[Solution] Permutation Value Codeforces Solution

B. Permutation Value

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

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

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

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

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

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

Input

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

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

Output

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

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 multiple such permutations, print any of them.

Note

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

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