51d5fefea69d).html
[ "Home > Research > Publications & Outputs > Measurement of the c-jet mistagging efficiency ...\n\n## Measurement of the c-jet mistagging efficiency in $$t\\bar{t}$$ events using pp collision data at $$\\sqrt{s}=13$$ $$\\text {TeV}$$ collected with the ATLAS detector\n\nResearch output: Contribution to Journal/MagazineJournal articlepeer-review\n\nPublished\n• ATLAS Collaboration\nClose\nArticle number 95 31/01/2022 European Physical Journal C 1 82 27 Published English\n\n### Abstract\n\nA technique is presented to measure the efficiency with which c-jets are mistagged as b-jets (mistagging efficiency) using $$t\\bar{t}$$ t t ¯ events, where one of the W bosons decays into an electron or muon and a neutrino and the other decays into a quark–antiquark pair. The measurement utilises the relatively large and known $$W\\rightarrow cs$$ W → c s branching ratio, which allows a measurement to be made in an inclusive c-jet sample. The data sample used was collected by the ATLAS detector at $$\\sqrt{s} = 13$$ s = 13 $$\\text {TeV}$$ TeV and corresponds to an integrated luminosity of 139 fb$$^{-1}$$ - 1 . Events are reconstructed using a kinematic likelihood technique which selects the mapping between jets and $$t\\bar{t}$$ t t ¯ decay products that yields the highest likelihood value. The distribution of the b-tagging discriminant for jets from the hadronic W decays in data is compared with that in simulation to extract the mistagging efficiency as a function of jet transverse momentum. The total uncertainties are in the range 3–17%. The measurements generally agree with those in simulation but there are some differences in the region corresponding to the most stringent b-jet tagging requirement." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.90364873,"math_prob":0.94232273,"size":1218,"snap":"2023-14-2023-23","text_gpt3_token_len":284,"char_repetition_ratio":0.10214168,"word_repetition_ratio":0.0,"special_character_ratio":0.22577997,"punctuation_ratio":0.042056076,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96763444,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-04T15:03:18Z\",\"WARC-Record-ID\":\"<urn:uuid:1ab863a5-5f4f-4f72-b247-e7d25e45a0c7>\",\"Content-Length\":\"32679\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:931372a3-e8fd-419d-a66d-a382907cc93e>\",\"WARC-Concurrent-To\":\"<urn:uuid:316884a4-9089-4677-81fd-2960ccf9be46>\",\"WARC-IP-Address\":\"148.88.22.128\",\"WARC-Target-URI\":\"https://www.research.lancs.ac.uk/portal/en/publications/measurement-of-the-cjet-mistagging-efficiency-in-tbart-events-using-pp-collision-data-at-sqrts13-text-tev-collected-with-the-atlas-detector(ca07f6bc-80c1-478e-ad10-51d5fefea69d).html\",\"WARC-Payload-Digest\":\"sha1:TTWRM7CM5T3PPHOWCKDQ3SEFZXLQAKJ3\",\"WARC-Block-Digest\":\"sha1:HBFBXAWQPRVMBR3NXAW4T2BKKAKXYYTL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224649986.95_warc_CC-MAIN-20230604125132-20230604155132-00282.warc.gz\"}"}
https://www.vedantu.com/question-answer/the-radius-of-the-first-bohr-orbit-n1-of-class-11-chemistry-cbse-5fd6f1320cf84502ba7e82bc
[ "", null, "The radius of the first bohr orbit (n=1) of hydrogen atom is 53.4 pm. The radius of bohr orbit having n=3 in $L{i^{2 + }}$will be :A. 53.4 pmB. 106.8 pmC. 120.1 pmD. 160.2 pm", null, "Verified\n118.8k+ views\nHint: We know that neil bohr was the first to explain the general features of hydrogen atom structure and its spectrum. Bohr’s theory can be applied on the ions containing only one electron similar to that of hydrogen atom like $L{i^{2 + }}$, $B{e^{3 + }}$ and $H{e^ + }$, such species are also called hydrogen like species.\n\nFormula used: For hydrogen like species, the radii expression from bohr’s theory is given as:\n${r_n} = \\dfrac{{{a_ \\circ }({n^2})}}{Z}pm$\n\nComplete step-by-step solution:\nLet us understand the electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus.\nThis energy and radius does not change with time but only as one moves from lower stationary state to higher stationary state when the electron absorbs the required amount of energy and emits the energy to move from higher state to lower state. These stationary states or orbits are denoted by an integral number known as principal quantum number which varies from n=1, 2, 3, 4 etc.\nThe radii of these stationary states can be expressed as:\n${r_n} = {n^2}{a_ \\circ }$\nwhere ${a_ \\circ }$ is the radius of the first stationary state and is called Bohr radius.\nIn the question above we have been given with first bohr orbit with n=1 therefore we can calculate the value of ${a_ \\circ }$by substituting the given values,\n${r_1} = {(1)^2}{a_ \\circ } \\\\ 53.4 = {a_ \\circ } \\\\$\nSimilarly for hydrogen like species such as lithium ion the radii expression from bohr’s theory is given as\n${r_n} = \\dfrac{{{a_ \\circ }({n^2})}}{Z}pm$\n$\\Rightarrow {r_n} = \\dfrac{{53.4({n^2})}}{Z}pm$\nNow we have been given n=3 and Z is the atomic number of lithium which is 3 therefore substituting we get,\n${r_3} = \\dfrac{{53.4({3^2})}}{3}pm = 160.2pm$\n\nHence, the correct option is D.\n\nNote: From the above we observe that the value of energy becomes more negative and that of radius becomes smaller with increase of atomic number Z, this means that the electron will be tightly bound to the nucleus." ]
[ null, "https://www.vedantu.com/cdn/images/seo-templates/seo-qna.svg", null, "https://www.vedantu.com/cdn/images/seo-templates/green-check.svg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8888025,"math_prob":0.9991235,"size":3881,"snap":"2022-05-2022-21","text_gpt3_token_len":1069,"char_repetition_ratio":0.12509672,"word_repetition_ratio":0.77272725,"special_character_ratio":0.2909044,"punctuation_ratio":0.0843061,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997502,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T19:59:48Z\",\"WARC-Record-ID\":\"<urn:uuid:07e97f2e-d811-4fc0-9057-9e1af74e23e1>\",\"Content-Length\":\"51289\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:956e13e6-212b-4c22-8ed6-e14b0a7aaf76>\",\"WARC-Concurrent-To\":\"<urn:uuid:55de7247-26da-4add-9b12-110017be821c>\",\"WARC-IP-Address\":\"18.67.65.77\",\"WARC-Target-URI\":\"https://www.vedantu.com/question-answer/the-radius-of-the-first-bohr-orbit-n1-of-class-11-chemistry-cbse-5fd6f1320cf84502ba7e82bc\",\"WARC-Payload-Digest\":\"sha1:BBVBWNFB5QNMKKGOUEF6AVKATZZI63UM\",\"WARC-Block-Digest\":\"sha1:7FLFFC4D3B3E6HXZLHNJ7VQCBE4JZZ5U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304872.21_warc_CC-MAIN-20220125190255-20220125220255-00419.warc.gz\"}"}
https://www.teachoo.com/3995/673/Example-41---If-R1--R2-are-equivalence-relations-in-set-A/category/Examples/
[ "Examples\n\nChapter 1 Class 12 Relation and Functions\nSerial order wise", null, "", null, "", null, "", null, "Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class\n\n### Transcript\n\nExample 18 If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence relation. R1 is an equivalence relation 1. R1 is symmetric (a, a) ∈ R1, for all a ∈ A. 2. R1 is reflexive If (a, b) ∈ R1 , then (b, a) ∈ R1 3. R1 is transitive If (a, b) ∈ R1 & (b, c) ∈ R1 , then (a, c) ∈ R1 R2 is an equivalence relation 1. R2 is symmetric (a, a) ∈ R2, for all a ∈ A. 2. R2 is reflexive If (a, b) ∈ R2 , then (b, a) ∈ R2 3. R2 is transitive If (a, b) ∈ R2 & (b, c) ∈ R2 , then (a, c) ∈ R2 We have to prove R1 ∩ R2 is equivalence relation Check reflexive For all a ∈ A (a, a) ∈ R1, & (a, a) ∈ R2 Hence, (a, a) ∈ both R1 & R2 Hence, (a, a) ∈ R1 ∩ R2 ∴ R1 ∩ R2 is reflexive. Check symmetric R1 is symmetric ,hence If (a, b) ∈ R1 , then (b, a) ∈ R1 R2 is symmetric, hence If (a, b) ∈ R2 , then (b, a) ∈ R2 From (1) and (2) If (a, b) ∈ R1 ∩ R2, then (b, a) ∈ R1 ∩ R2 Hence , R1 ∩ R2 is symmetric. Checking transitive R1 is transitive, Hence, if (a, b) ∈ R1 & (b, c) ∈ R1 , then (a, c) ∈ R1 R2 is transitive, Hence, if (a, b) ∈ R2 & (b, c) ∈ R2 , then (a, c) ∈ R2 From (3) & (4) If (a, b) ∈ R1 ∩ R2 and (b, c) ∈ R1 ∩ R2 , then (a, c) ∈ R1 ∩ R2, ∴ R1∩ R2 is transitive. Thus, R1 ∩ R2 is an equivalence relation.", null, "" ]
[ null, "https://d1avenlh0i1xmr.cloudfront.net/aec7188b-f3a8-4b39-84d6-5cbf7f6c0445/slide47.jpg", null, "https://d1avenlh0i1xmr.cloudfront.net/842436be-6cbe-46bf-b2a3-687f873e05da/slide48.jpg", null, "https://d1avenlh0i1xmr.cloudfront.net/3d5f139a-7612-49d2-82b2-76a499f0a79e/slide49.jpg", null, "https://d1avenlh0i1xmr.cloudfront.net/163bba07-283f-428c-a3fb-815e51616e2f/slide50.jpg", null, "https://www.teachoo.com/static/misc/Davneet_Singh.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8769599,"math_prob":0.9993765,"size":3147,"snap":"2023-40-2023-50","text_gpt3_token_len":1114,"char_repetition_ratio":0.25198856,"word_repetition_ratio":0.34115806,"special_character_ratio":0.35811883,"punctuation_ratio":0.10939907,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998621,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-10T21:13:24Z\",\"WARC-Record-ID\":\"<urn:uuid:a0e98783-9fff-4f41-bed7-ccda83a31bb3>\",\"Content-Length\":\"221554\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e5bcceb3-db72-4e2f-94cf-cbeca25eaad7>\",\"WARC-Concurrent-To\":\"<urn:uuid:f9a01a61-634d-47ea-9514-dc11a194566c>\",\"WARC-IP-Address\":\"52.21.227.162\",\"WARC-Target-URI\":\"https://www.teachoo.com/3995/673/Example-41---If-R1--R2-are-equivalence-relations-in-set-A/category/Examples/\",\"WARC-Payload-Digest\":\"sha1:V7UKCTSRMVTZ6QYIDXQC77OU5R5F6OA3\",\"WARC-Block-Digest\":\"sha1:X2H44JA7X5DTPBS2G74JHYH57TUFLOYB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679102637.84_warc_CC-MAIN-20231210190744-20231210220744-00839.warc.gz\"}"}
https://oeis.org/A343023
[ "The OEIS is supported by the many generous donors to the OEIS Foundation.", null, "Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)\n A343023 Number of cyclic cubic fields with discriminant n^2. 9\n 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)\n OFFSET 1,63 COMMENTS Equivalently, number of cubic fields with discriminant n^2. That is to say, it makes no difference if the word \"cyclic\" is omitted from the title. Let D be a discriminant of a cubic field F, then F is a cyclic cubic field if and only if D is a square. For D = k^2, k must be of the form (p_1)*(p_2)*...*(p_t) or 9*(p_1)*(p_2)*...*(p_{t-1}) with distinct primes p_i == 1 (mod 3), in which case there are exactly 2^(t-1) = 2^(omega(k)-1) (cyclic) cubic fields with discriminant D. See Page 17, Theorem 2.7 of the Ka Lun Wong link. Each term is 0 or a power of 2. The first occurrence of 2^t is 9*A121940(t) for t >= 1. LINKS Jianing Song, Table of n, a(n) for n = 1..16000 LMFDB, Cubic fields Wikipedia, Cubic field Ka Lun Wong, Maximal Unramified Extensions of Cyclic Cubic Fields, (2011), Theses and Dissertations, 2781. FORMULA a(n) = A160498(n)/2 for n > 1. EXAMPLE a(7) = 1 since there is only 1 (cyclic) cubic field with discriminant 7^2 = 49 is Q[x]/(x^3 - x^2 + x + 1). a(63) = 2 since there are 2 (cyclic) cubic fields with discriminant 63^2 = 3969: Q[x]/(x^3 - 21x - 28) and Q[x]/(x^3 - 21x - 35). a(819) = 4 since there are 4 (cyclic) cubic fields with discriminant 819^2 = 670761: Q[x]/(x^3 - 273x - 91), Q[x]/(x^3 - 273x - 728), Q[x]/(x^3 - 273x - 1547) and Q[x]/(x^3 - 273x - 1729). a(35) = 0 since it is not of form (p_1)*(p_2)*...*(p_t) or 9*(p_1)*(p_2)*...*(p_{t-1}) with distinct primes p_i == 1 (mod 3). Indeed, there are no (cyclic) cubic fields with discriminant 35^2 = 1225. PROG (PARI) a(n) = if(n<=1, 0, my(L=factor(n), w=omega(n)); for(i=1, w, if(!((L[i, 1]%3==1 && L[i, 2]==1) || L[i, 1]^L[i, 2] == 9), return(0))); 2^(w-1)) CROSSREFS Cf. A160498, A121940, A343000 (discriminants of cyclic cubic fields), A343001 (indices of positive terms). Sequence in context: A086071 A322212 A089813 * A337760 A037845 A037881 Adjacent sequences:  A343020 A343021 A343022 * A343024 A343025 A343026 KEYWORD nonn,easy AUTHOR Jianing Song, Apr 02 2021 STATUS approved\n\nLookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam\nContribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent\nThe OEIS Community | Maintained by The OEIS Foundation Inc.\n\nLast modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)" ]
[ null, "https://oeis.org/banner2021.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.67690575,"math_prob":0.99945766,"size":2504,"snap":"2022-05-2022-21","text_gpt3_token_len":1168,"char_repetition_ratio":0.2352,"word_repetition_ratio":0.20436507,"special_character_ratio":0.53833866,"punctuation_ratio":0.25689405,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9942977,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-18T13:07:57Z\",\"WARC-Record-ID\":\"<urn:uuid:ae5b3626-a71d-45c4-ac0a-0ef743975a03>\",\"Content-Length\":\"18458\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6668fa83-603e-43ef-8e1e-fe25de8733d5>\",\"WARC-Concurrent-To\":\"<urn:uuid:4ed10c2d-50de-4456-ab62-0e81771f49fe>\",\"WARC-IP-Address\":\"104.239.138.29\",\"WARC-Target-URI\":\"https://oeis.org/A343023\",\"WARC-Payload-Digest\":\"sha1:N32HMFZ6EON5M74HYRTPWERYAHT7KHTY\",\"WARC-Block-Digest\":\"sha1:E4TFNCY6226K2YSCM77ALXRJJDVNNRXV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320300849.28_warc_CC-MAIN-20220118122602-20220118152602-00087.warc.gz\"}"}
