Kevin and Permutation

Description:

Input:

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Description of the test cases follows.

The only line of each test case contains an integer $$$n$$$ ($$$2 \le n \leq 1\,000$$$) — the size of the set.

Output:

For each test case print a single line containing $$$n$$$ distinct integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$) describing the arrangement that maximizes the minimum absolute difference of consecutive elements.

Formally, you have to print a permutation $$$p$$$ which maximizes the value $$$\min \limits_{i=1}^{n - 1} \lvert p_{i + 1} - p_i \rvert$$$.

If there are multiple optimal solutions, print any of them.

Sample Input:

2
4
3

Sample Output:

2 4 1 3
1 2 3

Note:

In the first test case the minimum absolute difference of consecutive elements equals $$$\min \{\lvert 4 - 2 \rvert, \lvert 1 - 4 \rvert, \lvert 3 - 1 \rvert \} = \min \{2, 3, 2\} = 2$$$. It's easy to prove that this answer is optimal.

In the second test case each permutation of numbers $$$1, 2, 3$$$ is an optimal answer. The minimum absolute difference of consecutive elements equals to $$$1$$$.