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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;


/**
 *
 * @author Yash Nainsukha
 */
public class Solution {
    public static void main(String[] args){
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        
        int t = sc.nextInt();
        int n = 0, temp, odd = 1;
        int sum = 0;
        for(int i = 0; i < t; i++){
            n = sc.nextInt();
            if(n == 2 || (n/2)%2 != 0){
                System.out.println("NO");
            }else{
                System.out.println("YES");
                sum = 0;
                odd = -1;
                for(int j = 1; j <= n;j++){
                    if(j <= n/2){
                        temp = j*2;
                        sum += temp;
                        System.out.print(temp +" ");
                    }else{
                        if(j < n){
                            odd += 2;
                            sum -= odd;
                            System.out.print(odd +" ");
                        }else{
                            System.out.print(sum +" ");
                        }
                    }
                }
                System.out.println("");
            }
        }
    }
}