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 Codechef
{
   public static void main (String[] args) throws java.lang.Exception
	{
	    
// -----------------------------Fast IO using BufferedReader-----------------------------------------------------------------	    

// 		 BufferedReader br = new BufferedReader( 
//                               new InputStreamReader(System.in)); 
  
//         StringTokenizer st = new StringTokenizer(br.readLine());
//          PrintWriter out = new PrintWriter(System.out); 
//         int T = Integer.parseInt(st.nextToken()); 
        
// ----------------------------------------------------------------------------------------------------------	    
    Scanner sc=new Scanner(System.in); 
    int T=sc.nextInt();
		while(T-- >0)
		{
		  List<Integer> list=new ArrayList<>();
          int N=sc.nextInt();
		  if(N<4)
		  System.out.println(-1);
		  else
		  {
		      int boo=0;
		  if(N%2==0)
		    list.add(N-1);
		   else
		    list.add(N);
		    
		    int j=list.get(0);
		    while(j!=1)
		    {
		        j=j-2;
		        list.add(j);
		    }
		    
		    list.add(4);
		    list.add(2);
		    if(N>5)
		    {
		    int k=6;
		    list.add(6);
		    if(N%2==0)
		    {
		    while(k!=N)
		    {
		        k+=2;
		        list.add(k);
		    }
		    }
		    else
		    {
		        while(k!=N-1)
		    {
		        k+=2;
		        list.add(k);
		    }
		    }
		    }
		    
		        for(int i=0;i<list.size();i++)
		        System.out.print(list.get(i)+" ");
		        System.out.println();
		  }
		    
		      
		}
// 		out.close();   
	}
}
