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 code
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
          int n=sc.nextInt();
          int a[]=new int[n];
          int l=2,sum=0,sum1=0;
          for(int i=0;i<n/2;i++)
          {
              a[i]=l;
             l=l+2;
             sum+=a[i];
          }
          l=1;
          for(int i=n/2;i<n;i++)
          {
              a[i]=l;
              l=l+2;
              sum1+=a[i];
          }
          if(sum>sum1)
          {
              int m=sum-sum1;
                  a[n-1]+=m;
                  sum1+=m;
                  if(a[n-1]%2!=0 && sum==sum1)
                  {
                  System.out.println("YES");
                  for(int i=0;i<n;i++)
                  {
                      System.out.print(a[i]+" ");
                  }
                  System.out.println();
                  }
                  else
                  {
                      System.out.println("NO");
                  }
              }
          else
          {
              System.out.println("NO");
          }
        }
    }
}