https://www.convertunits.com/from/joule/metre/to/exanewton
[ "## ››Convert joule/metre to exanewton\n\n joule/metre exanewton\n\nHow many joule/metre in 1 exanewton? The answer is 1.0E+18.\nWe assume you are converting between joule/metre and exanewton.\nYou can view more details on each measurement unit:\njoule/metre or exanewton\nThe SI derived unit for force is the newton.\n1 newton is equal to 1 joule/metre, or 1.0E-18 exanewton.\nNote that rounding errors may occur, so always check the results.\nUse this page to learn how to convert between joules/meter and exanewtons.\nType in your own numbers in the form to convert the units!\n\n## ››Want other units?\n\nYou can do the reverse unit conversion from exanewton to joule/metre, or enter any two units below:\n\n## Enter two units to convert\n\n From: To:\n\n## ››Definition: Exanewton\n\nThe SI prefix \"exa\" represents a factor of 1018, or in exponential notation, 1E18.\n\nSo 1 exanewton = 1018 newtons.\n\nThe definition of a newton is as follows:\n\nIn physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was first used around 1904, but not until 1948 was it officially adopted by the General Conference on Weights and Measures (CGPM) as the name for the mks unit of force.\n\n## ››Metric conversions and more\n\nConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8200731,"math_prob":0.68965375,"size":1769,"snap":"2020-34-2020-40","text_gpt3_token_len":504,"char_repetition_ratio":0.196034,"word_repetition_ratio":0.0,"special_character_ratio":0.22950819,"punctuation_ratio":0.14127424,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9911962,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-11T07:41:21Z\",\"WARC-Record-ID\":\"<urn:uuid:87e087c5-509e-4acd-bd4b-6d7edbbb50d0>\",\"Content-Length\":\"34007\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88966650-9c04-48b6-ae14-02842c8d2415>\",\"WARC-Concurrent-To\":\"<urn:uuid:e26bb1ee-f3dc-4598-ba3f-7ba30558b442>\",\"WARC-IP-Address\":\"52.71.85.245\",\"WARC-Target-URI\":\"https://www.convertunits.com/from/joule/metre/to/exanewton\",\"WARC-Payload-Digest\":\"sha1:FZFK3DLN5SJJZZ3L6ITEWBO5LY7MSUQ3\",\"WARC-Block-Digest\":\"sha1:UL3CWXZJ642KZDNI2LZUMQHFAPI2TGDG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738735.44_warc_CC-MAIN-20200811055449-20200811085449-00215.warc.gz\"}"}
https://www.accountingformanagement.org/problem-4-pcs/
[ "# Problem 4: Equivalent units for materials and conversion costs\n\n## Problem 4 (a) – weighted average vs FIFO method\n\nTK Company has two processing departments – Department X and Department Y. The quantity report of Department X reveals the following information:\n\nRequired: Using the quantity report of Department X given above, compute equivalent units for materials and conversion costs under:\n\n1. weighted average method\n2. FIFO method\n\n## Problem 4 (b) – weighted average method\n\nFor May 2020, the cost department of Abraham Company received the following data from one of its five producing departments:\n\n• Received from preceding department: 50,000 kilograms\n• Processed and transferred to next department: 38,000 kilograms\n• Work in process ending inventory: 12,000 kilograms\n\nIn this department, three different types of materials are added to the product received from previous department. The materials are added at three different stages of production as follows:\n\n• Material M-1 is added when production process starts\n• Material M-2 is added when the production process is 25% completed\n• Material M-3 is added when the production process is 75% completed\n\nThe conversion costs are incurred uniformly throughout the production process.\n\nAn examination of work in process ending inventory revealed that 3,000 kilograms were 85% processed; 6,000 kilograms were 50% processed; 3,000 kilograms were 15% processed. There was no unfinished work at the beginning of May.\n\nRequired:\n\n1. Compute equivalent units of production for each type of materials.\n2. Compute equivalent units of production for conversion costs.\n\n### Solution\n\n#### 1. Equivalent units for materials\n\nExplanation:\n\n• Material M-1 is included in all the units in ending inventory because it is added at the start of manufacturing process.\n• Material M-2 is included in both 85% and 50% processed units because it is added when the processing is 25% completed.\n• Material M-3 is included only in 85% processed units because it is added when the processing is 75% completed." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9412815,"math_prob":0.83414054,"size":2186,"snap":"2023-40-2023-50","text_gpt3_token_len":448,"char_repetition_ratio":0.15032081,"word_repetition_ratio":0.12684366,"special_character_ratio":0.21866423,"punctuation_ratio":0.09408602,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95385456,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-29T08:56:01Z\",\"WARC-Record-ID\":\"<urn:uuid:f717021d-1272-4608-8ca9-bfab81016e13>\",\"Content-Length\":\"44183\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d6655fc2-d73a-4f09-a5ad-68dcf2bf0e92>\",\"WARC-Concurrent-To\":\"<urn:uuid:43f4943f-43c5-4a44-af6c-291faab799b6>\",\"WARC-IP-Address\":\"104.21.5.186\",\"WARC-Target-URI\":\"https://www.accountingformanagement.org/problem-4-pcs/\",\"WARC-Payload-Digest\":\"sha1:5U3UBU5FP5XSRADUDUCBFI4GMHPNDNTS\",\"WARC-Block-Digest\":\"sha1:OENNHBWKMOKZABTTXOYEXZPER2IKLAGV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100057.69_warc_CC-MAIN-20231129073519-20231129103519-00447.warc.gz\"}"}
http://mechatronics2018.dreslab.com/pages/190120
[ "", null, "## Rui Shi & Ziyi Zhang\n\n### Description\n\nThe goal of the project is to make a robotic arm which can hold a pen or something else and is able to write in a sheet. To construct such a system, we used two large motors, two gyros, a medium motor with a gear mounted on it to adjust the height of the \"pen\". To ensure each rotate part has the largest degree of freedom so that it can cover as much part of the sheet as possible, we connected three motors  in different horizontal level so they can rotate for almost 360°. Also, to avoid collision, one gyro was installed on the side of the motor rather than on top of it. Besides, we mounted a rod in the hole of the medium motor to make the arm capable to cover a larger area.", null, "", null, "", null, "", null, "### Challenge 1: Building the Robotic Arm\n\nAs shown in the pictures and video below, our motor is able to reach a much larger area than a 8.5*11 sheet.", null, "### Challenge 2: Calculate End Effector Positions\n\nFor challenge two, the code need to use the Gyro sensor to report the rotation angles of both parts of the arm and we need to make sure the report angles is the final angle of two parts. To achieve this, I wrote an if sentence in the while loop to achieve the function that the code can report values only when both parts of the arm already rotated and stopped rotating. When the rotation angle difference is smaller than 10, the code reports the value of two rotation angles for further calculation.\n\nIn the video, we used a green pad with grids as reference. The distance between two bold lines are one inch. The following picture shows the coordinate system we used to measure positions of the pen.", null, "### Challenge 3: Recording and Playing Back Positions\n\nFor challenge three, after getting the value of two rotation angles, we need to run the motor to return the arm to its origin shape. To achieve this function, first, we calculate the angle that two motors need to rotate. Then, we set two motors to rotate for that much in certain speed.\n\n```#!/usr/bin/env python3\nimport math\ndef main():\nev3 = Device('this')\n\n#Connect the #1 motor to port A\n#Connect 1the #2 motor to port B\nm1 = ev3.LargeMotor('outA')\nm2 = ev3.LargeMotor('outB')\n\n#Connect the #1 sensor to port 1\n#Connect 1the #2 motor to port 3\nsensor1 = ev3.GyroSensor('in1')\nsensor2 = ev3.GyroSensor('in3')\nsensor1.mode ='GYRO-ANG'\nsensor2.mode ='GYRO-ANG'\nangle1_origin = sensor1.value();\nangle2_origin = sensor2.value();\n\n#set the length of each part of the arm\nl1 = 8\nl2 = 9\nloop = 1\n\n#record the origin values of both sensors to prevent error\nprev1 = sensor1.value()\nprev2 = sensor2.value() - angle2_origin\n\n#this part use sensors to record the rotate angles of both parts of the arm\nwhile loop == 1:\nangle1 = sensor1.value()\nangle2 = sensor2.value() - angle2_origin\nprint(\"angle1 =%d, angle2 =%d\" % (angle1, angle2))\n\n#if both parts of the arm moved and already stoped moving, then break the loop and report the value of angle1 and angle2\nif abs(angle1 - angle1_origin) > 10 and abs(angle2 - angle2_origin) > 10 and abs(prev1 - angle1) < 10 and abs(prev2 - angle2) < 10:\nprev1 = angle1\nprev2 = angle2\nbreak\nsleep(1)\nprev1 = angle1\nprev2 = angle2\n\n#calculate angles that motor1 and motor2 should rotate, the angle motor2 should rotate equates to angle2 - angle1\ntheta1 = -(prev1)\ntheta2 = -(prev2 - prev1)\nprint(\"prev =%d, prev2 =%d\" % (theta1, theta2))\n\n#calculate x, y position\nx = l1 * math.cos(prev1*2*3.14/360) + l2 * math.cos(prev2*2*3.14/360)\ny = l1 * math.sin(prev1*2*3.14/360) + l2 * math.sin(prev2*2*3.14/360)\nprint(\"theta1 =%d, theta2 =%d\" % (theta1, theta2))\n\n#print x, y position\nprint(\"x =%d, y =%d\" % (x, y))]\n\n#run the motor to rotate back to its origin position\nm1.run_to_rel_pos(position_sp=theta1, speed_sp=100, stop_action=\"hold\")\nm2.run_to_rel_pos(position_sp=theta2, speed_sp=100, stop_action=\"hold\")\nsleep(2)\nm1.stop(stop_action=\"coast\")\nm2.stop(stop_action=\"coast\")\nif __name__ == '__main__':\nmain()```" ]
[ null, "http://mechatronics2018.dreslab.com/thumbs/pages/190120/hero-5f544028f20bc41ed4475e15a8b7b689.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/22-5a84e7a5a2ca5.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/33-5a84e7c2450e4.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/44-5a84e7dc4c104.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/55-5a84e7e908098.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/11-5a84e67739498.jpg", null, "http://mechatronics2018.dreslab.com/pages/190120/wechat-image_20180216142423-5a8733286371c.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8060435,"math_prob":0.97847486,"size":3899,"snap":"2020-24-2020-29","text_gpt3_token_len":1061,"char_repetition_ratio":0.13838254,"word_repetition_ratio":0.02764977,"special_character_ratio":0.29263914,"punctuation_ratio":0.10966057,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9895163,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,1,null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-03T10:22:54Z\",\"WARC-Record-ID\":\"<urn:uuid:5b289d3a-8203-400d-a506-cf18ad66f97f>\",\"Content-Length\":\"23473\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:191ddd8e-496d-4954-8c4b-dc7a4d73b971>\",\"WARC-Concurrent-To\":\"<urn:uuid:79a090a6-f298-4d84-a618-65ccb07a68d7>\",\"WARC-IP-Address\":\"130.64.112.173\",\"WARC-Target-URI\":\"http://mechatronics2018.dreslab.com/pages/190120\",\"WARC-Payload-Digest\":\"sha1:HL3T3LWU2BI6UUE3VUXZPFK2KENCLDML\",\"WARC-Block-Digest\":\"sha1:CCKFPJS6FIAQX7QIPBTI4755PMZP3JYD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655881984.34_warc_CC-MAIN-20200703091148-20200703121148-00181.warc.gz\"}"}
http://grinebiter.com/Numbers/Cardinal/489-four-hundred-eighty-nine.html
