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;
import java.util.*;

public class Helloworld {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int input = s.nextInt();
        while (input-- > 0) {
            int n = s.nextInt();
            int []ar=new int [n];
            if(n/2==2){
                System.out.println("YES");
                System.out.println("2 4 1 5");
            }
            else if ((n / 2) % 2 == 1) {
                System.out.println("NO");
            }
            else{
            int sum=0;
            for(int i=0,a=2;i<n/2;i++,a+=2){
                ar[i]=a;
                sum+=ar[i];
            }
            
            int sum1=0;
            for(int i=n/2,a=1;i<n-1;i++,a+=2){
            ar[i]=a;
            sum1+=ar[i];
            }
            ar[n-1]=sum-sum1;
            System.out.println("YES");
            for(int i=0;i<n;i++){
                    System.out.print(ar[i]+" ");
                    if(i==n-1)
                        System.out.println("");
            }
            }
            
    }
}
}