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.*;
public class Main1 {

	public static void main(String[] args) {
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		while(t!=0)
		{
			int n=s.nextInt();
			if(n<=3)
			{
				System.out.println("-1");
			}
			else
			{
				int x=0;
				LinkedList<Integer> ll=new LinkedList<>();
			for(int i=2;i<=n;i+=2)
			{
				System.out.print(i+" ");
				x=i;
			}
			int j=0;
			if(n%2==0)
			{
				j=x-1;
			}
			else
			{
				j=n;
			}
			while(x-j<2)
			{
				ll.add(j);
				j-=2;
			}
			System.out.print(j+" ");
			j-=2;
			for(Integer i: ll)
			{
				System.out.print(i+" ");
			}
			for(int h=j;h>=0;h-=2)
			{
				System.out.print(h+" ");
			}
			System.out.println();
			}
			t--;
		}

	}

}
