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:
/*package whatever //do not write package name here */

import java.io.*;

public class GFG {
	public static void main (String[] args) throws Exception{
		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)
		    System.out.println("NO");
		    else{
		         System.out.println("YES");
		         int even = 2;
		         int odd = 1;
		        for(int i=0;i<n/2;i++)
		        {
		            System.out.print(even+" ");
		            even+=2;
		        }
		        
		        
		        
		        for(int i=0;i<n/2;i++)
		        {
		      
		      if(i == (n/2)-1 )
		       System.out.print((odd+(n/2))+" ");
		       else
		        System.out.print(odd+" ");
		           odd+=2; 
		        }
		        System.out.println("");
		    }
		}
	}
}