[ "Four hundred eighty-nine\n\n Here is information about \"four hundred eighty-nine\" that you may find useful and interesting. Number Systems Four hundred eighty-nine is a decimal number and can be written with numbers: 489 Binary is a number system with only 0s and 1s. Four hundred eighty-nine in binary form is displayed below: 111101001 A Hexadecimal number has a base of 16 which means it includes the numbers 0 to 9 and A through F. Four hundred eighty-nine converted to hexadecimal is: 1E9 Roman Numerals is another number system. Below is four hundred eighty-nine in roman numerals: CDLXXXIX Scientific Notation Sometimes calculators and scientists shorten numbers using scientific notation. Here is four hundred eighty-nine as a scientific notation: 4.89E+02 Math Here are some math facts about Four hundred eighty-nine: Four hundred eighty-nine is a rational number and an integer. Four hundred eighty-nine is an odd number because it is not divisible by two. Four hundred eighty-nine is divisible by the following numbers: 1, 3, 163, 489 Four hundred eighty-nine is not a square number because no number multiplied by itself will equal four hundred eighty-nine. Number Lookup Four hundred eighty-nine is not the only number we have information about. Go here to look up other numbers.\n\n Translated Here we have translated four hundred eighty-nine into some of the most commonly used languages: Chinese: 四百八十九 French: quatre cent quatre-vingt-neuf German: vierhundert neunundachtzig Italian: quattrocento ottantanove Spanish: cuatrocientos ochenta y nueve\n\n Currency Here is four hundred eighty-nine written in different currencies: US Dollars: \\$489 Canadian Dollars: CA\\$489 Australian Dollars: A\\$489 British Pounds: £489 Indian Rupee: ₹489 Euros: €489\n\n Ordinal The cardinal number four hundred eighty-nine can also be written as an ordinal number: 489th Or if you want to write it with letters only: four hundred eighty-ninth.\n\n Four hundred ninety Go here for the next number on our list that we have information about." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8812162,"math_prob":0.95503074,"size":1267,"snap":"2019-13-2019-22","text_gpt3_token_len":279,"char_repetition_ratio":0.26682502,"word_repetition_ratio":0.02,"special_character_ratio":0.21704814,"punctuation_ratio":0.0882353,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.955251,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T11:50:51Z\",\"WARC-Record-ID\":\"<urn:uuid:a9d93d96-8298-4329-9263-7bc290725703>\",\"Content-Length\":\"10277\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d79dff2c-82c5-4f2d-bff1-e7e888d7b902>\",\"WARC-Concurrent-To\":\"<urn:uuid:2254dcd3-cc85-43c9-a898-f7c83f71afc6>\",\"WARC-IP-Address\":\"54.231.176.183\",\"WARC-Target-URI\":\"http://grinebiter.com/Numbers/Cardinal/489-four-hundred-eighty-nine.html\",\"WARC-Payload-Digest\":\"sha1:CUJ3ERS5YDGBN2U2KG7TL4XBFQMXPPVX\",\"WARC-Block-Digest\":\"sha1:6PCL36T6XB6EZAQ7O7DUD4IEQKT27MIW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202523.0_warc_CC-MAIN-20190321112407-20190321134407-00094.warc.gz\"}"}
https://scfr.savingadvice.com/2008/06/09/retirement-gift-for-in-laws_39908/
[ "User Real IP - 3.233.215.196\n```Array\n(\n => Array\n(\n => 182.68.68.92\n)\n\n => Array\n(\n => 101.0.41.201\n)\n\n => Array\n(\n => 43.225.98.123\n)\n\n => Array\n(\n => 2.58.194.139\n)\n\n => Array\n(\n => 46.119.197.104\n)\n\n => Array\n(\n => 45.249.8.93\n)\n\n => Array\n(\n => 103.12.135.72\n)\n\n => Array\n(\n => 157.35.243.216\n)\n\n => Array\n(\n => 209.107.214.176\n)\n\n => Array\n(\n => 5.181.233.166\n)\n\n => Array\n(\n => 106.201.10.100\n)\n\n => Array\n(\n => 36.90.55.39\n)\n\n => Array\n(\n => 119.154.138.47\n)\n\n => Array\n(\n => 51.91.31.157\n)\n\n => Array\n(\n => 182.182.65.216\n)\n\n => Array\n(\n => 157.35.252.63\n)\n\n => Array\n(\n => 14.142.34.163\n)\n\n => Array\n(\n => 178.62.43.135\n)\n\n => Array\n(\n => 43.248.152.148\n)\n\n => Array\n(\n => 222.252.104.114\n)\n\n => Array\n(\n => 209.107.214.168\n)\n\n => Array\n(\n => 103.99.199.250\n)\n\n => Array\n(\n => 178.62.72.160\n)\n\n => Array\n(\n => 27.6.1.170\n)\n\n => Array\n(\n => 182.69.249.219\n)\n\n => Array\n(\n => 110.93.228.86\n)\n\n => Array\n(\n => 72.255.1.98\n)\n\n => Array\n(\n => 182.73.111.98\n)\n\n => Array\n(\n => 45.116.117.11\n)\n\n => Array\n(\n => 122.15.78.189\n)\n\n => Array\n(\n => 14.167.188.234\n)\n\n => Array\n(\n => 223.190.4.202\n)\n\n => Array\n(\n => 202.173.125.19\n)\n\n => Array\n(\n => 103.255.5.32\n)\n\n => Array\n(\n => 39.37.145.103\n)\n\n => Array\n(\n => 140.213.26.249\n)\n\n => Array\n(\n => 45.118.166.85\n)\n\n => Array\n(\n => 102.166.138.255\n)\n\n => Array\n(\n => 77.111.246.234\n)\n\n => Array\n(\n => 45.63.6.196\n)\n\n => Array\n(\n => 103.250.147.115\n)\n\n => Array\n(\n => 223.185.30.99\n)\n\n => Array\n(\n => 103.122.168.108\n)\n\n => Array\n(\n => 123.136.203.21\n)\n\n => Array\n(\n => 171.229.243.63\n)\n\n => Array\n(\n => 153.149.98.149\n)\n\n => Array\n(\n => 223.238.93.15\n)\n\n => Array\n(\n => 178.62.113.166\n)\n\n => Array\n(\n => 101.162.0.153\n)\n\n => Array\n(\n => 121.200.62.114\n)\n\n => Array\n(\n => 14.248.77.252\n)\n\n => Array\n(\n => 95.142.117.29\n)\n\n => Array\n(\n => 150.129.60.107\n)\n\n => Array\n(\n => 94.205.243.22\n)\n\n => Array\n(\n => 115.42.71.143\n)\n\n => Array\n(\n => 117.217.195.59\n)\n\n => Array\n(\n => 182.77.112.56\n)\n\n => Array\n(\n => 182.77.112.108\n)\n\n => Array\n(\n => 41.80.69.10\n)\n\n => Array\n(\n => 117.5.222.121\n)\n\n => Array\n(\n => 103.11.0.38\n)\n\n => Array\n(\n => 202.173.127.140\n)\n\n => Array\n(\n => 49.249.249.50\n)\n\n => Array\n(\n => 116.72.198.211\n)\n\n => Array\n(\n => 223.230.54.53\n)\n\n => Array\n(\n => 102.69.228.74\n)\n\n => Array\n(\n => 39.37.251.89\n)\n\n => Array\n(\n => 39.53.246.141\n)\n\n => Array\n(\n => 39.57.182.72\n)\n\n => Array\n(\n => 209.58.130.210\n)\n\n => Array\n(\n => 104.131.75.86\n)\n\n => Array\n(\n => 106.212.131.255\n)\n\n => Array\n(\n => 106.212.132.127\n)\n\n => Array\n(\n => 223.190.4.60\n)\n\n => Array\n(\n => 103.252.116.252\n)\n\n => Array\n(\n => 103.76.55.182\n)\n\n => Array\n(\n => 45.118.166.70\n)\n\n => Array\n(\n => 103.93.174.215\n)\n\n => Array\n(\n => 5.62.62.142\n)\n\n => Array\n(\n => 182.179.158.156\n)\n\n => Array\n(\n => 39.57.255.12\n)\n\n => Array\n(\n => 39.37.178.37\n)\n\n => Array\n(\n => 182.180.165.211\n)\n\n => Array\n(\n => 119.153.135.17\n)\n\n => Array\n(\n => 72.255.15.244\n)\n\n => Array\n(\n => 139.180.166.181\n)\n\n => Array\n(\n => 70.119.147.111\n)\n\n => Array\n(\n => 106.210.40.83\n)\n\n => Array\n(\n => 14.190.70.91\n)\n\n => Array\n(\n => 202.125.156.82\n)\n\n => Array\n(\n => 115.42.68.38\n)\n\n => Array\n(\n => 102.167.13.108\n)\n\n => Array\n(\n => 117.217.192.130\n)\n\n => Array\n(\n => 205.185.223.156\n)\n\n => Array\n(\n => 171.224.180.29\n)\n\n => Array\n(\n => 45.127.45.68\n)\n\n => Array\n(\n => 195.206.183.232\n)\n\n => Array\n(\n => 49.32.52.115\n)\n\n => Array\n(\n => 49.207.49.223\n)\n\n => Array\n(\n => 45.63.29.61\n)\n\n => Array\n(\n => 103.245.193.214\n)\n\n => Array\n(\n => 39.40.236.69\n)\n\n => Array\n(\n => 62.80.162.111\n)\n\n => Array\n(\n => 45.116.232.56\n)\n\n => Array\n(\n => 45.118.166.91\n)\n\n => Array\n(\n => 180.92.230.234\n)\n\n => Array\n(\n => 157.40.57.160\n)\n\n => Array\n(\n => 110.38.38.130\n)\n\n => Array\n(\n => 72.255.57.183\n)\n\n => Array\n(\n => 182.68.81.85\n)\n\n => Array\n(\n => 39.57.202.122\n)\n\n => Array\n(\n => 119.152.154.36\n)\n\n => Array\n(\n => 5.62.62.141\n)\n\n => Array\n(\n => 119.155.54.232\n)\n\n => Array\n(\n => 39.37.141.22\n)\n\n => Array\n(\n => 183.87.12.225\n)\n\n => Array\n(\n => 107.170.127.117\n)\n\n => Array\n(\n => 125.63.124.49\n)\n\n => Array\n(\n => 39.42.191.3\n)\n\n => Array\n(\n => 116.74.24.72\n)\n\n => Array\n(\n => 46.101.89.227\n)\n\n => Array\n(\n => 202.173.125.247\n)\n\n => Array\n(\n => 39.42.184.254\n)\n\n => Array\n(\n => 115.186.165.132\n)\n\n => Array\n(\n => 39.57.206.126\n)\n\n => Array\n(\n => 103.245.13.145\n)\n\n => Array\n(\n => 202.175.246.43\n)\n\n => Array\n(\n => 192.140.152.150\n)\n\n => Array\n(\n => 202.88.250.103\n)\n\n => Array\n(\n => 103.248.94.207\n)\n\n => Array\n(\n => 77.73.66.101\n)\n\n => Array\n(\n => 104.131.66.8\n)\n\n => Array\n(\n => 113.186.161.97\n)\n\n => Array\n(\n => 222.254.5.7\n)\n\n => Array\n(\n => 223.233.67.247\n)\n\n => Array\n(\n => 171.249.116.146\n)\n\n => Array\n(\n => 47.30.209.71\n)\n\n => Array\n(\n => 202.134.13.130\n)\n\n => Array\n(\n => 27.6.135.7\n)\n\n => Array\n(\n => 107.170.186.79\n)\n\n => Array\n(\n => 103.212.89.171\n)\n\n => Array\n(\n => 117.197.9.77\n)\n\n => Array\n(\n => 122.176.206.233\n)\n\n => Array\n(\n => 192.227.253.222\n)\n\n => Array\n(\n => 182.188.224.119\n)\n\n => Array\n(\n => 14.248.70.74\n)\n\n => Array\n(\n => 42.118.219.169\n)\n\n => Array\n(\n => 110.39.146.170\n)\n\n => Array\n(\n => 119.160.66.143\n)\n\n => Array\n(\n => 103.248.95.130\n)\n\n => Array\n(\n => 27.63.152.208\n)\n\n => Array\n(\n => 49.207.114.96\n)\n\n => Array\n(\n => 102.166.23.214\n)\n\n => Array\n(\n => 175.107.254.73\n)\n\n => Array\n(\n => 103.10.227.214\n)\n\n => Array\n(\n => 202.143.115.89\n)\n\n => Array\n(\n => 110.93.227.187\n)\n\n => Array\n(\n => 103.140.31.60\n)\n\n => Array\n(\n => 110.37.231.46\n)\n\n => Array\n(\n => 39.36.99.238\n)\n\n => Array\n(\n => 157.37.140.26\n)\n\n => Array\n(\n => 43.246.202.226\n)\n\n => Array\n(\n => 137.97.8.143\n)\n\n => Array\n(\n => 182.65.52.242\n)\n\n => Array\n(\n => 115.42.69.62\n)\n\n => Array\n(\n => 14.143.254.58\n)\n\n => Array\n(\n => 223.179.143.236\n)\n\n => Array\n(\n => 223.179.143.249\n)\n\n => Array\n(\n => 103.143.7.54\n)\n\n => Array\n(\n => 223.179.139.106\n)\n\n => Array\n(\n => 39.40.219.90\n)\n\n => Array\n(\n => 45.115.141.231\n)\n\n => Array\n(\n => 120.29.100.33\n)\n\n => Array\n(\n => 112.196.132.5\n)\n\n => Array\n(\n => 202.163.123.153\n)\n\n => Array\n(\n => 5.62.58.146\n)\n\n => Array\n(\n => 39.53.216.113\n)\n\n => Array\n(\n => 42.111.160.73\n)\n\n => Array\n(\n => 107.182.231.213\n)\n\n => Array\n(\n => 119.82.94.120\n)\n\n => Array\n(\n => 178.62.34.82\n)\n\n => Array\n(\n => 203.122.6.18\n)\n\n => Array\n(\n => 157.42.38.251\n)\n\n => Array\n(\n => 45.112.68.222\n)\n\n => Array\n(\n => 49.206.212.122\n)\n\n => Array\n(\n => 104.236.70.228\n)\n\n => Array\n(\n => 42.111.34.243\n)\n\n => Array\n(\n => 84.241.19.186\n)\n\n => Array\n(\n => 89.187.180.207\n)\n\n => Array\n(\n => 104.243.212.118\n)\n\n => Array\n(\n => 104.236.55.136\n)\n\n => Array\n(\n => 106.201.16.163\n)\n\n => Array\n(\n => 46.101.40.25\n)\n\n => Array\n(\n => 45.118.166.94\n)\n\n => Array\n(\n => 49.36.128.102\n)\n\n => Array\n(\n => 14.142.193.58\n)\n\n => Array\n(\n => 212.79.124.176\n)\n\n => Array\n(\n => 45.32.191.194\n)\n\n => Array\n(\n => 105.112.107.46\n)\n\n => Array\n(\n => 106.201.14.8\n)\n\n => Array\n(\n => 110.93.240.65\n)\n\n => Array\n(\n => 27.96.95.177\n)\n\n => Array\n(\n => 45.41.134.35\n)\n\n => Array\n(\n => 180.151.13.110\n)\n\n => Array\n(\n => 101.53.242.89\n)\n\n => Array\n(\n => 115.186.3.110\n)\n\n => Array\n(\n => 171.49.185.242\n)\n\n => Array\n(\n => 115.42.70.24\n)\n\n => Array\n(\n => 45.128.188.43\n)\n\n => Array\n(\n => 103.140.129.63\n)\n\n => Array\n(\n => 101.50.113.147\n)\n\n => Array\n(\n => 103.66.73.30\n)\n\n => Array\n(\n => 117.247.193.169\n)\n\n => Array\n(\n => 120.29.100.94\n)\n\n => Array\n(\n => 42.109.154.39\n)\n\n => Array\n(\n => 122.173.155.150\n)\n\n => Array\n(\n => 45.115.104.53\n)\n\n => Array\n(\n => 116.74.29.84\n)\n\n => Array\n(\n => 101.50.125.34\n)\n\n => Array\n(\n => 45.118.166.80\n)\n\n => Array\n(\n => 91.236.184.27\n)\n\n => Array\n(\n => 113.167.185.120\n)\n\n => Array\n(\n => 27.97.66.222\n)\n\n => Array\n(\n => 43.247.41.117\n)\n\n => Array\n(\n => 23.229.16.227\n)\n\n => Array\n(\n => 14.248.79.209\n)\n\n => Array\n(\n => 117.5.194.26\n)\n\n => Array\n(\n => 117.217.205.41\n)\n\n => Array\n(\n => 114.79.169.99\n)\n\n => Array\n(\n => 103.55.60.97\n)\n\n => Array\n(\n => 182.75.89.210\n)\n\n => Array\n(\n => 77.73.66.109\n)\n\n => Array\n(\n => 182.77.126.139\n)\n\n => Array\n(\n => 14.248.77.166\n)\n\n => Array\n(\n => 157.35.224.133\n)\n\n => Array\n(\n => 183.83.38.27\n)\n\n => Array\n(\n => 182.68.4.77\n)\n\n => Array\n(\n => 122.177.130.234\n)\n\n => Array\n(\n => 103.24.99.99\n)\n\n => Array\n(\n => 103.91.127.66\n)\n\n => Array\n(\n => 41.90.34.240\n)\n\n => Array\n(\n => 49.205.77.102\n)\n\n => Array\n(\n => 103.248.94.142\n)\n\n => Array\n(\n => 104.143.92.170\n)\n\n => Array\n(\n => 219.91.157.114\n)\n\n => Array\n(\n => 223.190.88.22\n)\n\n => Array\n(\n => 223.190.86.232\n)\n\n => Array\n(\n => 39.41.172.80\n)\n\n => Array\n(\n => 124.107.206.5\n)\n\n => Array\n(\n => 139.167.180.224\n)\n\n => Array\n(\n => 93.76.64.248\n)\n\n => Array\n(\n => 65.216.227.119\n)\n\n => Array\n(\n => 223.190.119.141\n)\n\n => Array\n(\n => 110.93.237.179\n)\n\n => Array\n(\n => 41.90.7.85\n)\n\n => Array\n(\n => 103.100.6.26\n)\n\n => Array\n(\n => 104.140.83.13\n)\n\n => Array\n(\n => 223.190.119.133\n)\n\n => Array\n(\n => 119.152.150.87\n)\n\n => Array\n(\n => 103.125.130.147\n)\n\n => Array\n(\n => 27.6.5.52\n)\n\n => Array\n(\n => 103.98.188.26\n)\n\n => Array\n(\n => 39.35.121.81\n)\n\n => Array\n(\n => 74.119.146.182\n)\n\n => Array\n(\n => 5.181.233.162\n)\n\n => Array\n(\n => 157.39.18.60\n)\n\n => Array\n(\n => 1.187.252.25\n)\n\n => Array\n(\n => 39.42.145.59\n)\n\n => Array\n(\n => 39.35.39.198\n)\n\n => Array\n(\n => 49.36.128.214\n)\n\n => Array\n(\n => 182.190.20.56\n)\n\n => Array\n(\n => 122.180.249.189\n)\n\n => Array\n(\n => 117.217.203.107\n)\n\n => Array\n(\n => 103.70.82.241\n)\n\n => Array\n(\n => 45.118.166.68\n)\n\n => Array\n(\n => 122.180.168.39\n)\n\n => Array\n(\n => 