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.*;

public class ss
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        
        for(int i=0;i<t;i++)
        {
           long n=sc.nextLong();
           if(n==2)
           System.out.println("NO");
           else if((n/2)%2==1)
            System.out.println("NO");
           else
            {
                System.out.println("YES");
                long k=0,s1=0,s2=0;
                long l=0;
                long p=n/2;
                for(long j=0;j<n/2;j++)
                {
                	s1+=2+k;
                    System.out.print(2+k+" ");
                    k=k+2;
                }
                for(long j=p;j<n-1;j++)
                {
                	s2+=1+l;
                    System.out.print(1+l+" ");
                    l=l+2;
                }
                //System.out.println("s1: "+s1+" s2: "+(s2+(s1-s2)));
                System.out.print(s1-s2);
                System.out.println();
            }
        }
    }
}