Problem: 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

Solution (in JAVA):

Solution:


import java.util.Scanner;

public class problemA {

	public static void main(String[] args) {

		Scanner scn = new Scanner(System.in);

		int tc = scn.nextInt();

		while (tc-- > 0) {
			int n = scn.nextInt();

			int size = n / 2;
			if (size % 2 != 0 ) {
				System.out.println("NO");
			} else {
				System.out.println("YES");
				long sum = size * (size + 1);
				for (int i = 2; i <= n; i += 2) {
					System.out.print(i + " ");
				}
				oddIntegers(sum, size);
			}

		}

	}

public	static void oddIntegers(long n, int k) {

		int sum = 0;
		int i = 1;
		int j = 1;

		while (j < k) {
			sum = sum + i;
			System.out.print(i + " ");
			i = i + 2;
			j++;
		}

		long finalOdd = n - sum;

		System.out.println(finalOdd);
	}

}