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.io.*;
	public class BalancedArray{
		public static void main(String[] args)throws IOException{
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			int t = Integer.parseInt(br.readLine());
			while(t-->0)
			{
			int n = Integer.parseInt(br.readLine());
			if(n%4==0)
			{
				System.out.println("YES");
				int p = 2;
				for(int i = 0 ; i < n/2 ; i++)
				{
					System.out.print(p+" ");
					p=p+2;
				}
				p = 1;
				for(int i = 0 ; i < (n/2)-1 ; i++)
				{
					System.out.print(p+" ");
					p=p+2;
				}
				int m = 0,s=-1;
				while(m!=n)
				{
					m = m + 4;
					s = s +2;
				}
				System.out.println(n+s );
			}
			else
			{
				System.out.println("NO");
			}
		}
	}
	}