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 B1343 {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int cases = scanner.nextInt();
		for(int i = 0; i < cases; i++){
			int length = scanner.nextInt();
			if(length % 4 == 0) {
				System.out.println("YES");
				int[] even = new int[length / 2];
				int[] odd = new int[length / 2];
				int sum = 0;
				for(int j  = 0; j < even.length - 1; j ++){
					even[j] = (j + 1) * 2;
					odd[j] = even[j] - 1;
				}
				sum = even.length - 1;
				even[even.length - 1] = even[even.length - 2] + 2;
				sum += even[even.length - 1];
				odd[odd.length - 1] = sum;
				for(int j = 0; j < even.length; j++) 
					System.out.print(even[j] + " ");
				for(int j = 0; j < odd.length; j++) 
					System.out.print(odd[j] + " ");
				System.out.println();
			}
			else
				System.out.println("NO");
		}
	}
}