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.*;
// scanner.nextInt();
// gatogari.
public class Solution {
    public static void main(String[] args) {       

        Scanner scanner = new Scanner(System.in);
        int test_case = scanner.nextInt();
            
            for(int z = 0; z < test_case; ++z)
            {
                int n = scanner.nextInt();
                if(n == 2 || n == 3)
                {
                    System.out.println(-1);
                }
                else if(n == 4) System.out.println("3 1 4 2");
                else if(n == 5) System.out.println("5 3 1 4 2");
                else
                {
                    int k = n;
                    if(n % 2 == 0) --k;
                    String t = "";
                    for(; k > 0; --k)
                    {
                       t += k + " ";
                        --k;
                    }
                    t += "4 2 6 ";
                    for(int i = 8; i <= n; ++i)
                    {
                        t += i + " ";
                        ++i;
                    }
                    System.out.println(t);
                    //3 1 4 2
                    //7 5 3 1 4 2 6 8 10..
                }
		
            }
                    
    }
}