149.28.67.254\n)\n\n => Array\n(\n => 223.233.73.8\n)\n\n => Array\n(\n => 122.167.140.0\n)\n\n => Array\n(\n => 95.158.51.55\n)\n\n => Array\n(\n => 27.96.95.134\n)\n\n => Array\n(\n => 49.206.214.53\n)\n\n => Array\n(\n => 212.103.49.92\n)\n\n => Array\n(\n => 122.177.115.101\n)\n\n => Array\n(\n => 171.50.187.124\n)\n\n => Array\n(\n => 122.164.55.107\n)\n\n => Array\n(\n => 98.114.217.204\n)\n\n => Array\n(\n => 106.215.10.54\n)\n\n => Array\n(\n => 115.42.68.28\n)\n\n => Array\n(\n => 104.194.220.87\n)\n\n => Array\n(\n => 103.137.84.170\n)\n\n => Array\n(\n => 61.16.142.110\n)\n\n => Array\n(\n => 212.103.49.85\n)\n\n => Array\n(\n => 39.53.248.162\n)\n\n => Array\n(\n => 203.122.40.214\n)\n\n => Array\n(\n => 117.217.198.72\n)\n\n => Array\n(\n => 115.186.191.203\n)\n\n => Array\n(\n => 120.29.100.199\n)\n\n => Array\n(\n => 45.151.237.24\n)\n\n => Array\n(\n => 223.190.125.232\n)\n\n => Array\n(\n => 41.80.151.17\n)\n\n => Array\n(\n => 23.111.188.5\n)\n\n => Array\n(\n => 223.190.125.216\n)\n\n => Array\n(\n => 103.217.133.119\n)\n\n => Array\n(\n => 103.198.173.132\n)\n\n => Array\n(\n => 47.31.155.89\n)\n\n => Array\n(\n => 223.190.20.253\n)\n\n => Array\n(\n => 104.131.92.125\n)\n\n => Array\n(\n => 223.190.19.152\n)\n\n => Array\n(\n => 103.245.193.191\n)\n\n => Array\n(\n => 106.215.58.255\n)\n\n => Array\n(\n => 119.82.83.238\n)\n\n => Array\n(\n => 106.212.128.138\n)\n\n => Array\n(\n => 139.167.237.36\n)\n\n => Array\n(\n => 222.124.40.250\n)\n\n => Array\n(\n => 134.56.185.169\n)\n\n => Array\n(\n => 54.255.226.31\n)\n\n => Array\n(\n => 137.97.162.31\n)\n\n => Array\n(\n => 95.185.21.191\n)\n\n => Array\n(\n => 171.61.168.151\n)\n\n => Array\n(\n => 137.97.184.4\n)\n\n => Array\n(\n => 106.203.151.202\n)\n\n => Array\n(\n => 39.37.137.0\n)\n\n => Array\n(\n => 45.118.166.66\n)\n\n => Array\n(\n => 14.248.105.100\n)\n\n => Array\n(\n => 106.215.61.185\n)\n\n => Array\n(\n => 202.83.57.179\n)\n\n => Array\n(\n => 89.187.182.176\n)\n\n => Array\n(\n => 49.249.232.198\n)\n\n => Array\n(\n => 132.154.95.236\n)\n\n => Array\n(\n => 223.233.83.230\n)\n\n => Array\n(\n => 183.83.153.14\n)\n\n => Array\n(\n => 125.63.72.210\n)\n\n => Array\n(\n => 207.174.202.11\n)\n\n => Array\n(\n => 119.95.88.59\n)\n\n => Array\n(\n => 122.170.14.150\n)\n\n => Array\n(\n => 45.118.166.75\n)\n\n => Array\n(\n => 103.12.135.37\n)\n\n => Array\n(\n => 49.207.120.225\n)\n\n => Array\n(\n => 182.64.195.207\n)\n\n => Array\n(\n => 103.99.37.16\n)\n\n => Array\n(\n => 46.150.104.221\n)\n\n => Array\n(\n => 104.236.195.147\n)\n\n => Array\n(\n => 103.104.192.43\n)\n\n => Array\n(\n => 24.242.159.118\n)\n\n => Array\n(\n => 39.42.179.143\n)\n\n => Array\n(\n => 111.93.58.131\n)\n\n => Array\n(\n => 193.176.84.127\n)\n\n => Array\n(\n => 209.58.142.218\n)\n\n => Array\n(\n => 69.243.152.129\n)\n\n => Array\n(\n => 117.97.131.249\n)\n\n => Array\n(\n => 103.230.180.89\n)\n\n => Array\n(\n => 106.212.170.192\n)\n\n => Array\n(\n => 171.224.180.95\n)\n\n => Array\n(\n => 158.222.11.87\n)\n\n => Array\n(\n => 119.155.60.246\n)\n\n => Array\n(\n => 41.90.43.129\n)\n\n => Array\n(\n => 185.183.104.170\n)\n\n => Array\n(\n => 14.248.67.65\n)\n\n => Array\n(\n => 117.217.205.82\n)\n\n => Array\n(\n => 111.88.7.209\n)\n\n => Array\n(\n => 49.36.132.244\n)\n\n => Array\n(\n => 171.48.40.2\n)\n\n => Array\n(\n => 119.81.105.2\n)\n\n => Array\n(\n => 49.36.128.114\n)\n\n => Array\n(\n => 213.200.31.93\n)\n\n => Array\n(\n => 2.50.15.110\n)\n\n => Array\n(\n => 120.29.104.67\n)\n\n => Array\n(\n => 223.225.32.221\n)\n\n => Array\n(\n => 14.248.67.195\n)\n\n => Array\n(\n => 119.155.36.13\n)\n\n => Array\n(\n => 101.50.95.104\n)\n\n => Array\n(\n => 104.236.205.233\n)\n\n => Array\n(\n => 122.164.36.150\n)\n\n => Array\n(\n => 157.45.93.209\n)\n\n => Array\n(\n => 182.77.118.100\n)\n\n => Array\n(\n => 182.74.134.218\n)\n\n => Array\n(\n => 183.82.128.146\n)\n\n => Array\n(\n => 112.196.170.234\n)\n\n => Array\n(\n => 122.173.230.178\n)\n\n => Array\n(\n => 122.164.71.199\n)\n\n => Array\n(\n => 51.79.19.31\n)\n\n => Array\n(\n => 58.65.222.20\n)\n\n => Array\n(\n => 103.27.203.97\n)\n\n => Array\n(\n => 111.88.7.242\n)\n\n => Array\n(\n => 14.171.232.77\n)\n\n => Array\n(\n => 46.101.22.182\n)\n\n => Array\n(\n => 103.94.219.19\n)\n\n => Array\n(\n => 139.190.83.30\n)\n\n => Array\n(\n => 223.190.27.184\n)\n\n => Array\n(\n => 182.185.183.34\n)\n\n => Array\n(\n => 91.74.181.242\n)\n\n => Array\n(\n => 222.252.107.14\n)\n\n => Array\n(\n => 137.97.8.28\n)\n\n => Array\n(\n => 46.101.16.229\n)\n\n => Array\n(\n => 122.53.254.229\n)\n\n => Array\n(\n => 106.201.17.180\n)\n\n => Array\n(\n => 123.24.170.129\n)\n\n => Array\n(\n => 182.185.180.79\n)\n\n => Array\n(\n => 223.190.17.4\n)\n\n => Array\n(\n => 213.108.105.1\n)\n\n => Array\n(\n => 171.22.76.9\n)\n\n => Array\n(\n => 202.66.178.164\n)\n\n => Array\n(\n => 178.62.97.171\n)\n\n => Array\n(\n => 167.179.110.209\n)\n\n => Array\n(\n => 223.230.147.172\n)\n\n => Array\n(\n => 76.218.195.160\n)\n\n => Array\n(\n => 14.189.186.178\n)\n\n => Array\n(\n => 157.41.45.143\n)\n\n => Array\n(\n => 223.238.22.53\n)\n\n => Array\n(\n => 111.88.7.244\n)\n\n => Array\n(\n => 5.62.57.19\n)\n\n => Array\n(\n => 106.201.25.216\n)\n\n => Array\n(\n => 117.217.205.33\n)\n\n => Array\n(\n => 111.88.7.215\n)\n\n => Array\n(\n => 106.201.13.77\n)\n\n => Array\n(\n => 50.7.93.29\n)\n\n => Array\n(\n => 123.201.70.112\n)\n\n => Array\n(\n => 39.42.108.226\n)\n\n => Array\n(\n => 27.5.198.29\n)\n\n => Array\n(\n => 223.238.85.187\n)\n\n => Array\n(\n => 171.49.176.32\n)\n\n => Array\n(\n => 14.248.79.242\n)\n\n => Array\n(\n => 46.219.211.183\n)\n\n => Array\n(\n => 185.244.212.251\n)\n\n => Array\n(\n => 14.102.84.126\n)\n\n => Array\n(\n => 106.212.191.52\n)\n\n => Array\n(\n => 154.72.153.203\n)\n\n => Array\n(\n => 14.175.82.64\n)\n\n => Array\n(\n => 141.105.139.131\n)\n\n => Array\n(\n => 182.156.103.98\n)\n\n => Array\n(\n => 117.217.204.75\n)\n\n => Array\n(\n => 104.140.83.115\n)\n\n => Array\n(\n => 119.152.62.8\n)\n\n => Array\n(\n => 45.125.247.94\n)\n\n => Array\n(\n => 137.97.37.252\n)\n\n => Array\n(\n => 117.217.204.73\n)\n\n => Array\n(\n => 14.248.79.133\n)\n\n => Array\n(\n => 39.37.152.52\n)\n\n => Array\n(\n => 103.55.60.54\n)\n\n => Array\n(\n => 102.166.183.88\n)\n\n => Array\n(\n => 5.62.60.162\n)\n\n => Array\n(\n => 5.62.60.163\n)\n\n => Array\n(\n => 160.202.38.131\n)\n\n => Array\n(\n => 106.215.20.253\n)\n\n => Array\n(\n => 39.37.160.54\n)\n\n => Array\n(\n => 119.152.59.186\n)\n\n => Array\n(\n => 183.82.0.164\n)\n\n => Array\n(\n => 41.90.54.87\n)\n\n => Array\n(\n => 157.36.85.158\n)\n\n => Array\n(\n => 110.37.229.162\n)\n\n => Array\n(\n => 203.99.180.148\n)\n\n => Array\n(\n => 117.97.132.91\n)\n\n => Array\n(\n => 171.61.147.105\n)\n\n => Array\n(\n => 14.98.147.214\n)\n\n => Array\n(\n => 209.234.253.191\n)\n\n => Array\n(\n => 92.38.148.60\n)\n\n => Array\n(\n => 178.128.104.139\n)\n\n => Array\n(\n => 212.154.0.176\n)\n\n => Array\n(\n => 103.41.24.141\n)\n\n => Array\n(\n => 2.58.194.132\n)\n\n => Array\n(\n => 180.190.78.169\n)\n\n => Array\n(\n => 106.215.45.182\n)\n\n => Array\n(\n => 125.63.100.222\n)\n\n => Array\n(\n => 110.54.247.17\n)\n\n => Array\n(\n => 103.26.85.105\n)\n\n => Array\n(\n => 39.42.147.3\n)\n\n => Array\n(\n => 137.97.51.41\n)\n\n => Array\n(\n => 71.202.72.27\n)\n\n => Array\n(\n => 119.155.35.10\n)\n\n => Array\n(\n => 202.47.43.120\n)\n\n => Array\n(\n => 183.83.64.101\n)\n\n => Array\n(\n => 182.68.106.141\n)\n\n => Array\n(\n => 171.61.187.87\n)\n\n => Array\n(\n => 178.162.198.118\n)\n\n => Array\n(\n => 115.97.151.218\n)\n\n => Array\n(\n => 196.207.184.210\n)\n\n => Array\n(\n => 198.16.70.51\n)\n\n => Array\n(\n => 41.60.237.33\n)\n\n => Array\n(\n => 47.11.86.26\n)\n\n => Array\n(\n => 117.217.201.183\n)\n\n => Array\n(\n => 203.192.241.79\n)\n\n => Array\n(\n => 122.165.119.85\n)\n\n => Array\n(\n => 23.227.142.218\n)\n\n => Array\n(\n => 178.128.104.221\n)\n\n => Array\n(\n => 14.192.54.163\n)\n\n => Array\n(\n => 139.5.253.218\n)\n\n => Array\n(\n => 117.230.140.127\n)\n\n => Array\n(\n => 195.114.149.199\n)\n\n => Array\n(\n => 14.239.180.220\n)\n\n => Array\n(\n => 103.62.155.94\n)\n\n => Array\n(\n => 118.71.97.14\n)\n\n => Array\n(\n => 137.97.55.163\n)\n\n => Array\n(\n => 202.47.49.198\n)\n\n => Array\n(\n => 171.61.177.85\n)\n\n => Array\n(\n => 137.97.190.224\n)\n\n => Array\n(\n => 117.230.34.142\n)\n\n => Array\n(\n => 103.41.32.5\n)\n\n => Array\n(\n => 203.90.82.237\n)\n\n => Array\n(\n => 125.63.124.238\n)\n\n => Array\n(\n => 103.232.128.78\n)\n\n => Array\n(\n => 106.197.14.227\n)\n\n => Array\n(\n => 81.17.242.244\n)\n\n => Array\n(\n => 81.19.210.179\n)\n\n => Array\n(\n => 103.134.94.98\n)\n\n => Array\n(\n => 110.38.0.86\n)\n\n => Array\n(\n => 103.10.224.195\n)\n\n => Array\n(\n => 45.118.166.89\n)\n\n => Array\n(\n => 115.186.186.68\n)\n\n => Array\n(\n => 138.197.129.237\n)\n\n => Array\n(\n => 14.247.162.52\n)\n\n => Array\n(\n => 103.255.4.5\n)\n\n => Array\n(\n => 14.167.188.254\n)\n\n => Array\n(\n => 5.62.59.54\n)\n\n => Array\n(\n => 27.122.14.80\n)\n\n => Array\n(\n => 39.53.240.21\n)\n\n => Array\n(\n => 39.53.241.243\n)\n\n => Array\n(\n => 117.230.130.161\n)\n\n => Array\n(\n => 118.71.191.149\n)\n\n => Array\n(\n => 5.188.95.54\n)\n\n => Array\n(\n => 66.45.250.27\n)\n\n => Array\n(\n => 106.215.6.175\n)\n\n => Array\n(\n => 27.122.14.86\n)\n\n => Array\n(\n => 103.255.4.51\n)\n\n => Array\n(\n => 101.50.93.119\n)\n\n => Array\n(\n => 137.97.183.51\n)\n\n => Array\n(\n => 117.217.204.185\n)\n\n => Array\n(\n => 95.104.106.82\n)\n\n => Array\n(\n => 5.62.56.211\n)\n\n => Array\n(\n => 103.104.181.214\n)\n\n => Array\n(\n => 36.72.214.243\n)\n\n => Array\n(\n => 5.62.62.219\n)\n\n => Array\n(\n => 110.36.202.4\n)\n\n => Array\n(\n => 103.255.4.253\n)\n\n => Array\n(\n => 110.172.138.61\n)\n\n => Array\n(\n => 159.203.24.195\n)\n\n => Array\n(\n => 13.229.88.42\n)\n\n => Array\n(\n => 59.153.235.20\n)\n\n => Array\n(\n => 171.236.169.32\n)\n\n => Array\n(\n => 14.231.85.206\n)\n\n => Array\n(\n => 119.152.54.103\n)\n\n => Array\n(\n => 103.80.117.202\n)\n\n => Array\n(\n => 223.179.157.75\n)\n\n => Array\n(\n => 122.173.68.249\n)\n\n => Array\n(\n => 188.163.72.113\n)\n\n => Array\n(\n => 119.155.20.164\n)\n\n => Array\n(\n => 103.121.43.68\n)\n\n => Array\n(\n => 5.62.58.6\n)\n\n => Array\n(\n => 203.122.40.154\n)\n\n => Array\n(\n => 222.254.96.203\n)\n\n => Array\n(\n => 103.83.148.167\n)\n\n => Array\n(\n => 103.87.251.226\n)\n\n => Array\n(\n => 123.24.129.24\n)\n\n => Array\n(\n => 137.97.83.8\n)\n\n => Array\n(\n => 223.225.33.132\n)\n\n => Array\n(\n => 128.76.175.190\n)\n\n => Array\n(\n => 195.85.219.32\n)\n\n => Array\n(\n => 139.167.102.93\n)\n\n => Array\n(\n => 49.15.198.253\n)\n\n => Array\n(\n => 45.152.183.172\n)\n\n => Array\n(\n => 42.106.180.136\n)\n\n => Array\n(\n => 95.142.120.9\n)\n\n => Array\n(\n => 139.167.236.4\n)\n\n => Array\n(\n => 159.65.72.167\n)\n\n => Array\n(\n => 49.15.89.2\n)\n\n => Array\n(\n => 42.201.161.195\n)\n\n => Array\n(\n => 27.97.210.38\n)\n\n => Array\n(\n => 171.241.45.19\n)\n\n => Array\n(\n => 42.108.2.18\n)\n\n => Array\n(\n => 171.236.40.68\n)\n\n => Array\n(\n => 110.93.82.102\n)\n\n => Array\n(\n => 43.225.24.186\n)\n\n => Array\n(\n => 117.230.189.119\n)\n\n => Array\n(\n => 124.123.147.187\n)\n\n => Array\n(\n => 216.151.184.250\n)\n\n => Array\n(\n => 49.15.133.16\n)\n\n => Array\n(\n => 49.15.220.74\n)\n\n => Array\n(\n => 157.37.221.246\n)\n\n => Array\n(\n => 176.124.233.112\n)\n\n => Array\n(\n => 118.71.167.40\n)\n\n => Array\n(\n => 182.185.213.161\n)\n\n => Array\n(\n => 47.31.79.248\n)\n\n => Array\n(\n => 223.179.238.192\n)\n\n => Array\n(\n => 79.110.128.219\n)\n\n => Array\n(\n => 106.210.42.111\n)\n\n => Array\n(\n => 47.247.214.229\n)\n\n => Array\n(\n => 193.0.220.108\n)\n\n => Array\n(\n => 1.39.206.254\n)\n\n => Array\n(\n => 123.201.77.38\n)\n\n => Array\n(\n => 115.178.207.21\n)\n\n => Array\n(\n => 37.111.202.92\n)\n\n => Array\n(\n => 49.14.179.243\n)\n\n => Array\n(\n => 117.230.145.171\n)\n\n => Array\n(\n => 171.229.242.96\n)\n\n => Array\n(\n => 27.59.174.209\n)\n\n => Array\n(\n => 1.38.202.211\n)\n\n => Array\n(\n => 157.37.128.46\n)\n\n => Array\n(\n => 49.15.94.80\n)\n\n => Array\n(\n => 123.25.46.147\n)\n\n => Array\n(\n => 117.230.170.185\n)\n\n => Array\n(\n => 5.62.16.19\n)\n\n => Array\n(\n => 103.18.22.25\n)\n\n => Array\n(\n => 103.46.200.132\n)\n\n => Array\n(\n => 27.97.165.126\n)\n\n => Array\n(\n => 117.230.54.241\n)\n\n => Array\n(\n => 27.97.209.76\n)\n\n => Array\n(\n => 47.31.182.109\n)\n\n => Array\n(\n => 47.30.223.221\n)\n\n => Array\n(\n => 103.31.94.82\n)\n\n => Array\n(\n => 103.211.14.45\n)\n\n => Array\n(\n => 171.49.233.58\n)\n\n => Array\n(\n => 65.49.126.95\n)\n\n => Array\n(\n => 69.255.101.170\n)\n\n => Array\n(\n => 27.56.224.67\n)\n\n => Array\n(\n => 117.230.146.86\n)\n\n => Array\n(\n => 27.59.154.52\n)\n\n => Array\n(\n => 132.154.114.10\n)\n\n => Array\n(\n => 182.186.77.60\n)\n\n => Array\n(\n => 117.230.136.74\n)\n\n => Array\n(\n => 43.251.94.253\n)\n\n => Array\n(\n => 103.79.168.225\n)\n\n => Array\n(\n => 117.230.56.51\n)\n\n => Array\n(\n => 27.97.187.45\n)\n\n => Array\n(\n => 137.97.190.61\n)\n\n => Array\n(\n => 193.0.220.26\n)\n\n => Array\n(\n => 49.36.137.62\n)\n\n => Array\n(\n => 47.30.189.248\n)\n\n => Array\n(\n => 109.169.23.84\n)\n\n => Array\n(\n => 111.119.185.46\n)\n\n => Array\n(\n => 103.83.148.246\n)\n\n => Array\n(\n => 157.32.119.138\n)\n\n => Array\n(\n => 5.62.41.53\n)\n\n => Array\n(\n => 47.8.243.236\n)\n\n => Array\n(\n => 112.79.158.69\n)\n\n => Array\n(\n => 180.92.148.218\n)\n\n => Array\n(\n => 157.36.162.154\n)\n\n => Array\n(\n => 39.46.114.47\n)\n\n => Array\n(\n => 117.230.173.250\n)\n\n => Array\n(\n => 117.230.155.188\n)\n\n => Array\n(\n => 193.0.220.17\n)\n\n => Array\n(\n => 117.230.171.166\n)\n\n => Array\n(\n => 49.34.59.228\n)\n\n => Array\n(\n => 111.88.197.247\n)\n\n => Array\n(\n => 47.31.156.112\n)\n\n => Array\n(\n => 137.97.64.180\n)\n\n => Array\n(\n => 14.244.227.18\n)\n\n => Array\n(\n => 113.167.158.8\n)\n\n => Array\n(\n => 39.37.175.189\n)\n\n => Array\n(\n => 139.167.211.8\n)\n\n => Array\n(\n => 73.120.85.235\n)\n\n => Array\n(\n => 104.236.195.72\n)\n\n => Array\n(\n => 27.97.190.71\n)\n\n => Array\n(\n => 79.46.170.222\n)\n\n => Array\n(\n => 102.185.244.207\n)\n\n => Array\n(\n => 37.111.136.30\n)\n\n => Array\n(\n => 50.7.93.28\n)\n\n => Array\n(\n => 110.54.251.43\n)\n\n => Array\n(\n => 49.36.143.40\n)\n\n => Array\n(\n => 103.130.112.185\n)\n\n => Array\n(\n => 37.111.139.202\n)\n\n => Array\n(\n => 49.36.139.108\n)\n\n => Array\n(\n => 37.111.136.179\n)\n\n => Array\n(\n => 123.17.165.77\n)\n\n => Array\n(\n => 49.207.143.206\n)\n\n => Array\n(\n => 39.53.80.149\n)\n\n => Array\n(\n => 223.188.71.214\n)\n\n => Array\n(\n => 1.39.222.233\n)\n\n => Array\n(\n => 117.230.9.85\n)\n\n => Array\n(\n => 103.251.245.216\n)\n\n => Array\n(\n => 122.169.133.145\n)\n\n => Array\n(\n => 43.250.165.57\n)\n\n => Array\n(\n => 39.44.13.235\n)\n\n => Array\n(\n => 157.47.181.2\n)\n\n => Array\n(\n => 27.56.203.50\n)\n\n => Array\n(\n => 191.96.97.58\n)\n\n => Array\n(\n => 111.88.107.172\n)\n\n => Array\n(\n => 113.193.198.136\n)\n\n => Array\n(\n => 117.230.172.175\n)\n\n => Array\n(\n => 191.96.182.239\n)\n\n => Array\n(\n => 2.58.46.28\n)\n\n)\n```\nRetirement Gift for In-Laws: scfr's Personal Finance Blog\n << Back to all Blogs Login or Create your own free blog Layout: Blue and Brown (Default) Author's Creation\nHome > Retirement Gift for In-Laws", null, "", null, "", null, "June 9th, 2008 at 03:46 am\n\nMy in-laws are easing (or should I say lurching) in to retirement. FIL is 72 and MIL is 68. They both worked very hard all of their lives. FIL owned his own business (with several employees) and MIL worked with him part-time, running the office. FIL has had a series of health issues in the past few years, and after several years of talking about how he was going to retire soon, MIL decided to take charge and push him along. She talked him in to putting their house up for sale. It sold fairly quickly, and then they rented a place in a more rural area. MIL moved in to the rental in late-April, but FIL stayed behind (moving in to SIL's house) to wrap things up with the business. He goes and visits MIL on the weekends, and has promised he will have tied up all of the loose ends with the business on June 20th, when he will permanently moving to the country. The entire family is saying \"we'll believe it when we see it,\" as he really seems to be having a hard time actually taking the final steps.\n\nI'm so proud of my MIL. She has been really ready to retire for about 8 years now, and she has put up with many promises deferred. Because of her culture and her personality, she generally takes a fairly submissive role in the marriage, but I guess she decided she had had enough and she put her foot down! The rest of the family has really gotten a kick out of watching her put her assert herself and (hopefully) drag FIL kicking and screaming in to a well-deserved retirement.\n\nI think it's hard for FIL to deal with because at this stage in his life he really doesn't have interests outside of work (other than watching TV and reading the paper). Hopefully he won't turn in to a total couch potato. He is interested in gardening, and now that they have a place in the country hopefully he can get more involved in that. MIL on the other had is quite a social butterfly, especially with her religious group. She visits with her group members, makes friends quickly with the neighbors, keeps house, and likes to read. She will thrive in retirement, no doubt.\n\nAnyway ... DH & I want to give them a nice retirement gift. We have come up with 2 ideas, and would love to hear any other suggestions. If we ask them what they want, they will say they don't want anything. So we have to take the approach of offering them option A, B, or C and letting them choose.\n\nIf anyone who has already retired has suggestions of what they would have liked to have received when they retired, please share. If anyone has done something like this for their parents or have thought about doing something like this for their folks, or just dreams about being able to do something like this for their parents some day, please share suggestions.\n\nDon't be afraid to venture a bit into \"just dreaming\" sorts of ideas. FIL is not facing imminent death, but he is not going to be around forever, and this gift is our way of \"giving him roses while he is still alive.\" We are able to do something nice for them, and we very much want to.\n\nThe 2 ideas we have are:\n\n1. A 2-week cruise in their region (they live in another country) ... They have not cruised before, but they have enjoyed travelling in the past, and we thought they would feel more comfortable if they stuck close to home, especially given FIL's medical problems.\n\n2. Business Class tickets to visit us here in the USA, plus some domestic travel with us (perhaps via Amtrak in a sleeper car) ... DH & I always fly coach, as have my in-laws in the past, but we think at their age they deserve to travel in comfort.\n\nWe thought about replacing their old car for them, but MIL does not drive and we do not know how much longer FIL will be able to drive. DH thinks it would be best if they just drive the current car for as long as it lasts, and when it dies, to encourage them to just rely on public transportation (which is excellent where they live).\n\nI'd like to have at least another one or two options to toss out to them but am stumped, so any and all suggestions are welcome! Thank you!\n\n### 5 Responses to “Retirement Gift for In-Laws”\n\n1. Carolina Bound Says:\n\nI really appreciated getting a Barnes & Noble gift card when I retired.\n\nAnything related to travel is good, or something to help fund hobbies. I would have loved theater tickets, but of course, that depends on your in-laws.\n\n2. pretty cheap jewelry Says:\n\nI cruised once and it is not what all cracked up to be. (Of course, I am prone to sea sickness). It is but a temporary diversion and I am more in favor of lasting impacts.\n\nSort of the same opinion on train travel. There is a LOT of 'boring' time.\n\nOK now for the help!\nMy parents retired but only about a year ago, my mom so worried she wouldn't know what to do! Now? She has no free time! Lesson-it takes a little adjustment time, but they will find what they love and devote time toward.\n\nThey love to travel? Send a 'dream' basket of travel ideas with a coupon redeemable at your checking account for a portion of the trip. Include maps, food samples from various countries (ie Italian coffee, Hawaiian pineapple, etc), language translation booklets (small ones), a disposable camera, and more.\n\nNo grandkids? If so, there could be a 'playdate' themed gift with travel to the kids, and tickets to a zoo or somewhere.\n\nHow about throwing a surprise 'Welcome to Free Time' party (or some such fun title). The MIL sounds like she has plenty to invite. But if you are far away, it would be tough to arrange. Any best friend of hers that would work with you? Hold it at a community center, with photos and food. Let the guests write one line of a poem about the couple, or 'roast' them.\n\nhmmm, let me think some more and I'll come back if I can.\n\n3. pretty cheap jewelry Says:\n\nLast thoughts:\nSo they are going to be in the country, do they garden? do they need outdoor tools? Is there a nearby town with activities/groups of interest?\n\nI joined the local art association in our weekend property town. It is active and a big help in getting to know residents. Give them a membership or make a donation to such a group they will be near. Maybe there is a historic society, a Sierra Club chapter, or something you think will get them out of the house!\n\nGood luck!\n\n4. scfr Says:\n\nThanks for the great ideas!\n\nA party? Why didn't I think of that? I'll add that to the list. And we may add a gardening center certificate as well (we'll have to find out if their rental house allows them to make significant changes).\n\nPCJ - I hear you about the cruise. But the one I had picked out includes daily on-shore excursions (included in the price of the cruise) that sound really interesting, and there are daily after-dinner educational lectures. It's definitely aimed at the 55+ active learner crowd. Not much in the way of on-board activities. Sounds like the daily routine is\n\n- Breakfast on-board\n- Daily excursion in to town, including walking about (age-appropriate exercise)\n- Dinner on-board\n- After dinner lecture\n- Perhaps a bit of unwinding w/ TV (in each room) or reading\n- Sleep to get ready to do the same thing the next day\n\nOn this particular cruise, the boat seems to serve as a floating hotel & restaurant only, to keep you fed (without having to decide where to go) and get you from place to place in comfort (without having to pack & unpack every day).\n\nSince this particular cruise focuses on their home country, I thought it might introduce them to new places that they could go back and explore more in-depth on their own. Given their age & health, their long overseas travelling days are over. Just too grueling.\n\n5. pretty cheap jewelry Says:\n\noh yes yes, the educational cruises might be better\n\nFor a party wouldn't it be a hoot if each guest were to bring one 'Idea' for retirement activities? Some folks are not crafty/clever so you could even supply a 'form' for guests to fill out and make a binder with them.\n\nhave a good experience in whatever happens!\n\n(Note: If you were logged in, we could automatically fill in these fields for you.)\n Name: * Email: Will not be published. Subscribe: Notify me of additional comments to this entry. URL: Verification: * Please spell out the number 4.  [ Why? ]\n\nvB Code: You can use these tags: [b] [i] [u] [url] [email]" ]
[ null, "https://www.savingadvice.com/blogs/images/search/top_left.php", null, "https://www.savingadvice.com/blogs/images/search/top_right.php", null, "https://www.savingadvice.com/blogs/images/search/bottom_left.php", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9856378,"math_prob":0.99441385,"size":8616,"snap":"2020-10-2020-16","text_gpt3_token_len":1987,"char_repetition_ratio":0.107640505,"word_repetition_ratio":0.2384807,"special_character_ratio":0.2349118,"punctuation_ratio":0.10094287,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99364555,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-09T04:15:58Z\",\"WARC-Record-ID\":\"<urn:uuid:d1dd1c54-c1cb-42ff-875a-9440eee3c28b>\",\"Content-Length\":\"107082\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:77012839-c02a-4a16-bda1-033f6f38de48>\",\"WARC-Concurrent-To\":\"<urn:uuid:42f1d23e-f13a-4c44-bd25-721cc41ae384>\",\"WARC-IP-Address\":\"173.231.200.26\",\"WARC-Target-URI\":\"https://scfr.savingadvice.com/2008/06/09/retirement-gift-for-in-laws_39908/\",\"WARC-Payload-Digest\":\"sha1:VUZPTIKWGXENREDXZ4H4F3YYNEPDFD3X\",\"WARC-Block-Digest\":\"sha1:JJXP23XBWKC5BF7PEOQ6DIWPJ2GWYFFZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371829677.89_warc_CC-MAIN-20200409024535-20200409055035-00469.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-7-algebraic-fractions-7-4-addition-and-subtraction-of-algebraic-fractions-and-simplifying-complex-fractions-problem-set-7-4-page-300/71
