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 n/2 elements of a are even (divisible by 2);
• the second 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 (∑{i=1}^{n/2} a_i = ∑{i=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 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 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, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input

5 2 4 6 8 10

Output

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

inputFormat

Input

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

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

outputFormat

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, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input

5 2 4 6 8 10

Output

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

样例

5
2
4
6
8
10

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

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