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.Scanner;
import java.util.Arrays;
import java.lang.Math;
import java.math.BigInteger;
import java.util.Collections;
import java.util.HashMap;
public class balanced_array{
    public static void main(String[] args){
      Scanner sc= new Scanner(System.in);
      int t=sc.nextInt();
      for(int j=0;j<t;j++){
      int k=1,a=0,cnt=0,n=sc.nextInt();
      if((n%2==0)&&((n/2)%2==0)){
         System.out.println("YES");
         int[] ar=new int[n];
         for(int i=0;i<n;i++){
            if(i<n/2){
               ar[i]=2*(i+1);
               cnt=cnt+ar[i];
            }
            else if(i!=n-1){
               ar[i]=k;
               k=k+2;
               a=a+ar[i];
            }
            else ar[i]=cnt-a;

            System.out.print(ar[i]+" ");
         }   
      }
      else System.out.print("NO");
      System.out.println("");
      }
   }       
}