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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class Solution {

	public static void main(String[] args) {
		
	//  BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
	   Scanner sc=new Scanner(System.in);
	   int t=sc.nextInt();
	   while(t-->0) {
		  int n=sc.nextInt();
		  int v=n/2;
		  if(v%2!=0)
			  System.out.println("NO");
		  else
		  {
			  System.out.println("YES");
			  int even=2;
			  int odd=1;
			  int s=n/2;
			  int evensum=0;
			  while(s>0) {
				  System.out.print(even+" ");
				  evensum+=even;
				  even+=2;
				  s--;
			  }
			  
			  s=n/2;
			  int oddsum=0;
			  while(s>1) {
				  System.out.print(odd+" ");
				  oddsum+=odd;
				  odd+=2;
				  s--;
			  }
			  
			  int g=evensum-oddsum;
			  System.out.println(g);
		  }
	   }
	}    
	  
	
 }