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.io.*;
public class main
{
 static Hashtable<Integer ,Integer>hash=new Hashtable<>();
 static int dp[][];
 static int ans[]=new int[2001];
	public static void main(String args[]) throws java.lang.Exception
	{
	  
 	BufferedReader inp = new BufferedReader (new InputStreamReader(System.in));
int t=Integer.parseInt(inp.readLine());
while(t-->0)
{
   // int y=Integer.parseInt(inp.readLine());
   String h[]=inp.readLine().split(" ");
   int k=Integer.parseInt(h[1]);
   String hh[]=inp.readLine().split(" ");
   int cnt[]=new int[2*k+2];
   int pre[]=new int[2*k+2];
   int n=hh.length;
   for(int i=0;i<hh.length/2;i++)
   {
   	cnt[Integer.parseInt(hh[i])+Integer.parseInt(hh[n-1-i])]+=1;
   	pre[Math.min(Integer.parseInt(hh[i]),Integer.parseInt(hh[n-1-i]))+1]+=1;
   	pre[Math.max(Integer.parseInt(hh[i]),Integer.parseInt(hh[n-1-i]))+k+1]-=1;
   }
   int min=n-pre[0]-cnt[0];
   for(int i=1;i<pre.length;i++)
   {
   	pre[i]+=pre[i-1];
   	min=Math.min(n-pre[i]-cnt[i],min);
   }
   System.out.println(min);
   // System.out.println(min);


}
	   
	   
	}

}

  class Pair
  {
     String a;
     int b;
     Pair(String c , int d){a=c;b=d;}
  }