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.util.Scanner;

public class prince {
	
	public static void main(String[] args) {
	Scanner scan=new Scanner(System.in);
	int t=scan.nextInt();
	while(t>0)
	{
	
		
		int n=scan.nextInt();
		
		
		if(n==2||n==3)
		{
		System.out.println("-1");	
		}
		else {
		int i;
		ArrayList<Integer>e=new ArrayList<Integer>();
		ArrayList<Integer>o=new ArrayList<Integer>();
		
	for(i=1;i<=n;i++)
	{
		if(i%2!=0)
		o.add(i);
		else
		e.add(i);
		
	}
		
	
	for(int data:e)
	System.out.print(data+" ");
	
	
	Collections.sort(o,Collections.reverseOrder());
	
	if(n%2!=0)
	{
		Collections.swap(o, 0, 2);
		Collections.swap(o, 1, 2);
	}
	else
	Collections.swap(o, 0, 1);	
	
	for(int data:o)
		System.out.print(data+" ");
	
	
	
	System.out.println();
	
		}
	
	
	
	
	
	
		t--;
	}
	
	
}
}
