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 

/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	static void solve(int n){
		if(n<4){
			System.out.println(-1);
			return;
		}
		for(int i=n;i>=1;i--){
			if((i&1)==1){
				System.out.print(i+" ");
			}
		}
		System.out.print(4+" "+2+" ");
		for(int i = 6;i<=n;i+=2){
			System.out.print(i+" ");
		}
		System.out.println();
	}
	
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner scan = new Scanner(System.in);
		int t = scan.nextInt();
		while(t-- >0){
			int n = scan.nextInt();
			solve(n);
		}
		// your code goes here
	}
}