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.*;
public class R633D3B {

	public static void main(String[] args) throws Exception{
		int num = 998244353;
		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		int t = Integer.parseInt(bf.readLine());
 		
 		for(int i = 0;i<t;i++){
 			int a = Integer.parseInt(bf.readLine());
 			if (a%4 != 0){
 				System.out.println("NO");
 			}
 			else{
 				System.out.println("YES");
 				for(int j = 0;j<a/2;j++){
 					System.out.print(2*(j+1) + " ");
 					
 				}
 				for(int j = 0;j<a/2;j++){
 					if (j == a/2-1){
 						if (j%2 == 0)
 	 						System.out.println((3*a/2-1));
 	 					else
 	 						System.out.println((3*a/2-1));
 					}
 					else{
	 					if (j%2 == 0)
	 						System.out.print((2*j+1) + " ");
	 					else
	 						System.out.print((2*j+1) + " ");
	 					}
 				}
 				
 			}
 			
 		}
 		
 		
	}

}