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 Cp {//implements Comparable<Cp>{

    public static void main(String[] args) {
        Scanner in =  new Scanner(System.in);
        int t = in.nextInt();
        int n = 2*100000;
        int x = 2;
        int a[] = new int[n/2];
        int b[] = new int[n/2];
        boolean v = true;
        for(int i=0;i<n/2;i++){
            a[i] = x;
            if(v)
                x+=2;
            else
                x+=4;
            v = !v;
        }
        v = true;
        for(int i=0;i<n/2;i++){
            if(v)
                b[i] = a[i]-1;
            else
                b[i] = a[i]+1;
             v = !v;
        }
        while(t-->0){
            n = in.nextInt();
            if((n/2)%2!=0){
                System.out.println("NO");
            }else{
                System.out.println("YES");
                for(int i=0;i<n/2;i++)
                    System.out.print(a[i]+" ");
                for(int i=0;i<n/2;i++)
                    System.out.print(b[i]+" ");
                System.out.println("");
            }
        }
    }
}