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.*;

public class Solution {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
		StringBuilder result = new StringBuilder();
		for(int i = 0; i < t; i++) {
			int n = scan.nextInt();
			if((n/2)%2==0) {
				result.append("YES\n");
				int temp1 = 2;
				int temp2 = 2;
				boolean inc = true;
				for(int k = 0; k < n; k++) {
					if(k < (n/2)) {
						result.append(temp1 + " ");
						temp1 += 4;
					} else {
						if(inc) temp2--; else temp2++;
						result.append(temp2 + " ");
						if(inc) temp2 += 5; else temp2 += 3;
						inc = !inc;
					}
				}
			} else {
				result.append("NO");
			}
			result.append("\n");
		}
		System.out.println(result);
    }
}