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.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class C{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        long mod=1000000007l;
        int cases=sc.nextInt();

        while(cases>0)
        {
            cases--;
            int x=sc.nextInt();
            if(x>=4) {
                int arr[] = new int[x];
                int ind = 0;
                int c = 1;
                for (int j = 0; j < (x + 1) / 2; j++) {
                    arr[j] = c;
                    c = c + 2;
                    ind++;
                }
                int copy = ind;
                c--;
                if (x % 2 == 0) {
                    c = x;
                } else {
                    c = x - 1;
                    ind=ind+2;
                }
                for (int j = copy; j < x; j++) {
                    arr[j] = c;
                    c = c - 2;
                }


                ind--;
                ind--;
                int temp = arr[ind];
                arr[ind] = arr[ind + 1];
                arr[ind+1] = temp;

                StringBuilder ans=new StringBuilder();
                for(int j=0;j<x;j++)
                {
                    ans.append(arr[j]+" ");
                }
                System.out.println(ans);
            }
            else
            {
                System.out.println(-1);
            }



        }

    }
}
