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.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		sc.nextLine();
		while(n-->0) {
			int k=sc.nextInt();
			int[] a=new int[k+1];
			if(k%4!=0) {
				System.out.println("NO");
			}
			else {
				int j=2;
				for(int i=1;i<=k/2;i++) {
					a[i]=j;
					j+=2;
				}
				j=1;
				for(int i=k/2+1;i<=k;i++) {
					if(i==k)
						a[i]=k/2+a[k/2]-1;
					else {
						a[i]=j;
						j+=2;
					}
						
				}
				System.out.println("YES");
				for(int i=1;i<=k;i++) {
					System.out.print(a[i]+" ");
				}
				System.out.printf("\n");
			}
		}
		
	}

}