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 scan = new Scanner(System.in);
        int t = scan.nextInt();
        int res[][] = new int[t][];
        for (int i = 0 ; i < t ; i++) {
            int n = scan.nextInt();
            if (n % 4 == 0) {
                res[i] = new int[n];
                int num1 = 2, num2 = 1;
                for (int j = 0 ; j < n/2 ; j++, num1+=2, num2+=2) {
                    res[i][j] = num1;
                    res[i][j + (n/2)] = num2;
                }
                int total = 0;
                for (int j = 0 ; j < n/2 ; j++) {
                    total += res[i][j];
                }
                for (int j = n/2 ; j < n-1 ; j++) {
                    total -= res[i][j];
                }
                res[i][n-1] = total;
            }
        }
        for (int[] s : res) {
            if (s != null) {
                System.out.println("YES");
                for (int x : s) System.out.print(x + " ");
                System.out.println();
            }
            else System.out.println("NO");
        }
    }
}