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.*;
import java.lang.*;

public class problem{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int t = sc.nextInt();

		if(t>=1 && t<= Math.pow(10,4)){

			int count[] = new int[t];

			for(int y=0;y<t;y++){
				count[y] = sc.nextInt();
			}

			for(int y=0;y<t;y++){

				int n = count[y];
				int even_number = 2;
				int odd_number = 1;
				int even_sum=0;
				int odd_sum=0;
				int rem;

				if(n>=2 && n<= 2*Math.pow(10,5)){

					int a[] = new int[n];

					for(int i=0;i<n;i++){
						a[i] =0;
					}

					for(int i=0;i<n/2;i++){
						a[i] = even_number;
						even_sum+=a[i];
						even_number+=2;
					}

					for(int i=n/2;i<n-1;i++){
						a[i] = odd_number;
						odd_sum+=a[i];
						odd_number+=2;
					}

					rem = even_sum - odd_sum;

					if(rem%2!=0){
						a[n-1]=rem;
						System.out.println("YES");

						for(int j=0;j<n;j++){
							System.out.print(a[j]+" ");
						}
						System.out.println("\r");				
						

					}
					else{
						System.out.println("NO");
						continue;
					}

















































				}
				else{
					return;
				}
			}
























































		}
		else{
			return;
		}























	
}}