| Consider a grid graph with $n$ rows and $n$ columns. Let the cell in row $x$ and column $y$ be $(x,y)$. There exists a directed edge from $(x,y)$ to $(x+1,y)$, with non-negative integer value $d_{x,y}$, for all $1\le x < n, 1\le y \le n$, and there also exists a directed edge from $(x,y)$ to $(x,y+1)$, with non-negative integer value $r_{x,y}$, for all $1\le x \le n, 1\le y < n$. | |
| Initially, you are at $(1,1)$, with an empty set $S$. You need to walk along the edges and eventually reach $(n,n)$. Whenever you pass an edge, its value will be inserted into $S$. Please maximize the MEX$^{\text{∗}}$ of $S$ when you reach $(n,n)$. | |
| $^{\text{∗}}$The MEX (minimum excluded) of an array is the smallest non- negative integer that does not belong to the array. For instance: | |
| * The MEX of $[2,2,1]$ is $0$, because $0$ does not belong to the array. * The MEX of $[3,1,0,1]$ is $2$, because $0$ and $1$ belong to the array, but $2$ does not. * The MEX of $[0,3,1,2]$ is $4$, because $0, 1, 2$, and $3$ belong to the array, but $4$ does not. | |
| Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le100$). The description of the test cases follows. | |
| The first line of each test case contains a single integer $n$ ($2\le n\le20$) — the number of rows and columns. | |
| Each of the next $n-1$ lines contains $n$ integers separated by single spaces — the matrix $d$ ($0\le d_{x,y}\le 2n-2$). | |
| Each of the next $n$ lines contains $n-1$ integers separated by single spaces — the matrix $r$ ($0\le r_{x,y}\le 2n-2$). | |
| It is guaranteed that the sum of all $n^3$ does not exceed $8000$. | |
| For each test case, print a single integer — the maximum MEX of $S$ when you reach $(n,n)$. | |
| In the first test case, the grid graph and one of the optimal paths are as follows: | |
|  | |
| In the second test case, the grid graph and one of the optimal paths are as follows: | |
|  |