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 balanced_array{


    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int [] T ;
        int [] s = new int[n];
        for(int i=0;i<n;i++){
             s[i] = scan.nextInt();
        }
        for(int i=0;i<n;i++){
            if(sum(s[i])%2!=0)
                System.out.println("NO");
            else{
                System.out.println("YES");
                T = arr(s[i]);
                for(int j=0;j<T.length;j++)
                    System.out.print(T[j] + " ");
                System.out.println();
            } 
              




        }
        scan.close();
    }
    public static int sum(int t){
        if(t==0)
            return 0;

        return t + sum(t-1);

    }
    public static int[] arr(int t){
        int [] T = new int[t];
        for(int i=0;i<T.length/2; i++)
            T[i]=(i+1)*2;
        for(int i=0;i<T.length/2;i++)
            T[i + T.length/2]= i*2 +1;
            
         T[t-1]=T[t-1]+T.length/2;   
        return T;
    
}
}