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.Arrays;
import java.util.Scanner;

public class Test{
	public static void main(String[] args) {
		
		Scanner input = new Scanner(System.in);
		int n = input.nextInt(), num;
		int[] a;
				
		for(int i = 0; i < n; i++) {
			
			num = input.nextInt();
			a = new int[num];
			
			if(num / 2 % 2 == 0) {	
				System.out.println("YES");
				for(int j = 0; j < num; j++) {
					if(j < num / 2) {
						a[j] = 2 * (j + 1);
						System.out.print(a[j] + " ");
					} else {
						if (j == num - 1) a[j] = a[num / 2 - 1] + num / 2 - 1;
						else a[j] = (int) (a[Math.abs(num / 2  - j)] - 1);
						System.out.print(a[j] + " ");
					}					
				}	
			} else System.out.println("NO");			
		}	
	}
}