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 s = new Scanner(System.in);
        String[] ans = { "NO", "YES" };
        int t = s.nextInt();
        int n;
        for (int i = 0; i < t; i++) {
            n = s.nextInt();
            if(n%4 != 0) {
                System.out.println(ans[0]);
                continue;
            }else {
                System.out.println(ans[1]);
                for(int j =2 ;j<=n;j+=2) {
                    System.out.print(j+" ");
                }
                for(int k = 1; k<n-2;k+=2) {
                    System.out.print(k+" ");
                }
                System.out.println(n+n/2-1);
            }
        }
    }
}