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.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		while(t>0){
		    int n=in.nextInt();
		    int[] a=new int[n];
		    if((n/2)%2==0&&n!=2){
		        int e=2;int es=0;int o=1;int os=0;int count=0;
		        for(int i=0;count<n/2;i++){
		            a[i]=e;
		            es+=e;
		            e+=2;
		            count++;
		        }
		        count=0;
		        for(int i=n/2;count<n/2-1;i++){
		            a[i]=o;
		            os+=o;
		            o+=2;
		            count++;
		        }
		        a[n-1]=es-os;
		        System.out.println("YES");
		        for(int i=0;i<n;i++)
		        System.out.print(a[i]+" ");
		        
		        System.out.println();
		    }else
		    System.out.println("NO");
		    
		    t--;
		}
	}
}