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 java.lang.Math;

public class Solution
{
    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);

        int numTC = sc.nextInt();

        for (int i = 0; i < numTC; i++)
        {
            int num = sc.nextInt();

            if (num == 2 || num == 3)
            {
                System.out.println("-1");
                continue;
            }

            if (num == 4)
            {
                System.out.println("3 1 4 2");
                continue;
            }

            ArrayList<Integer> list = new ArrayList<>();

            for (int j = 1; j <= num; j+=2)
            {
                list.add(j);
            }

            if (num % 2 == 0)
            {
               for (int j = num - 4; j >= 2; j -=2)
               {
                   list.add(j);
               }
            }
            else
            {
                for (int j = num - 3; j >= 2; j -=2)
                {
                    list.add(j);
                }
            }

            if (num % 2 == 0)
            {
                if (num > 4)
                {
                    list.add(list.size() / 2 + 2, num - 2);
                }
                else
                {
                    list.add(0, num - 2);
                }
            }
            else
            {
                if (num > 4)
                {
                    list.add(list.size() / 2 + 2, num - 1);
                }
                else
                {
                    list.add(0, num - 1);
                }
            }

            if (num % 2 == 0)
            {
                list.add(list.size() / 2 + 2, num);
            }

            for (int j = 0; j < list.size(); j++)
            {
                System.out.print(list.get(j) + " ");
            }

            System.out.println("");
        }

    }
}