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.*;
import java.util.*;

public class B_636 {

	public static void main(String[] args)throws IOException {
		
		BufferedReader ob=new BufferedReader(new InputStreamReader(System.in));
		StringBuffer sb=new StringBuffer();
		
		int test=Integer.parseInt(ob.readLine());
		while(test-->0)
		{
			int n=Integer.parseInt(ob.readLine());
			if(n%4!=0)
			{
				sb.append("NO\n");
				continue;
			}
			sb.append("YES\n");
			int l=0;
			int no=2;
			int sum=0;
			int ans[]=new int[n];
			int i=0;
			while(l<n/2)
			{
				ans[i]=no;
				no+=2;
				sum+=no;
				l++;
				i++;
			}
			int sum2=0;
			no=1;
			i=n/2;
			while(l<n)
			{
				ans[i]=no;
				no+=2;
				sum2+=no;
				l++;
				i++;
			}
			if(sum!=sum2)
			{
				ans[n-1]+=Math.abs(sum-sum2);
			}
			for(int x : ans)
				sb.append(x+" ");
			sb.append("\n");
		}
		System.out.println(sb);

	}

}