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.*;
public class JavaApplication148 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc=new Scanner(System.in);
     int t=sc.nextInt();
   while(t--!=0){
       int n=sc.nextInt();
       int a[]=new int[n];
       if(n%4==0)
       {
           int x=-1;
           int temp=4;
           for(int i=0;i<n/2;i++)
           {
               a[i]=temp;
               temp=temp+4;
           }
           for(int i=n/2;i<n;i++)
           {
               if(x==-1)
               {
                   a[i]=a[i-n/2]+x;
                   x=1;
               }
               else
               {
                    a[i]=a[i-n/2]+x;
                   x=-1;
               }
               
           }
           System.out.println("YES");
           for(int i=0;i<n;i++)
           {
               System.out.print(a[i]+" ");
           }
           System.out.println();
           
       }
       else
           System.out.println("NO");
               
     
   }
      
       
        
    }
    
}