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 Main {
	static BufferedReader br;
	static PrintWriter pr;
	static int cin() throws Exception
	{
		return Integer.valueOf(br.readLine());
	}
	static int[] split() throws Exception
	{
		String[] cmd=br.readLine().split(" ");
		int[] ans=new int[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Integer.valueOf(cmd[i]);
		}
		return ans;
	}
	static long[] splitL() throws IOException
	{
		String[] cmd=br.readLine().split(" ");
		long[] ans=new long[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Long.valueOf(cmd[i]);
		}
		return ans;
	}
	static int sum(long n)
	{
		int ans=0;
		while(n!=0)
		{
			ans=ans+(int)(n%10);
			n=n/10;
		}
		return ans;
	}
	static int gcd(int x,int y)
	{
		if(x==0)
			return y;
		if(y==0)
			return x;
		if(x>y)
			return gcd(x%y,y);
		else
			return gcd(x,y%x);
	}
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		br=new BufferedReader(new InputStreamReader(System.in));
		pr=new PrintWriter(new OutputStreamWriter(System.out));
		int cases=cin();
		while(cases!=0)
		{
			cases--;
			int[]ar=split();
			int n=ar[0];
			int k=ar[1];
			int[]arr=split();
			int[]cnt=new int[2*k+1];
			int[]pre=new int[2*k+1];
			for(int i=0;i<n/2;i++)
			{
				int x=arr[i];
				int y=arr[n-i-1];
				cnt[x+y]++;
				int l=Math.min(x, y)+1;
				int r=Math.max(x, y)+k;
				pre[l]+=1;
				if(r+1<=2*k)
				pre[r+1]-=1;
			}
			int s=0;
			for(int i=0;i<=2*k;i++)
			{
				s+=pre[i];
				pre[i]=s;
			}
			int ans=100000000;
			for(int i=2;i<=2*k;i++)
			{
				ans=Math.min(ans,pre[i]-cnt[i]+2*((n/2)-pre[i]));
			}
			System.out.println(ans);
		}
	}
}