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.util.*;
public class fg
{
    public static void main(String[] args) {
        Scanner in =new Scanner(System.in);
        int p=in.nextInt();
        for (int h=0;h<p;h++)
        {
        ArrayList<Integer> arr=new ArrayList<Integer>();
        arr.add(3);
        arr.add(1);
        arr.add(4);
        arr.add(2);
        int a=in.nextInt();
        if (a==4)
        {
            arr.forEach((n)->System.out.print(n+" "));
          
        }
        else if(a>4)
        {
            for (int i=5;i<a+1;i++)
            {
                for(int j=1;j<arr.size();j++)
                {
                    int d1=Math.abs(i-arr.get(j));
                    int d2=Math.abs(i-arr.get(j-1));
                    if (((d1>=2)&&(d1<=4))&&((d2>=2)&&(d2<=4)))
                    {
                        arr.add(j,i);
                        break;
                    }

                }
            }
            arr.forEach((n)->System.out.print(n+" "));
            
        }
        else System.out.println("-1");

    }
}
}