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.lang.*;
import java.util.*;
public class Codeforces
{
	public static void main(String[] args) throws IOException{
		BufferedReader  br=new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
		int t=Integer.parseInt(br.readLine());
		while(t-->0)
		{
		    int n=Integer.parseInt(br.readLine());
		    int r=n/2;
		    if(r%2==1)
		    {
		        bw.write("NO\n");
		    }
		    else
		    {
		        bw.write("YES\n");
		        int k=2;
		        int sum=0;
		        for(int i=0;i<r;i++)
		        {
		            bw.write(k+" ");
		            sum+=k;
		            k=k+2;
		        }
		        k=1;
		        int prev=0;
		        for(int i=1;i<r;i++)
		        {
		            prev+=k;
		            bw.write(k+" ");
		            k=k+2;
		        }
		        bw.write((sum-prev)+"\n");
		    }
		}
		bw.flush();
	}
}