You are given an integer $n$. You need to construct a permutation$^{\text{∗}}$ $a_1, a_2, \ldots, a_n$ using integers from $1$ to $n$ such that the following condition is satisfied:

$$a_1 \bmod a_2 \ge a_2 \bmod a_3 \geq \ldots \ge a_{n-1} \bmod a_{n},$$where$u$mod$v$denotes the remainder of dividing$u$by$v$.</p><p>If multiple valid permutations exist, you may output any of them.</p><p>It can be shown that a valid permutation always exists for every$n \ge 2$.</p><div class="statement-footnote"><p>$^{\text{∗}}$A permutation of length$n$is an array consisting of$n$distinct integers from$1$to$n$in arbitrary order. For example,$[2,3,1,5,4]$is a permutation, but$[1,2,2]$is not a permutation ($2$appears twice in the array), and$[1,3,4]$is also not a permutation ($n=3$but there is$4$ in the array). ## Input Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows. The first line of each test case contains a single integer $n$ ($2 \le n \le 100$). ## Output For each test case, output on a single line $n$ space-separated integers $a_1, a_2, \ldots a_n$. If multiple valid permutations exist, you may output any of them. ## Note In the second test case, $2 \bmod 3 \ge 3 \bmod 1$, so the permutation $[2, 3, 1]$ is valid. In the third test case, $2 \bmod 4 \ge 4 \bmod 3 \ge 3 \bmod 1$, so the permutation $[2, 4, 3, 1]$ is valid. ## Samples ```input1 4 2 3 4 5 ``` ```output1 2 1 2 3 1 2 4 3 1 3 5 4 2 1 ```$$