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.*;
public class Soltion {
    
     static public boolean isPowerOfTwo (int x) 
    { 
     
        return x!=0 && ((x&(x-1)) == 0); 
          
    } 
    
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      int t=sc.nextInt();
      for(int id=0;id<t;id++)
      {
          int n=sc.nextInt();
         int[] ans=new int[n];
         int sum1=0;
         int sum2=0;
         int k=2;
         for(int i=0;i<n/2;i++)
         {
             ans[i]=k;
             k+=2;
             sum1+=ans[i];
         }
         int l=1;
         for(int i=n/2;i<n-1;i++)
         {
             ans[i]=l;
             l+=2;
             sum2+=ans[i];
         }
         ans[n-1]=sum1-sum2;
         if(ans[n-1]%2!=0){
         System.out.println("YES");
         for(int i=0;i<n;i++)
         {
             System.out.print(ans[i]+" ");
         }
         System.out.println();
         }
         else
         {
             System.out.println("NO");
         }

      }
    }
}