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 Main {
 
	public static void main(String[] args) throws IOException,InterruptedException{
        Scanner sc = new Scanner(System.in);
	       int t=sc.nextInt();
	       while(t-->0) {
	    	int n=sc.nextInt();
	    	LinkedList<Integer> ll=new LinkedList<>();
	    	if (n<4) {
				System.out.println(-1);
			}else if(n==4) {
				System.out.println("3 1 4 2");
			}else {
				ll.add(3);
		    	ll.add(1);
		    	ll.add(4);
		    	ll.add(2);
		    	for (int i = 5; i <= n; i++) {
					if(i%2==0) ll.add(i);
					else ll.addFirst(i);
				}
		    	for (int i : ll) {
					System.out.print(i+" ");
				}
		    	System.out.println();	
			}
	       }
    }
}