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.*;
import java.util.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class CodeF
{
	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)
				out.println("NO");
				
			else
			{
				out.println("YES");
				int i=0;
				for(i=2;i<=n;i+=2)
					out.print(i+" ");
				for(i=1;i<n-1;i+=2)
					out.print(i+" ");
								
				out.print(i+(n/2));
				out.println();
			}
			
			
		}
	  		 
	}
}