A15284 | Best Permutation

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 $p = [4, 5, 1, 2, 3, 6]$ , 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.

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

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

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