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.*;
import java.lang.*;
import java.io.*;
public class Solution
{  

    public static void main (String[] args) throws java.lang.Exception
    {
       Scanner sc=new Scanner(System.in);
      int T=sc.nextInt();
      for(int z=0;z<T;z++){
          int n=sc.nextInt();   
          int t=n/2;
          if(t%2==0){
             int b[]=new int[n];
             int esum=0,osum=0,ec=2,oc=1;
             for(int i=0;i<n;i++)
             {
                if(i<n/2)
                {
                  b[i]=ec;
                  esum+=b[i];
                  ec+=2;
                } 
                else{
                    if(i==n-1)
                    {
                        //System.out.println("esum="+esum+"   osum= "+osum);
                       b[i]=esum-osum;
                    }
                else{
                     b[i]=oc;
                   osum+=b[i];
                   oc+=2;
                }
                }
             }
             System.out.println("YES");
            for(int i=0;i<n;i++)
            {
                 System.out.print(b[i]+" ");
            }
            System.out.println();
          }
          else{
              System.out.println("NO");
          }
      }



}
}