[ "## Elementary Algebra\n\n$96/b$\nWe use the equation for the area of a triangle: $$A=1/2 bh\\\\ 48 = 1/2 bh \\\\ 48 \\times 2 = bh \\\\ h = 96/b$$" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8565926,"math_prob":0.9999788,"size":385,"snap":"2021-21-2021-25","text_gpt3_token_len":105,"char_repetition_ratio":0.10761155,"word_repetition_ratio":0.0,"special_character_ratio":0.2987013,"punctuation_ratio":0.0625,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986203,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-11T09:55:09Z\",\"WARC-Record-ID\":\"<urn:uuid:d868c430-50ec-4edd-ba49-7a372a1bf63c>\",\"Content-Length\":\"73395\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13ffd780-58c4-4e91-afba-000a702e418f>\",\"WARC-Concurrent-To\":\"<urn:uuid:20a87ef5-22e3-4140-a2ad-141170c3b89b>\",\"WARC-IP-Address\":\"54.83.50.97\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-7-algebraic-fractions-7-4-addition-and-subtraction-of-algebraic-fractions-and-simplifying-complex-fractions-problem-set-7-4-page-300/71\",\"WARC-Payload-Digest\":\"sha1:HXQA5F7BOSMNQXP33Q25MQ3KAEEB4XJB\",\"WARC-Block-Digest\":\"sha1:BKW2SHX64YBFZQ7SAHWQVJ2XILR45V2H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991982.8_warc_CC-MAIN-20210511092245-20210511122245-00349.warc.gz\"}"}
https://encyclopediaofmath.org/wiki/Elliptic_genera
[ "# Elliptic genera\n\nThe name elliptic genus has been given to various multiplicative cobordism invariants taking values in a ring of modular forms. The following is an attempt to present the simplest case — level- $2$ genera in characteristic $\\neq 2$— in a unified way. It is convenient to use N. Katz's approach to modular forms (cf. [a7]) and view a modular form as a function of elliptic curves with a chosen invariant differential (cf. also Elliptic curve). A similar approach to elliptic genera was used by J. Franke [a3].\n\n## Jacobi functions.\n\nLet $K$ be any perfect field of characteristic $\\neq 2$ and fix an algebraic closure ${\\overline{K}\\; }$ of $K$( cf. Algebraically closed field). Consider a triple $( E, \\omega, \\alpha )$ consisting of:\n\ni) an elliptic curve $E$ over $K$, i.e. a smooth curve of genus $1$ with a specified $K$- rational base-point $O$;\n\nii) an invariant $K$- rational differential $\\omega$;\n\niii) a $K$- rational primitive $2$- division point $\\alpha$. Following J.I. Igusa [a6] (up to a point), one can associate to these data two functions, $x$ and $y$, as follows.\n\nThe set $E _ {4} \\subset E ( {\\overline{K}\\; } )$ of $4$- division points on $E$ can be described as follows. There are four $2$- division points $t$( $\\alpha$ is one of them), four primitive $4$- division points $r$ such that $2r = \\alpha$, and eight primitive $4$- division points $s$ such that $2s \\neq \\alpha$. Consider the degree- $0$ divisor $D = \\sum ( t ) - \\sum ( r )$. Since $\\sum t - \\sum r = 0$ in $E$ and since Galois symmetries transform $D$ into itself, Abel's theorem (cf., for example, [a11], III.3.5.1, or Abel theorem) implies that there is a function $x \\in K ( E ) ^ \\times$, uniquely defined up to a multiplicative constant, such that ${ \\mathop{\\rm div} } ( x ) = D$.\n\nThe function $x$ is odd, satisfies $x ( u + \\alpha ) \\equiv x ( u )$, and undergoes sign changes under the two other translations of exact order $2$. Moreover, if $r \\in E _ {4}$ satisfies $2r = \\alpha$, then translation by $r$ transforms $x$ into $Cx ^ {- 1 }$ for some non-zero constant $C$. This constant depends on the choice of $r$ but only up to sign. It follows that $x ^ {2} ( u + r ) x ^ {2} ( u )$ does not depend on the choice of $r$. This constant is written as $\\varepsilon ^ {- 1 }$, i.e.\n\n$$\\varepsilon \\equiv x ^ {- 2 } ( u + r ) x ^ {- 2 } ( u ) .$$\n\nOne also defines\n\n$$\\delta = { \\frac{1}{8} } \\sum x ^ {- 2 } ( s )$$\n\n(the summation is over the primitive $4$- division points $s$ such that $2s \\neq \\alpha$). If $a$ is one of the values of $x ( s )$, the other values are $\\pm a, \\pm \\varepsilon ^ {- {1 / 2 } } a ^ {- 1 }$, each taken twice. It follows that\n\n$$\\delta = { \\frac{1}{2} } ( a ^ {- 2 } + \\varepsilon a ^ {2} )$$\n\nand\n\n$$\\prod ( X - x ( s ) ) = \\varepsilon ^ {- 2 } ( 1 - 2 \\delta X ^ {2} + \\varepsilon X ^ {4} ) ^ {2} = \\varepsilon ^ {- 2 } R ( X ) ^ {2} .$$\n\nIt is now easy to see that\n\n$${ \\mathop{\\rm div} } ( R ( x ) ) = 2 \\left ( \\sum ( s ) - 2 \\sum ( r ) \\right ) .$$\n\nUsing once more Abel's theorem, one sees that there is a unique $y \\in K ( E ) ^ \\times$ such that ${ \\mathop{\\rm div} } ( y ) = \\sum ( s ) - 2 \\sum ( r )$, and $y ( O ) = 1$. Since $x ( O ) = 0$, one has $y ^ {2} = R ( x )$.\n\nThe differential $dx$ has four double poles $r$. Also, it is easy to see that $s$ is a double zero of $x - x ( s )$, hence a simple zero of $dx$. One concludes that\n\n$${ \\mathop{\\rm div} } ( dx ) = \\sum ( s ) - 2 \\sum ( r ) = { \\mathop{\\rm div} } ( y ) .$$\n\nand that ${ {dx } / y }$ is an invariant differential on $E$.\n\nA slight modification of the argument given in [a6] shows that the Jacobi elliptic functions satisfy the Euler addition formula\n\n$$x ( u + v ) ( 1 - \\varepsilon x ^ {2} ( u ) x ^ {2} ( v ) ) = x ( u ) y ( v ) + x ( v ) y ( u ) .$$\n\nAccordingly, one defines the Euler formal group law $F ( U,V ) \\in K [ [ U,V ] ]$ by\n\n$$F ( U,V ) = { \\frac{U \\sqrt {R ( V ) } + V \\sqrt {R ( U ) } }{1 - \\varepsilon U ^ {2} V ^ {2} } } .$$\n\nNotice that since ${ \\mathop{\\rm char} } K \\neq 2$, $F ( U,V )$ is defined over $K$.\n\n## The elliptic genus.\n\nAt this point, one normalizes $x$ over $K$ by requiring that ${ {dx } / y } = \\omega$( the given invariant differential). All the objects $x, y, \\delta, \\varepsilon$, and $F ( U,V )$ are now completely determined by the initial data. Replacing $\\omega$ by $\\lambda \\omega$( $\\lambda \\in K ^ \\times$) yields:\n\n$$\\tag{a1 } x \\asR \\lambda x, \\quad y \\asR y, \\quad \\delta \\asR \\lambda ^ {- 2 } \\delta,$$\n\n$$\\varepsilon \\asR \\lambda ^ {- 4 } \\varepsilon, \\quad F ( U,V ) \\asR \\lambda F ( \\lambda ^ {- 1 } U, \\lambda ^ {- 1 } V ) .$$\n\nAs any formal group law, $F ( U,V )$ is classified by a unique ring homomorphism\n\n$$\\psi : {\\Omega _ {*} ^ { { \\mathop{\\rm U} } } } \\rightarrow K$$\n\nfrom the complex cobordism ring. Since $F ( - U, - V ) = - F ( U,V )$, it is easy to see that $\\psi$ uniquely factors through a ring homomorphism\n\n$$\\varphi : {\\Omega _ {*} ^ { { \\mathop{\\rm SO} } } } \\rightarrow K$$\n\nfrom the oriented cobordism ring. By definition, $\\varphi$ is the level- $2$ elliptic genus. Suppose now that ${ \\mathop{\\rm char} } K = 0$. Define a local parameter $z$ near $O$ so that $z ( O ) = 0$ and $dz = \\omega$. Then $x$ can be expanded into a formal power series $x ( z ) \\in K [ [ z ] ]$ which clearly satisfies $x ( z ) = z + o ( z )$ and $x ( - z ) = - x ( z )$. In this case, the elliptic genus can be defined as the Hirzebruch genus (cf. [a4] or [a5]) corresponding to the series $P ( z ) = {z / {x ( z ) } }$. Since ${ {d x ( z ) } / {dz } } = y ( z )$, the logarithm $g ( z )$ of this elliptic genus is given by the elliptic integral\n\n$$\\tag{a2 } g ( z ) = \\int\\limits _ { 0 } ^ { z } { \\frac{dt }{\\sqrt {1 - 2 \\delta t ^ {2} + \\varepsilon t ^ {4} } } } ,$$\n\nwhich gives the original definition in [a9].\n\n## Modularity.\n\nFor any closed oriented manifold $M$ of dimension $4k$, $\\varphi ( M )$ is a function of the triple $( E, \\omega, \\alpha )$. As easily follows from (a1), multiplying $\\omega$ by $\\lambda$ results in multiplying $\\varphi ( M )$ by $\\lambda ^ {- 2k }$. Also, $\\varphi ( M )$ depends only on the isomorphism class of the triple $( E, \\omega, \\alpha )$ and commutes with arbitrary extensions of the scalar field $K$. In the terminology of Katz ([a7]; adapted here to modular forms over fields), $\\varphi ( M )$ is a modular form of level $2$ and weight $2k$. Let ${\\mathcal M} _ {*}$ be the graded ring of all such modular forms. Then $\\varphi ( M ) \\in {\\mathcal M} _ {2k }$, $\\delta \\in {\\mathcal M} _ {2}$, $\\varepsilon \\in {\\mathcal M} _ {4}$. Moreover, one can prove that ${\\mathcal M} _ {*} \\cong \\mathbf Z [ {1 / 2 } , \\delta, \\varepsilon ]$. If one identifies these two isomorphic rings, the elliptic genus becomes the Hirzebruch genus\n\n$$\\varphi : {\\Omega _ {*} ^ { { \\mathop{\\rm SO} } } } \\rightarrow {\\mathbf Z [ {1 / 2 } , \\delta, \\varepsilon ] }$$\n\nwith logarithm given by the formal integral (a2).\n\n## Integrality.\n\nConsider\n\n$${ {\\widetilde \\varphi } } : {\\Omega _ {*} ^ { { \\mathop{\\rm Spin} } } } \\rightarrow { {\\mathcal M} _ {*} } ,$$\n\ni.e., the composition of $\\varphi$ with the forgetful homomorphism $\\Omega _ {*} ^ { { \\mathop{\\rm Spin} } } \\rightarrow \\Omega _ {*} ^ { { \\mathop{\\rm SO} } }$. As is shown in [a2],\n\n$${\\widetilde \\varphi } ( \\Omega _ {*} ^ { { \\mathop{\\rm Spin} } } ) = \\mathbf Z [ 8 \\delta, \\varepsilon ] .$$\n\nThe ring $\\mathbf Z [ 8 \\delta, \\varepsilon ]$ agrees with the ring ${\\mathcal M} _ {*} ( \\mathbf Z )$ of modular forms over $\\mathbf Z$. Thus: If $M$ is a ${ \\mathop{\\rm Spin} }$- manifold of dimension $4k$, then $\\varphi ( M ) \\in {\\mathcal M} _ {2k } ( \\mathbf Z )$.\n\n## Example: the Tate curve.\n\nLet $K$ be a local field, complete with respect to a discrete valuation $v$, and let $q \\in K ^ \\times$ be any element satisfying $v ( q ) < 0$. Consider $E = K ^ \\times /q ^ {2 \\mathbf Z }$. It is well-known (cf. [a11], § C.14) that $E$ can be identified with the elliptic curve (known as the Tate curve)\n\n$$E _ {q ^ {2} } : Y ^ {2} + XY = X ^ {3} + a _ {4} X + a _ {6} ,$$\n\nwhere\n\n$$a _ {4} = \\sum _ {m \\geq 1 } ( - 5m ^ {3} ) { \\frac{q ^ {2m } }{1 - q ^ {2m } } } ,$$\n\n$$a _ {6} = \\sum _ {m \\geq 1 } \\left ( - { \\frac{5m ^ {3} + 7m ^ {5} }{12 } } \\right ) { \\frac{q ^ {2m } }{1 - q ^ {2m } } } .$$\n\n$E$ can be treated as an elliptic curve over $K$ with $O = 1$. Fix the invariant differential $\\omega = { {du } / u }$( $u \\in K ^ \\times$) on $E$( $\\omega$ corresponds to the differential $\\omega _ {\\textrm{ can } } = { {dX } / {( 2Y + X ) } }$ on the Tate curve). $E$ has three $K$- rational primitive $2$- division points: $- 1$, $q$ and $- q$. To describe the corresponding Jacobi function $x$, consider the theta-function\n\n$$\\Theta ( u ) = ( 1 - u ^ {- 2 } ) \\prod _ {n > 0 } ( 1 - q ^ {2n } u ^ {- 2 } ) ( 1 - q ^ {2n } u ^ {2} ) .$$\n\nThis is a \"holomorphic\" function on $K ^ \\times$ with simple zeros at points of $\\pm q ^ {\\mathbf Z}$( cf. [a10] for a justification of this terminology), satisfying\n\n$$\\Theta ( - u ) = \\Theta ( u ) , \\quad \\Theta ( q ^ {- 1 } u ) = - u ^ {2} \\Theta ( u ) .$$\n\nConsider the case where $\\alpha = - 1$. Let $i \\in {\\overline{K}\\; }$ be any square root of $- 1$, and let\n\n$$\\tag{a3 } f ( u ) = { \\frac{\\Theta ( u ) }{\\Theta ( iu ) } } =$$\n\n$$= { \\frac{u ^ {2} - 1 }{u ^ {2} + 1 } } \\prod _ {n > 0 } { \\frac{( 1 - q ^ {2n } u ^ {- 2 } ) ( 1 - q ^ {2n } u ^ {2} ) }{( 1 + q ^ {2n } u ^ {- 2 } ) ( 1 + q ^ {2n } u ^ {2} ) } } .$$\n\n$f$ is a meromorphic function on $E$ satisfying $f ( iu ) = {1 / {f ( u ) } }$ and\n\n$${ \\mathop{\\rm div} } ( f ) = ( 1 ) + ( - 1 ) + ( q ) + ( - q ) +$$\n\n$$- ( i ) - ( - i ) - ( iq ) - ( - iq ) ,$$\n\ni.e., $f$ is a multiple of the Jacobi function $x$ of $( E, \\omega, - 1 )$.\n\nNotice now that the normalization condition ${ {du } / u } = { {dx } / y }$ can be written as $y ( u ) = ux ^ \\prime ( u )$, where $x ^ \\prime ( u )$ is the derivative with respect to $u$. Since $y ( 1 ) = 0$, one has $x ^ \\prime ( 1 ) = 1$. Differentiating (a3), one obtains\n\n$$f ^ \\prime ( 1 ) = \\prod _ {n > 0 } \\left ( { \\frac{1 - q ^ {2n } }{1 + q ^ {2n } } } \\right ) ^ {2} ,$$\n\n$$x ( u ) = { \\frac{u ^ {2} - 1 }{u ^ {2} + 1 } } \\prod _ {n > 0 } { \\frac{( 1 - q ^ {2n } u ^ {- 2 } ) ( 1 - q ^ {2n } u ^ {2} ) ( 1 + q ^ {2n } ) ^ {2} }{( 1 + q ^ {2n } u ^ {- 2 } ) ( 1 + q ^ {2n } u ^ {2} ) ( 1 - q ^ {2n } ) ^ {2} } } ,$$\n\nand\n\n$$\\varepsilon = \\prod _ {n > 0 } \\left ( { \\frac{1 - q ^ {2n } }{1 + q ^ {2n } } } \\right ) ^ {8} .$$\n\nFinally, if ${ \\mathop{\\rm char} } K = 0$, the function $z = { \\mathop{\\rm log} } u$ satisfies $dz = { {du } / u }$. It follows that the generating series $P ( z ) = {z / {x ( z ) } }$ is given by\n\n$$P ( z ) =$$\n\n$$= { \\frac{z}{ { \\mathop{\\rm tanh} } z } } \\prod _ {n > 0 } { \\frac{( 1 + q ^ {2n } e ^ {- 2z } ) ( 1 + q ^ {2n } e ^ {2z } ) ( 1 - q ^ {2n } ) ^ {2} }{( 1 - q ^ {2n } e ^ {- 2z } ) ( 1 - q ^ {2n } e ^ {2z } ) ( 1 + q ^ {2n } ) ^ {2} } } .$$\n\nThe cases where $\\alpha = q$ or $\\alpha = - q$ are treated similarly, with\n\n$$f ( u ) = { \\frac{u \\Theta ( u ) }{\\Theta ( q ^ {- 1/2 } u ) } }$$\n\nand\n\n$$f ( u ) = { \\frac{u \\Theta ( u ) }{\\Theta ( iq ^ {- 1/2 } u ) } } ,$$\n\nrespectively.\n\n## Strict multiplicativity.\n\nThe following theorem, also known (in an equivalent form) as the Witten conjecture, was proven first by C. Taubes [a12], then by R. Bott and Taubes [a1]. Let $P$ be a principal $G$- bundle (cf. also Principal $G$- object) over an oriented manifold $B$, where $G$ is a compact connected Lie group, and suppose $G$ acts on a compact ${ \\mathop{\\rm Spin} }$- manifold $M$. Then\n\n$$\\varphi ( P \\times _ {G} M ) = \\varphi ( B ) \\varphi ( M ) .$$\n\nFor the history of this conjecture, cf. [a8].\n\nHow to Cite This Entry:\nElliptic genera. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elliptic_genera&oldid=46811\nThis article was adapted from an original article by S. Ochanine (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.5662714,"math_prob":0.99999774,"size":14155,"snap":"2022-40-2023-06","text_gpt3_token_len":5146,"char_repetition_ratio":0.12168752,"word_repetition_ratio":0.20856394,"special_character_ratio":0.46442953,"punctuation_ratio":0.13920124,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000094,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-28T20:41:06Z\",\"WARC-Record-ID\":\"<urn:uuid:40ec836c-7f3e-421d-ae69-83b29ed4cde1>\",\"Content-Length\":\"35480\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b9fa6f4d-607c-4725-aaf9-6ff1038c2cd3>\",\"WARC-Concurrent-To\":\"<urn:uuid:69945a08-a6df-4e13-8cb7-f6d6238f8585>\",\"WARC-IP-Address\":\"34.96.94.55\",\"WARC-Target-URI\":\"https://encyclopediaofmath.org/wiki/Elliptic_genera\",\"WARC-Payload-Digest\":\"sha1:HSXXJ6LDIHGOS4TE6F4HWRLYCRV57TPU\",\"WARC-Block-Digest\":\"sha1:PPZFSCBIW3J4OEIR6YCMMHF3AQYXRVQ2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499654.54_warc_CC-MAIN-20230128184907-20230128214907-00284.warc.gz\"}"}
