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 BalancedArray {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn = new Scanner(System.in);
		int test = scn.nextInt();
		while (test > 0) {
			int N = scn.nextInt();
			int c = N / 2;
			if (c % 2 != 0) {
				System.out.println("NO");
			} else {
				if (N == 1) {
					System.out.println("NO");
				} else {
					System.out.println("YES");
					int[] arr = new int[N];
					for (int i = 0; i < N / 2; i++) {
						int a = i + 1;
						arr[i] = 2 * a;
					}
					int q = 1;
					for (int i = N / 2; i < N - 1; i++) {
						int a = q;
						arr[i] = 2 * a - 1;
						q++;
					}
					int rl = (N / 2) / 2;
					int re = (N / 2) - 1 + rl + 1;
					arr[arr.length - 1] = 2 * re - 1;
					for (int i = 0; i < N; i++) {
						System.out.print(arr[i] + " ");
					}
					System.out.println();}}
			test--;}}}