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.ArrayList;
import java.util.Scanner;

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

		int t=s.nextInt();
		for(int ie=0;ie<t;ie++) {
			int n=s.nextInt();
			ArrayList<Integer> list=new ArrayList<>();
			
			for(int i=1;i<=n;i++) {
				if(i%2!=0) {
					list.add(i);
				}
			}
			ArrayList<Integer> list2=new ArrayList<>();
			if(n>=4) {
				list2.add(4);
				list2.add(2);
				
				for(int i=6;i<=n;i++) {
					if(i%2==0) {
						list2.add(i);
					}
				}
				
				for(int i=list2.size()-1;i>=0;i--) {
					System.out.print(list2.get(i)+" ");
				}
				for(int i=0;i<list.size();i++) {
					System.out.print(list.get(i)+" ");
				}
				System.out.println();
				
			}else {
				System.out.println(-1);
			}
			
			
		}
		
	}
}