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;

public class AZ {

	public static void main(String[] args) 
	{
		Scanner cin= new Scanner(System.in);
		int t=cin.nextInt();
		for (int i = 0; i < t; i++)
		{
			int n=cin.nextInt();
			StringBuilder str= new StringBuilder();
			if(n<4)
			{
				System.out.println("-1");
			}
			else
			{
				str.append(3);
				str.append(" ");
				str.append(1);
				str.append(" ");
				str.append(4);
				str.append(" ");
				str.append(2);
				str.append(" ");
				for (int j = 5; j <=n; j++)
				{
					if(j%2==0)
					{
						str.append(j);
						str.append(" ");
					}
					else
					{
						str.insert(0," ");
						str.insert(0, j);
					}
				}
				System.out.println(str);
				
			}
		}
	}

}
