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

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

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.

见题面 Input 部分

见题面 Output 部分