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 Main1343B {
	public static void main(String args[])
	{
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		int n,sum,max;
		for(int i=0;i<t;i++)
		{
			n=in.nextInt();
			if((n/2)%2!=0) System.out.println("NO");
			else 
			{
				max=0;
				sum=0;
				System.out.println("YES");
				for(int j=0;j<n/2;j++) 
					{
						System.out.print((j+1)*2+" ");
						max+=(j+1)*2;
					}
				for(int j=0;j<n/2;j++) 
				{
					if(j==n/2-1) System.out.println(max-sum);
					else 
						{
							System.out.print((j*2+1)+" ");
							sum+=j*2+1;
						}
				}
			}
		}
		in.close();
	}
}