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.io.*;

public class Solution{

	public static Integer INT(String s) {
		return Integer.parseInt(s);
	}
	public static Long LONG(String s) {
		return Long.parseLong(s);
	}

	static int mod=(int)1e9+7, oo=Integer.MAX_VALUE, _oo=Integer.MIN_VALUE;
	static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));	
	static Scanner in=new Scanner(System.in); 
	static StringBuilder out=new StringBuilder();

	//==================================================================================================================================================

	public static void main(String args[]) throws IOException {
		
		int t=in.nextInt();
		HashSet<Integer> set=new HashSet<>();
		int a[]=new int[8000];

		label:
		while(t--!=0) {

			int n=in.nextInt();

			if(n<=3) {
				out.append("-1\n");
				continue label;
			}

			LinkedList<Integer> list=new LinkedList<>();
			list.add(2);
			list.add(4);
			list.add(1);
			list.add(3);

			for(int i=5; i<=n; i++)
				if(i%2==0)
					list.addFirst(i);
				else
					list.addLast(i);

			for(int item: list)
				out.append(item+" ");
			out.append("\n");
		}

		System.out.print(out);
	}
}