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.Scanner;

public class Solution {

	public static void solver(int n) {
		if (n < 4) {
			System.out.println(-1);
			return;
		}
		int[] arr = new int[n];
		int start = n - (n + 1) % 2;
		int i = 0;
		while (start >= 1) {
			arr[i] = start;
			i++;
			start -= 2;
		}
		arr[i] = 4;
		i++;
		start = 2;
		for (; i < n; i++) {

			arr[i] = start;
			if (start == 2) {
				start = start + 4;
			} else {
				start = start + 2;
			}
		}
		for (int j = 0; j < n; j++) {
			System.out.print(arr[j] + " ");
		}
		System.out.println();
	}

	public static void main(String[] args) {

		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		s.nextLine();
		for (int i = 0; i < t; i++) {
			int n = s.nextInt();
			solver(n);
		}
	}
}