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.io.*;
import java.lang.*;

public class z{
    public static void main(String[] args) throws IOException {
        Scanner s = new Scanner(System.in);
       int n = s.nextInt();
       while(n-->0){
           int a = s.nextInt();
           if((a/2)%2!=0){
               System.out.println("NO");
           }else{
               System.out.println("YES");
               int x = a/2;
               int b = a/2;
               int y = a/2-1;
               while(x>0){
                   System.out.print(2*x + " ");
                   x--;
               }
               int sum = b*(b+1);
               
               int oddsum = 0;
               while(y-->0){
                   int odd = y*2+1;
                   System.out.print(odd + " ");
                   oddsum = oddsum+odd;
               }
               System.out.print(sum-oddsum);
               System.out.println("");
           }
       }
       
       
       

    }
       
      
   
}