https://chemistry.stackexchange.com/questions/73504/water-vapor-equilibrium-calculations
[ "Water vapor equilibrium calculations\n\nThe first part said:\n\nCalculate the amount of water required to saturate a vessel of volume 82 L at 300 K given that the vapor pressure of water is 38 torr at 300 K.\n\nThe solution went like this:\n\nSince we have to saturate the vessel, we have to find the minimum number of moles that will occupy the given volume (that is what I understood).\n\nNow, applying the gas equation\n\n$$PV=nRT$$\n\n$$\\frac{1}{20}*82 = n * 0.82 * 300$$\n\n$$n = \\frac{1}{6}; w=n * M = 3 gm$$\n\nThis part is fine.\n\nNow the second part:\n\nIf 5 gm of water is introduced in the vessel (initially evacuated), then, calculate the amount of water remaining.\n\nSo, my teacher said that, 3 gm will evaporate and 2 gm will remain. But, 3 gm will evaporate for 82 L. So, when I pour 5 gm of water, shouldn't the volume decrease?\n\n• You are correct that there will initially be a volume of 82L - 5cc. Then 3cc evaporates, so the volume of the container is 82 L - 0.002 L. Will this make a difference in your calculation that will show up in a 2 significant figure answer? Apr 28 '17 at 1:47\n• @airhuff then, in the first question also, the volume should be 82-0.003. right? Apr 28 '17 at 1:54\n• But the point for the second question, is would it matter if you just ignored the effect of the volume of the liquid water? In the first question there is no liquid water left because it all evaporated and you have nothing but water vapor. Back to the second question: 82L - 0.002L = 81.998L, which rounds to 82L (note that you are only given 2 significant figures in the problem), and for that matter it rounds to 82.00L! So, is the volume of the small amount of water insignificant compared to the size of the container in this question (hint, hint), such that you can just ignore it? Apr 28 '17 at 2:07\n• You are not supposed to write \"Thanks\" or \"Help is appreciated\" or any statements of weaknesses in your post. And fix that Vap0r in the title. [I edited his post, apparently he rejected it] Apr 28 '17 at 12:18" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.92688817,"math_prob":0.9772719,"size":801,"snap":"2022-05-2022-21","text_gpt3_token_len":225,"char_repetition_ratio":0.122961104,"word_repetition_ratio":0.0,"special_character_ratio":0.30212235,"punctuation_ratio":0.123595506,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9908814,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-17T02:39:03Z\",\"WARC-Record-ID\":\"<urn:uuid:0e574007-7a86-48d3-96e1-2cfcb714e96e>\",\"Content-Length\":\"131220\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a40accdc-b6fe-462a-ad46-a0dd2233c8bb>\",\"WARC-Concurrent-To\":\"<urn:uuid:92fa3122-b5ed-40a2-9d9f-ca9d530ed69a>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://chemistry.stackexchange.com/questions/73504/water-vapor-equilibrium-calculations\",\"WARC-Payload-Digest\":\"sha1:4UJUZGWUUWSSQGCXGSIJARQUO6OQWFJP\",\"WARC-Block-Digest\":\"sha1:XMH35OYPAHOXVE4TO3BG5WK3RIPA6N7N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320300253.51_warc_CC-MAIN-20220117000754-20220117030754-00509.warc.gz\"}"}
https://flylib.com/books/en/2.253.1/namespaces.html
[ "# namespaces\n\nA program includes many identifiers defined in different scopes. Sometimes a variable of one scope will \"overlap\" (i.e., collide) with a variable of the same name in a different scope, possibly creating a naming conflict. Such overlapping can occur at many levels. Identifier overlapping occurs frequently in third-party libraries that happen to use the same names for global identifiers (such as functions). This can cause compiler errors.\n\nGood Programming Practice 24.1", null, "Avoid identifiers that begin with the underscore character, which can lead to linker errors. Many code libraries use names that begin with underscores.\n\nThe C++ standard attempts to solve this problem with namespaces. Each namespace defines a scope in which identifiers and variables are placed. To use a namespace member, either the member's name must be qualified with the namespace name and the binary scope resolution operator (::), as in\n\nMyNameSpace::member\n\nor a using declaration or using directive must appear before the name is used in the program. Typically, such using statements are placed at the beginning of the file in which members of the namespace are used. For example, placing the following using directive at the beginning of a source-code file\n\n```using namespace MyNameSpace;\n```\n\nspecifies that members of namespace MyNameSpace can be used in the file without preceding each member with MyNameSpace and the scope resolution operator (::).\n\nA using declaration (e.g., using std::cout;) brings one name into the scope where the declaration appears. A using directive (e.g., using namespace std;) brings all the names from the specified namespace into the scope where the directive appears.\n\nSoftware Engineering Observation 24.1", null, "Ideally, in large programs, every entity should be declared in a class, function, block or namespace. This helps clarify every entity's role.\n\nError-Prevention Tip 24.2", null, "Precede a member with its namespace name and the scope resolution operator (::) if the possibility exists of a naming conflict.\n\nNot all namespaces are guaranteed to be unique. Two third-party vendors might inadvertently use the same identifiers for their namespace names. Figure 24.2 demonstrates the use of namespaces.\n\nFigure 24.2. Demonstrating the use of namespaces.\n\n(This item is displayed on pages 1204 - 1205 in the print version)\n\n``` 1 // Fig. 24.2: fig24_02.cpp\n2 // Demonstrating namespaces.\n3 #include\n4 using namespace std; // use std namespace\n5\n6 int integer1 = 98; // global variable\n7\n8 // create namespace Example\n9 namespace Example\n10 {\n11 // declare two constants and one variable\n12 const double PI = 3.14159;\n13 const double E = 2.71828;\n14 int integer1 = 8;\n15\n16 void printValues(); // prototype\n17\n18 // nested namespace\n19 namespace Inner\n20 {\n21 // define enumeration\n22 enum Years { FISCAL1 = 1990, FISCAL2, FISCAL3 };\n23 } // end Inner namespace\n24 } // end Example namespace\n25\n26 // create unnamed namespace\n27 namespace\n28 {\n29 double doubleInUnnamed = 88.22; // declare variable\n30 } // end unnamed namespace\n31\n32 int main()\n33 {\n34 // output value doubleInUnnamed of unnamed namespace\n35 cout << \"doubleInUnnamed = \" << doubleInUnnamed;\n36\n37 // output global variable\n38 cout << \"\n(global) integer1 = \" << integer1;\n39\n40 // output values of Example namespace\n41 cout << \"\nPI = \" << Example::PI << \"\nE = \" << Example::E\n42 << \"\ninteger1 = \" << Example::integer1 << \"\nFISCAL3 = \"\n43 << Example::Inner::FISCAL3 << endl;\n44\n45 Example::printValues(); // invoke printValues function\n46 return 0;\n47 } // end main\n48\n49 // display variable and constant values\n50 void Example::printValues()\n51 {\n52 cout << \"\nIn printValues:\ninteger1 = \" << integer1 << \"\nPI = \"\n53 << PI << \"\nE = \" << E << \"\ndoubleInUnnamed = \"\n54 << doubleInUnnamed << \"\n(global) integer1 = \" << ::integer1\n55 << \"\nFISCAL3 = \" << Inner::FISCAL3 << endl;\n56 } // end printValues\n```\n\n ``` doubleInUnnamed = 88.22 (global) integer1 = 98 PI = 3.14159 E = 2.71828 integer1 = 8 FISCAL3 = 1992 In printValues: integer1 = 8 PI = 3.14159 E = 2.71828 doubleInUnnamed = 88.22 (global) integer1 = 98 FISCAL3 = 1992 ```\n\nUsing the std Namespace\n\nLine 4 informs the compiler that namespace std is being used. The contents of header file are all defined as part of namespace std. [Note: Most C++ programmers consider it poor practice to write a using directive such as line 4 because the entire contents of the namespace are included, thus increasing the likelihood of a naming conflict.]\n\nThe using namespace directive specifies that the members of a namespace will be used frequently throughout a program. This allows the programmer to access all the members of the namespace and to write more concise statements such as\n\n```cout << \"double1 = \" << double1;\n```\n\nrather than\n\n```std::cout << \"double1 = \" << double1;\n```\n\nWithout line 4, either every cout and endl in Fig. 24.2 would have to be qualified with std::, or individual using declarations must be included for cout and endl as in:\n\n```using std::cout;\nusing std::endl;\n```\n\nThe using namespace directive can be used for predefined namespaces (e.g., std) or programmer-defined namespaces.\n\nDefining Namespaces\n\nLines 924 use the keyword namespace to define namespace Example. The body of a namespace is delimited by braces ({}). Namespace Example's members consist of two constants (PI and E at lines 1213), an int (integer1 at line 14), a function (printValues at line 16) and a nested namespace (Inner at lines 1923). Notice that member integer1 has the same name as global variable integer1 (line 6). Variables that have the same name must have different scopesotherwise compilation errors occur. A namespace can contain constants, data, classes, nested namespaces, functions, etc. Definitions of namespaces must occupy the global scope or be nested within other namespaces.\n\nLines 2730 create an unnamed namespace containing the member doubleInUnnamed. The unnamed namespace has an implicit using directive, so its members appear to occupy the global namespace, are accessible directly and do not have to be qualified with a namespace name. Global variables are also part of the global namespace and are accessible in all scopes following the declaration in the file.\n\nSoftware Engineering Observation 24.2", null, "Each separate compilation unit has its own unique unnamed namespace; i.e., the unnamed namespace replaces the static linkage specifier.\n\nAccessing Namespace Members with Qualified Names\n\nLine 35 outputs the value of variable doubleInUnnamed, which is directly accessible as part of the unnamed namespace. Line 38 outputs the value of global variable integer1. For both of these variables, the compiler first attempts to locate a local declaration of the variables in main. Since there are no local declarations, the compiler assumes those variables are in the global namespace.\n\nLines 4143 output the values of PI, E, integer1 and FISCAL3 from namespace Example. Notice that each must be qualified with Example:: because the program does not provide any using directive or declarations indicating that it will use members of namespace Example. In addition, member integer1 must be qualified, because a global variable has the same name. Otherwise, the global variable's value is output. Notice that FISCAL3 is a member of nested namespace Inner, so it must be qualified with Example::Inner::.\n\nFunction printValues (defined at lines 5056) is a member of Example, so it can access other members of the Example namespace directly without using a namespace qualifier. The output statement in lines 5255 outputs integer1, PI, E, doubleInUnnamed, global variable integer1 and FISCAL3. Notice that PI and E are not qualified with Example. Variable doubleInUnnamed is still accessible, because it is in the unnamed namespace and the variable name does not conflict with any other members of namespace Example. The global version of integer1 must be qualified with the unary scope resolution operator (::), because its name conflicts with a member of namespace Example. Also, FISCAL3 must be qualified with Inner::. When accessing members of a nested namespace, the members must be qualified with the namespace name (unless the member is being used inside the nested namespace).\n\nCommon Programming Error 24.1", null, "Placing main in a namespace is a compilation error.\n\nAliases for Namespace Names\n\nNamespaces can be aliased. For example the statement\n\n```namespace CPPHTP5E = CPlusPlusHowToProgram5E;\n```\n\ncreates the alias CPPHTP5E for CPlusPlusHowToProgram5E.", null, "C++ How to Program (5th Edition)\nISBN: 0131857576\nEAN: 2147483647\nYear: 2004\nPages: 627", null, "" ]
