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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.io.*;
import java.util.Locale; 
import java.util.*;
import java.io.BufferedOutputStream;
import java.io.BufferedWriter;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.lang.StringBuilder;
	public class Solution{
	    
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }     
	    
	public static void main(String args[])throws IOException
	{
		FastReader sc=new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = sc.nextInt();
		StringBuilder res = new StringBuilder("");
		for(int test = 0; test < t; test++ )
		{
			long n = sc.nextLong();
			if(n%4 != 0)
			    res.append("NO\n");
			 else
			 {
			     res.append("YES\n");
			     StringBuilder s = new StringBuilder("");
			     int countEven = 0, countOdd = 0;
			     for(int i = 2; i <= n; i=i+2)
			     {
			         s.append(Integer.toString(i) + " ");
			         countEven += i;
			     }
			     for(int i = 1;i < (n-1); i=i+2)
			     {
			         s.append(Integer.toString(i) + " ");
			         countOdd += i;
			     }
			     int dif = countEven - countOdd;
			     s.append(Integer.toString(dif));
			     res.append(s + "\n");
			 }
		}
		System.out.println(res);
	}
}