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 

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

/**
 *
 * @author HP
 */
public class PermutationCodef {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t= Integer.parseInt(br.readLine());
        List<Integer> list= new ArrayList<Integer>();
        int temp=0;
        
        
        
        
        while(t-- >0)
                {
                    
                    
                    int n= Integer.parseInt(br.readLine());
                    int arr[]= new int[n];
                    int count=0;
                    int a=n;
                    int j=0;
                    
                    
                    
                    
                    if(n<4)
                    {
                        System.out.println("-1");
                    }
                    
                    else
                    {
                        
                    
                    
                    
                    
                    for(int i=0;i<n;i++)
                    {
                        arr[i]= i+1;
                    }
                    
                    for(int i=0;i<n;i++)
                    {
                        
                        if(a%2==1)
                        {
                            arr[j]=a;
                            j++;
                            
                        }
                        
                        a--;
                        
                    }
                    
                   arr[j]=4;
                   j++;
                   arr[j]=2;
                   j++;
                   
                   for(int i=6;i<n;i++)
                   {
                       
                       if(i%2==0)
                       {
                           arr[j]=i;
                           j++;
                       }
                       
                   }
                   
                   
                   for(int i=0;i<n;i++)
                   {
                       
                       System.out.print(arr[i]+" ");
                   }
                   
                        System.out.println("");
                        //j=0;
                        
                    
                    
                    
                    
                    
                    
                    
                    } 
}
    
}
    

}