Yes, this is another one of those constructive permutation problems.

You are given an integer $$$n$$$. You have to construct a permutation $$$p$$$ of size $$$n$$$, i. e. an array of $$$n$$$ integers, where every integer from $$$1$$$ to $$$n$$$ appears exactly once.

Every pair of adjacent elements in the permutation ($$$p_i$$$ and $$$p_{i+1}$$$) must meet the following condition:

- if one of them is divisible by the other, the condition $$$p_i < p_{i+1}$$$ must hold;
- otherwise, the condition $$$p_i > p_{i+1}$$$ must hold.

Input format:
The first line contains one integer $$$t$$$ ($$$1 \le t \le 99$$$) — the number of test cases.

Each test case consists of one line, containing one integer $$$n$$$ ($$$2 \le n \le 100$$$).
Output format:
For each test case, print the answer as follows:

- if no permutation of size $$$n$$$ meeting the conditions from the statement exists, print $$$-1$$$;
- otherwise, print $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ — the required permutation. If there are mutliple answers, print any of them.
Example Input 0:
2
5
10

Example Output 0:
1 5 2 4 3
1 2 10 9 7 4 8 3 6 5



Example input:
2
5
10


Example output:
1 5 2 4 3
1 2 10 9 7 4 8 3 6 5