Permutation Value

2000ms

524288K

Description:

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 $$$n$$$.

Input:

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.

Output:

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.

Sample Input:

2
5
6

Sample Output:

1 4 3 5 2
4 1 6 2 5 3

Note:

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 $$$2$$$.

Informação

Provedor Codeforces

Código CF1743B