[Solution] Best Permutation Codeforces Solution

B. Best Permutation

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Let's define the value of the permutation 𝑝$p$ of 𝑛$n$ integers 1$1$, 2$2$, ..., 𝑛$n$ (a permutation is an array where each element from 1$1$ to 𝑛$n$ occurs exactly once) as follows:

• initially, an integer variable 𝑥$x$ is equal to 0$0$;
• if 𝑥<𝑝1$x<p_1$, then add 𝑝1$p_1$ to 𝑥$x$ (set 𝑥=𝑥+𝑝1$x=x+p_1$), otherwise assign 0$0$ to 𝑥$x$;
• if 𝑥<𝑝2$x<p_2$, then add 𝑝2$p_2$ to 𝑥$x$ (set 𝑥=𝑥+𝑝2$x=x+p_2$), otherwise assign 0$0$ to 𝑥$x$;
• ...
• if 𝑥<𝑝𝑛$x<p_n$, then add 𝑝𝑛$p_n$ to 𝑥$x$ (set 𝑥=𝑥+𝑝𝑛$x=x+p_n$), otherwise assign 0$0$ to 𝑥$x$;
• the value of the permutation is 𝑥$x$ at the end of this process.

For example, for 𝑝=[4,5,1,2,3,6]$p=[4,5,1,2,3,6]$, the value of 𝑥$x$ changes as follows: 0,4,9,0,2,5,11$0,4,9,0,2,5,11$, so the value of the permutation is 11$11$.

You are given an integer 𝑛$n$. Find a permutation 𝑝$p$ of size 𝑛$n$ with the maximum possible value among all permutations of size 𝑛$n$. If there are several such permutations, you can print any of them.

Input

The first line contains one integer 𝑡$t$ (1≤𝑡≤97$1\le t\le 97$) — the number of test cases.

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The only line of each test case contains one integer 𝑛$n$ (4≤𝑛≤100$4\le n\le 100$).

Output

For each test case, print 𝑛$n$ integers — the permutation 𝑝$p$ of size 𝑛$n$ with the maximum possible value among all permutations of size 𝑛$n$.