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.Scanner;
public class Solution {
	public static void main(String[] args) {
       Scanner sc= new Scanner (System.in);
       int t =sc.nextInt();
       for(int j = 0;j<t;j++)
       {
    	    int n  =sc.nextInt();
    	    if((n/2)%2==1)
    	    	System.out.println("NO");
    	    else 
    	    {   
    	    	System.out.println("YES");
    	    	int div =n/2;
    	    	int sume =0;
    	    	int  q =2;
    	    	for(int i =0;i<div;i++){
    	    		System.out.print(q+" ");
    	    		sume +=q;
    	    		q=q+2;
    	    	}
    	    	 q =1;
    	    	 int sumo =0;
    	    	for(int i =0;i<div-1;i++)
    	    	{ 
    	    		System.out.print(q+" ");
    	    		sumo +=q;
    	    		q=q+2;
    	    	}
    	    	System.out.print(sume-sumo);
    	    }
    	    System.out.println();
    	   
       }
		
    }
	
}