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.*;
import java.lang.*;
import java.io.*;
public class Main {
	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 tc=Integer.parseInt(br.readLine());
        while(tc-- >0)
        {
        	int n=Integer.parseInt(br.readLine());
        	int[] arr=new int[n];
        	int eve_val=2,odd_val=1;
        	int even_sum=0,odd_sum=0;
        	for(int i=0;i<n/2;i++)
        	{
        		arr[i]=eve_val;
        		even_sum+=arr[i];
        		eve_val+=2;
        	}
        	for(int i=n/2;i<n-1;i++)
        	{
        		arr[i]=odd_val;
        		odd_sum+=arr[i];
        		odd_val+=2;
        	}
        	if(odd_sum==0 || even_sum==0)
        	{
        		bw.write("NO"+"\n");
        		continue;
        	}
        /*	for(int i=0;i<n;i++)
        		{
        			bw.write(arr[i]+" ");
        		}
        		bw.write(even_sum+"\n");
        		bw.write(odd_sum+"\n");*/
        		//bw.write(even_sum-odd_sum+"\n");
        	if((even_sum-odd_sum)%2==1)
        	{
        		arr[n-1]=even_sum-odd_sum;
        		bw.write("YES"+"\n");
        		for(int i=0;i<n;i++)
        		{
        			bw.write(arr[i]+" ");
        		}
        		bw.write("\n");
        		//continue;
        	}
        	else{
        		bw.write("NO"+"\n");
        	}
        }
        bw.flush();
	}
}