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.*;
import javafx.util.Pair;
import java.util.Comparator;


public class Main
{
    public static void Even(int n)
    {
        int N=n-1;
        n+=2;
        while (n!=2)
        {
            n-=2;
            System.out.print(n+" ");
        }
        n+=3;
        System.out.print(n+" ");
        n-=4;
        System.out.print(n+" ");
        n+=2;
        System.out.print(n+" ");
        n+=4;
        System.out.print(n+" ");
        while (n!=N)
        {
            n+=2;
            System.out.print(n+" ");
        }
    }

    public static void Odd(int n)
    {
        int N=n-1;
        n+=2;
        while (n!=1)
        {
            n-=2;
            System.out.print(n+" ");
        }
        n+=3;
        System.out.print(n+" ");
        n-=2;
        System.out.print(n+" ");
        n+=4;
        System.out.print(n+" ");
        while (n!=N)
        {
            n+=2;
            System.out.print(n+" ");
        }
    }


    public static void main(String[] args)
    {
        Scanner in=new Scanner(System.in);
        int t;
        t=in.nextInt();
        while (t-- > 0)
        {
            int n=in.nextInt();
            if (n<4)
            {
                System.out.println(-1);
            }
            else if (n==4)
            {
                System.out.println("3 1 4 2");
            }
            else if (n==5)
            {
                System.out.println("1 4 2 5 3");
            }
            else if (n==6)
            {
                System.out.println("1 3 5 2 4 6");
            }
            else
            {
                if (n%2==0) Even(n);
                else Odd(n);
            }

        }
    }
}