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 Bal_Array
{
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-- > 0)
        {
            int n=sc.nextInt();
            int n2=n/2;
            int a[]=new int[n2];
            int b[]=new int[n2];
            int p=2,sum1=0,sum2=0;
            for(int i=0;i<n2;i++)
            {
                a[i]=p;
                sum1=sum1+a[i];
                p=p+2;
            }
            p=1;
            for(int i=0;i<n2;i++)
            {
                b[i]=p;
                sum2=sum2+b[i];
                p=p+2;
            }
            int sum3=0;
            int f=0;
            if(sum1==sum2)
            {
                f=1;
            }
            if(sum1!=sum2)
            {
               sum3=Math.abs(sum1-sum2);
               if(sum3%2==0)
               {
                   b[n2-1]=b[n2-1]+sum3;
                   f=1;
               }
            }
            if(f==1)
            {
                System.out.println("YES");
                for(int i=0;i<n2;i++)
                {
                    System.out.print(a[i]+" ");
                }
                for(int i=0;i<n2;i++)
                {
                    System.out.print(b[i]+" ");
                }
                System.out.println();
            }
            else
                System.out.println("NO");
        }
    }
}