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.io.*;
public class balanced
{
	public static void main(String args[])throws IOException
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		
		int t=Integer.parseInt(br.readLine());
		while(t-->0)
		{
					int n=Integer.parseInt(br.readLine());

					
					if(n%4==0)
					{
						int[] a=new int[n];
						System.out.println("YES");
						for(int i=1,j=0,k=n/2;i<=n;i++)
						{
							if(i%2!=0)
							{
								if(i==n-1)
								{
								a[k]=i+n/2;
								}
								else{
								a[k]=i;
								}
								k++;
							}
							if(i%2==0)
							{
								a[j]=i;
								j++;
							}
							
						}
							for(int i=0;i<n;i++)
			{
				System.out.print(a[i]+" ");
			}
							
						
						
					}
					else
					{
						System.out.println("NO");
					}
			
			
		}
	}
}