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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		try {
		    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("YES");
		            int ev_sum = 0,odd_sum = 0;
		            for ( int i = 2 ; i <=n ; i+=2 ){
		                ev_sum+=i;
		                System.out.print(i+" ");
		                
		            }
		            for ( int i = 1 ; i<n-1 ; i+=2 ){
		                odd_sum+=i;
		                System.out.print(i+" ");
		            }
		            System.out.print(Math.abs(ev_sum-odd_sum)+" ");
		          
		            System.out.println("");      
		        }else
		            System.out.println("NO");
		        
		    }
		} catch(Exception e) {
		return;}
	}
}