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.*;
import java.util.*;
public class a
{
    public static void main(String ar[])
    {
        Scanner sc=new Scanner(System.in);
        //System.out.println();
        int t=0,i,j;
        t=sc.nextInt();
        StringBuffer sbf=new StringBuffer();
        while(t-->0)
        {
            int n=sc.nextInt();
            if(n<4)
            {
                sbf.append("-1\n");
                continue;
            }
            int a[]=new int[n];
            int num=n;
            int total=0;
            int in=0;
            while(total<n-4){
                a[in]=num;
                num--;
                total++;
                if(total==n-4)
                break;
                a[n-1-in]=num;
                num--;
                total++;
                in++;
            }
            for(i=0;i<n;i++)
            {
                if(a[i]!=0)
                sbf.append(a[i]+" ");
                else
                {
                    sbf.append("3 1 4 2 ");
                    i=i+3;
                }
            }
            sbf.append("\n");
        }
        System.out.println(sbf);
    }
}