A13412. Balanced Array

You are given a positive integer $n$ , it is guaranteed that $n$ is even (i.e. divisible by $2$ ).

You want to construct the array $a$ of length $n$ such that:

- The first $\frac{n}{2}$ elements of $a$ are even (divisible by $2$ );
- the second $\frac{n}{2}$ elements of $a$ are odd (not divisible by $2$ );
- all elements of $a$ are distinct and positive;
- the sum of the first half equals to the sum of the second half ( $\sum\limits_{i=1}^{\frac{n}{2}} a_i = \sum\limits_{i=\frac{n}{2} + 1}^{n} a_i$ ).

If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the length of the array. It is guaranteed that that $n$ is even (i.e. divisible by $2$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ ).

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a1,a2,…,an (1≤ai≤10^9) satisfying conditions from the problem statement on the second line.