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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
public class BalancedArray
{
  
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc = new Scanner(System.in);
	    int t= sc.nextInt();
	    for(int j=0;j<t;j++)
	    {
	      int n = sc.nextInt();
        int arr[] = new int[n];
        if((n/2)%2==1)
        {
          System.out.println("NO");
        }
        else
        {
          int even = 2, odd = 1;
          System.out.println("YES");
          for(int i=0;i<n/2;i++)
          {
            arr[i] = even;
            even = even + 2;
            arr[n/2+i] = odd;
            odd = odd + 2;
          }
          arr[n-1] = arr[n-1]+n/2;
          for(int i=0;i<n;i++)
          {
            System.out.print(arr[i] + " ");
          }
        }
        
        
	    }
	}
}