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 BalancedArray {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int q;
        q = input.nextInt();
        for (int j = 0; j < q; j++) {
            int n, s = 2, n1, s1 = 1, sum = 0, sum1 = 0;
            n = input.nextInt();
            int[] a = new int[n];

            for (int i = 0; i < n / 2; i++) {               
                    a[i] = s;                
                sum = sum + a[i];
                s = s + 2;
            }
            n1 = n / 2;           
            for (int i = n/2; i < n-1; i++) {
                  a[i] = s1;
                  sum1=sum1+a[i];
                  s1=s1+2;
                 
            }
            a[n-1]=sum-sum1;
                  
                if(a[n-1]%2!=0 && a[n-2]<a[n-1]){
                    System.out.println("yes");
                     for (int i = 0; i < n; i++){
                          System.out.print(a[i]+" ");
                     }
                     System.out.println();
                }else{
                      System.out.println("no");
                }
            
            
            
        }
    }
}