A permutation of length n is an array p=[p_1,p_2,...,p_n], which contains every integer from 1 to n (inclusive) and, moreover, each number appears exactly once. For example, p=[3,1,4,2,5] is a permutation of length 5.

For a given number n (n ≥ 2), find a permutation p in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between 2 and 4, inclusive. Formally, find such permutation p that 2 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ i < n).

Print any such permutation for the given integer n or determine that it does not exist.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.

Each test case is described by a single line containing an integer n (2 ≤ n ≤ 1000).

Output

Print t lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input


6
10
2
4
6
7
13


Output


9 6 10 8 4 7 3 1 5 2 
-1
3 1 4 2 
5 3 6 2 4 1 
5 1 3 6 2 4 7 
13 9 7 11 8 4 1 3 5 2 6 10 12 
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;



/* Name of the class has to be "Main" only if the class is public. */
public class Main
 
 
{
    static Scanner in = new Scanner(System.in);
    
    public static void solve()
    {
      int n=in.nextInt();
      
      if(n==4)
      {
          System.out.println("2 4 1 3");
      }
   else  if(n>3)
    {
        int k=1;
       
        if(n%2==0)
        {
             for(int i=1;i<=n-4;i=i+2,k=i)
        {
            System.out.print(i+" ");
        }
        System.out.print(k+2+" "+k+" ");
            for(int i=n;i>=2;i=i-2)
        {
            System.out.print(i+" ");
        }
        }
        else
        {
            
            for(int i=1;i<=n;i=i+2)
        {
            System.out.print(i+" ");
        }
         System.out.print(n-3+" "+(n-1)+" ");
            for(int i=n-5;i>=2;i=i-2)
        {
            System.out.print(i+" ");
        } 
        }
        System.out.println();
    }
    else
    System.out.println(-1);
      
      
     
      
    }
    

    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		
		int t=in.nextInt();
		//in.nextLine();
		
		while(t>0)
		{
		    
		   solve();
		    t--;
		}
		
		
	
	//	System.out.println(x);
	}
}
