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.*;
import java.math.BigInteger; 


public class Main {
	public static void main (String[] args)  throws Exception {
	    
	    
	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String testCase = br.readLine();  
        
        for(int i =0;i<Integer.parseInt(testCase);i++)
        {
            String arrSize = br.readLine();
            int n = Integer.parseInt(arrSize);
            
            if(n%4!=0)
            {
                System.out.print("NO");
            }
            else
            {
                int arr[] = new int[n];
                int hLength = n/2; // half Length
                int dhLength = n/4; // double half Length
                
                for(int j = 0;j<hLength;j++)
                {
                    arr[j]=2*j+2;
                }
                System.out.println("YES");
                for(int j=hLength;j<hLength+dhLength;j++)
                {
                    arr[j]=arr[j-hLength]-1;
                }
                
                for(int j=hLength+dhLength;j<n;j++)
                {
                    arr[j]=arr[j-hLength]+1;
                }
                
                for(int j=0;j<n;j++)
                {
                    System.out.print(arr[j]+" ");
                }
            }
            System.out.println();
        }
              
    }
}