| There is an integer sequence $a$ of length $n$, where each element is initially $-1$. | |
| Misuki has two typewriters where the first one writes letters from left to right, with a pointer initially pointing to $1$, and another writes letters from right to left with a pointer initially pointing to $n$. | |
| Misuki would choose one of the typewriters and use it to perform the following operations until $a$ becomes a permutation of $[1, 2, \ldots, n]$ | |
| * write number: write the minimum positive integer that isn't present in the array $a$ to the element $a_i$, $i$ is the position where the pointer points at. Such operation can be performed only when $a_i = -1$. * carriage return: return the pointer to its initial position (i.e. $1$ for the first typewriter, $n$ for the second) * move pointer: move the pointer to the next position, let $i$ be the position the pointer points at before this operation, if Misuki is using the first typewriter, $i := i + 1$ would happen, and $i := i - 1$ otherwise. Such operation can be performed only if after the operation, $1 \le i \le n$ holds. | |
| Your task is to construct any permutation $p$ of length $n$, such that the minimum number of carriage return operations needed to make $a = p$ is the same no matter which typewriter Misuki is using. | |
| Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. The description of the test cases follows. | |
| The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the permutation. | |
| It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$. | |
| For each test case, output a line of $n$ integers, representing the permutation $p$ of length $n$ such that the minimum number of carriage return operations needed to make $a = p$ is the same no matter which typewriter Misuki is using, or $-1$ if it is impossible to do so. | |
| If there are multiple valid permutations, you can output any of them. | |
| In the |