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 ($um\limits_{i=1}^{\frac{n}{2}} a_i = um\limits_{i=\frac{n}{2} + 1}^{n} a_i$).

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.

Input

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 $2 \cdot 10^5$ ($um n \le 2 \cdot 10^5$).

Output

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 $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) satisfying conditions from the problem statement on the second line.

Samples

5
2
4
6
8
10

NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO