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# [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 $p$ of $n$ integers $1$$2$, ..., $n$ (a permutation is an array where each element from $1$ to $n$ occurs exactly once) as follows:

• initially, an integer variable $x$ is equal to $0$;
• if $x<{p}_{1}$, then add ${p}_{1}$ to $x$ (set $x=x+{p}_{1}$), otherwise assign $0$ to $x$;
• if $x<{p}_{2}$, then add ${p}_{2}$ to $x$ (set $x=x+{p}_{2}$), otherwise assign $0$ to $x$;
• ...
• if $x<{p}_{n}$, then add ${p}_{n}$ to $x$ (set $x=x+{p}_{n}$), otherwise assign $0$ to $x$;
• the value of the permutation is $x$ at the end of this process.

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

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

Input

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

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

Output

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