A15383. Permutation Value

You are given an integer $n$ . You have to construct a permutation of size $n$ .

A permutation is an array where each integer from $1$ to $s$ (where $s$ is the size of permutation) occurs exactly once. For example, $[2, 1, 4, 3]$ is a permutation of size $4$ ; $[1, 2, 4, 5, 3]$ is a permutation of size $5$ ; $[1, 4, 3]$ is not a permutation (the integer $2$ is absent), $[2, 1, 3, 1]$ is not a permutation (the integer $1$ appears twice).

A subsegment of a permutation is a contiguous subsequence of that permutation. For example, the permutation $[2, 1, 4, 3]$ has $10$ subsegments: $[2]$ , $[2, 1]$ , $[2, 1, 4]$ , $[2, 1, 4, 3]$ , $[1]$ , $[1, 4]$ , $[1, 4, 3]$ , $[4]$ , $[4, 3]$ and $[3]$ .

The value of the permutation is the number of its subsegments which are also permutations. For example, the value of $[2, 1, 4, 3]$ is $3$ since the subsegments $[2, 1]$ , $[1]$ and $[2, 1, 4, 3]$ are permutations.

You have to construct a permutation of size $n$ with minimum possible value among all permutations of size $n$ .

The first line contains one integer $t$ ( $1 \le t \le 48$ ) — the number of test cases.

Then, $t$ lines follow. The $i$ -th of them contains one integer $n$ ( $3 \le n \le 50$ ) representing the $i$ -th test case.

For each test case, print $n$ integers — the permutation of size $n$ with minimum possible value. If there are multiple such permutations, print any of them.

In the first example, the permutation $[1, 4, 3, 5, 2]$ is one of the possible answers; its value is $2$ .

In the second example, the permutation $[4, 1, 6, 2, 5, 3]$ is one of the possible answers; its value is $2$ .