[ null, "https://flylib.com/books/2/253/1/html/2/images/good.jpg", null, "https://flylib.com/books/2/253/1/html/2/images/software.jpg", null, "https://flylib.com/books/2/253/1/html/2/images/error.jpg", null, "https://flylib.com/books/2/253/1/html/2/images/software.jpg", null, "https://flylib.com/books/2/253/1/html/2/images/software.jpg", null, "https://flylib.com/icons/4544-small.jpg", null, "https://flylib.com/media/images/top.png", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7040618,"math_prob":0.78562,"size":9420,"snap":"2022-40-2023-06","text_gpt3_token_len":2104,"char_repetition_ratio":0.16992353,"word_repetition_ratio":0.021985343,"special_character_ratio":0.23715499,"punctuation_ratio":0.1388889,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9514784,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-02T12:11:11Z\",\"WARC-Record-ID\":\"<urn:uuid:a73bdb0e-1935-4435-b43c-bc39e171ebc4>\",\"Content-Length\":\"82175\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6cb4bcd2-25ff-4a48-8172-afcec542586f>\",\"WARC-Concurrent-To\":\"<urn:uuid:036956a4-80e9-4605-9d2b-d3258f250d87>\",\"WARC-IP-Address\":\"179.43.157.53\",\"WARC-Target-URI\":\"https://flylib.com/books/en/2.253.1/namespaces.html\",\"WARC-Payload-Digest\":\"sha1:OPH5MOKOQNTIUXS4XNDO5HPZ6K34BEO4\",\"WARC-Block-Digest\":\"sha1:PR52IXYW7DEEODHNQE26WC2M2LS54ZXI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500017.27_warc_CC-MAIN-20230202101933-20230202131933-00018.warc.gz\"}"}
https://www.worldsrichpeople.com/what-number-is-12-of-150/
[ "# What number is 12% of 150?\n\n## What number is 12% of 150?\n\n12 percent of 150 is 18.\n\n## How do you find 150 percent of a number?\n\n1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y\n\n1. Convert the problem to an equation using the percentage formula: P% * X = Y.\n2. P is 10%, X is 150, so the equation is 10% * 150 = Y.\n3. Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.\n\nHow do you calculate percentages in a worksheet?\n\nThe basic formula for calculating a percentage is =part/total. Say you want to reduce a particular amount by 25%, like when you’re trying to apply a discount. Here, the formula will be: =Price*1-Discount %. (Think of the “1” as a stand-in for 100%.)\n\n### How do you find the percentage of a number practice?\n\nWorksheet on Percentage of a Number\n\n1. We know, to find the percent of a number we obtain the given number and then multiply the number by the required percent i.e., x % of a = x100 × a.\n2. (x) 34 % of \\$ 780.\n3. (xiv) 35 % of 725 cm.\n\n### What number is 8% of 150?\n\n8 percent of 150 is 12.\n\nHow do we convert a percent to decimal decimal to percent?\n\nTo convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25. To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right). For example, 0.065 = 6.5% and 3.75 = 375%.\n\n## What is the percentage of 150?\n\nRelated Standard Percentage Calculations on 10 is what percent of 150\n\nX is Percentage(P) of Y\n97.5 65 150\n99 66 150\n100.5 67 150\n102 68 150\n\n## Can you have 150 percent?\n\nTechnically, “percent” should mean “for every hundred”. So, I would think that it’s perfectly fine to say “150%”. However, in common usage, people rarely say percentages greater than a hundred.\n\nHow do I convert to percentage in Excel?\n\nPercentages are calculated by using the equation amount / total = percentage. For example, if a cell contains the formula =10/100, the result of that calculation is 0.1. If you then format 0.1 as a percentage, the number will be correctly displayed as 10%.\n\n### How do I calculate 15% of a number in Excel?\n\nTo subtract 15%, use =1-15% as the formula….Here’s how to do it:\n\n1. Enter the numbers you want to multiply by 15% into a column.\n2. In an empty cell, enter the percentage of 15% (or 0.15), and then copy that number by pressing Ctrl-C.\n3. Select the range of cells A1:A5 (by dragging down the column).\n\n### How do you find the percentage of two numbers worksheet?\n\nAnswer: To find the percentage of a number between two numbers, divide one number with the other and then multiply the result by 100.\n\nHow do you work out 100 percent from a percentage?\n\nIn order to do this, we:\n\n1. Either add/subtract the percentage given in the problem from 100% to determine what percentage we have.\n2. Find 1% by dividing by percentage found in previous step.\n3. Find 100% (original amount) by multiplying your answer in step 2 by 100.\n\n## What percent is 12 of 150?\n\nSteps to solve “what percent is 12 of 150?” To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100 If you are using a calculator, simply enter 12÷150×100 which will give you 8 as the answer.\n\n## How do you write 12% as a percentage?\n\n“Percent” or “%” means “out of 100” or “per 100”, Therefore 12% can be written as 12 100. When dealing with percents the word “of” means “times” or “to multiply”.\n\nWhat is the value of 100% of 150?\n\n1. We assume, that the number 150 is 100% – because it’s the output value of the task. 2. We assume, that x is the value we are looking for. 3. If 100% equals 150, so we can write it down as 100%=150.\n\n### What is the value of X if 12 is 100%?\n\nWe assume, that the number 12 is 100% – because it’s the output value of the task. 2. We assume, that x is the value we are looking for. 3. If 12 is 100%, so we can write it down as 12=100%. 4. We know, that x is 150% of the output value, so we can write it down as x=150%. 5. Now we have two simple equations: 6.\n\nBegin typing your search term above and press enter to search. Press ESC to cancel." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.8831072,"math_prob":0.9984592,"size":3956,"snap":"2022-40-2023-06","text_gpt3_token_len":1125,"char_repetition_ratio":0.16902834,"word_repetition_ratio":0.0926893,"special_character_ratio":0.33493426,"punctuation_ratio":0.1367713,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999554,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-05T00:36:17Z\",\"WARC-Record-ID\":\"<urn:uuid:9110fb8f-0a1e-4162-bbb3-62d1ea7c31f8>\",\"Content-Length\":\"54741\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ddb55c47-b684-460b-99a8-26d7d9cb7564>\",\"WARC-Concurrent-To\":\"<urn:uuid:3a8bdc06-36d1-405c-b5dd-e414b7b4fbda>\",\"WARC-IP-Address\":\"172.67.200.214\",\"WARC-Target-URI\":\"https://www.worldsrichpeople.com/what-number-is-12-of-150/\",\"WARC-Payload-Digest\":\"sha1:NVQVWCKBSEX7UZOVIXXJFVPBZHK374WP\",\"WARC-Block-Digest\":\"sha1:PMGGWVA3O5BVVGYLSX5L7OPKMFPAXH6L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500158.5_warc_CC-MAIN-20230205000727-20230205030727-00156.warc.gz\"}"}
https://flylib.com/books/en/3.150.1.84/1/
[ "# IIf", null, "We mentioned IIf earlier in the book (Chapter 4), and warned you of its dangers (all of the arguments are run), but there are some times when it can be really useful. For example, suppose we want to print our report out double sided, and would like the page numbers to appear at the outer edge on both odd and even numbered pages. This means that for some pages it must be on the left, and for the others it must be on the right. Note that as an alternative, we could write our own function to do this: we probably would if we wanted more flexibility than the IIf function offers.\n\n### Try It Out-The IIf Function\n\n1. Switch the form back into design mode.\n\n2. Move the page number field to the very left of the page, and set the text to be left aligned using the Align Left button on the toolbar.\n\n3. Modify the Control Source property of the page number field, so it now looks like this:\n\n` =IIf([Page] Mod 2 = 0, \"Page \" & [Page] & \" of \" & [Pages], \"\") `\n4. Add another textbox, this time at the right of the page and set the text to be right aligned using the Align Right button on the toolbar. You can delete the label again.\n\n5. Add the following code to this textbox's Control Source property:\n\n` =IIf([Page] Mod 2 = 1, \"Page \" & [Page] & \" of \" & [Pages], \"\") `\n6. Now switch to preview mode to see what effect the changes have had. Step forward a few pages to see what happens for odd and even pages.\n\nNotice that for the first page, and all odd numbered pages, the page numbers are on the right of the page. For all even numbers they are on the left.\n\nHow It Works\n\nLet's look again at the arguments for the IIf function:\n\n` IIf (Expression, TruePart, FalsePart) `\n\nThe arguments are:\n\n• Expression , which is the expression to test\n\n• TruePart , which is the value to return if Expression is True\n\n• FalsePart , which is the value to return if Expression is False\n\nSo, for the page numbers on the left we have this:\n\n` =IIf([Page] Mod 2 = 0, \"Page \" & [Page] & \" of \" & [Pages], \"\") `\n\nThat means the Expression we are testing is:\n\n` [Page] Mod 2 = 0 `\n\nThis uses Mod to return the integer remainder of dividing the page number by two. This will be if the page number is even, so the expression will only be True on even pages.\n\nIf the Expression is True , then the TruePart of the IIf function:\n\n` \"Page \" & [Page] & \" of \" & [Pages] `\n\nis returned.\n\nIf Expression is False , then the FalsePart of the IIf function is returned, which is empty.\n\nSo this whole field will only show up on even numbered pages, which produces the page count we are looking for.\n\nThe page number field for page numbers on the right is pretty similar. The only difference is in the expression to test:\n\n` [Page] Mod 2 = 1 `\n\nHere we check to see whether the page number is odd or not. If it is, then the same TruePart is returned.\n\nThis shows that with just one simple function you've made your report look much better than it did before.\n\nStill confused about Mod ? We need to use it because we don't have a programmatic concept of what is an odd or even page, and so we use the Mod operator to help us out. We know that if we set the Mod operator to 2 , that all page numbers (numerator) will be divided by 2 (denominator). It just so happens that whenever a page number is divided by two that if there is a remainder the page number is odd and whenever there is no remainder the page number is even.\n\nSo by using Mod 2 in this instance we can determine an odd from an even page number.\n\nYou can find more about the Mod operator by keying \"Mod\" into the help index when in the V-E (remember online help is context sensitive).", null, "", null, "Beginning Access 2002 VBA (Programmer to Programmer)\nISBN: 0764544020\nEAN: 2147483647\nYear: 2003\nPages: 256" ]
[ null, "https://flylib.com/books/3/150/1/html/2/images/libtag.gif", null, "https://flylib.com/books/3/150/1/html/2/images/libtag.gif", null, "https://flylib.com/icons/6415-small.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.9034121,"math_prob":0.93335885,"size":3505,"snap":"2021-43-2021-49","text_gpt3_token_len":839,"char_repetition_ratio":0.15566981,"word_repetition_ratio":0.08733624,"special_character_ratio":0.2470756,"punctuation_ratio":0.09292649,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9787525,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,10,null,10,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-20T03:24:00Z\",\"WARC-Record-ID\":\"<urn:uuid:02bb5b7e-85ce-41fe-8dae-68d91a564435>\",\"Content-Length\":\"22376\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:24803db1-e22b-48bc-8390-b85938030108>\",\"WARC-Concurrent-To\":\"<urn:uuid:824517de-ce92-4f5f-b0ef-b7cece67285a>\",\"WARC-IP-Address\":\"179.43.157.53\",\"WARC-Target-URI\":\"https://flylib.com/books/en/3.150.1.84/1/\",\"WARC-Payload-Digest\":\"sha1:EPZ2YIBPXCJJAYVGBVWVWWQLT3GRJYDW\",\"WARC-Block-Digest\":\"sha1:7BEB6VSUYZGT2673YNGTK3JP5RKF66II\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585302.56_warc_CC-MAIN-20211020024111-20211020054111-00368.warc.gz\"}"}