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 Main {

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int T = Integer.parseInt(sc.next());
        StringBuilder sb = new StringBuilder();
        for(int t = 0; t < T; t++){
            int n = Integer.parseInt(sc.next());
            int n2 = n/2;
            int k = Integer.parseInt(sc.next());
            int[] a = new int[n];
            for(int i = 0; i < n; i++){
                a[i] = Integer.parseInt(sc.next());
            }
            int[] e = new int[k*2+2];
            for(int i = 1; i <= n2; i++){
                int c = a[i-1];
                int d = a[n-i];
                if(c > d){
                    c += k;
                    d += 1;
                    e[d]++;
                    e[c+1]--;
                }else{
                    c += 1;
                    d += k;
                    e[c]++;
                    e[d+1]--;
                }
            }
            for(int i = 1; i <= k*2; i++){
                e[i] += e[i-1];
            }
            int[] f = new int[k*2+1];
            for(int i = 1; i <= n2; i++){
                int c = a[i-1] + a[n-i];
                f[c]++;
            }
            int min = Integer.MAX_VALUE;
            for(int i = 1; i <= n2; i++){
                int c = a[i-1] + a[n-i];
                min = Math.min(min, n2 - f[c] + (n2 - e[c]));
            }
            min = Math.min(min, n2);
            sb.append(min).append(System.lineSeparator());
        }
        System.out.print(sb);
    }
}