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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
 
public class Solution 
{ 
    
    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){
                  System.out.println("YES");
                  int sum=0;int[]a=new int[n];
                  int k=2;
                  for(int i=0;i<n/2;i++ ){
                      a[i]=k;k+=2;
                      sum+=a[i];
                  }k=1;
                  for(int i=n/2;i<n-1;i++){
                      a[i]=k;k+=2;
                      sum-=a[i];
                  }
                  a[n-1]=sum;
                  for(int i=0;i<n;i++){
                      System.out.print(a[i]+" ");
                  }
                  System.out.println();
              }else{
                  System.out.println("NO");
              }
                 
                //   int[]x=new int[n];
                //   int[]y=new int[n];
                //   for(int j=0;j<n;j++)
                //   {    StringTokenizer sa=new StringTokenizer(br.readLine());
                //         x[j] = Integer.parseInt(sa.nextToken());
                //       y[j]=Integer.parseInt(sa.nextToken());
            
                //   }
                 
                   
                  
            }     
                
                     
    }
    }