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 specperm {
	static int n;
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		int t = in.nextInt();
		for (int ti = 0; ti < t; ti++) {
			n = in.nextInt();
			boolean found = false;
			for (int x = 1; x <= n/2; x++) {
				order = new int[n];
				vis = new boolean[n+1];
				if (dfs(x, 0)) {
					found = true;
					break;
				}
			}
			if (!found) System.out.println(-1);
		}
		
		in.close();

	}
	
	static int[] off = {-4, -3, -2, 2, 3, 4};
	static int[] order;
	static boolean[] vis;
	static boolean dfs(int cur, int i) {
		vis[cur] = true;
		order[i] = cur;
		if (i >= n-1) {
			System.out.print(order[0]);
			for (int oi = 1; oi < order.length; oi++) {
				System.out.print(" "+order[oi]);
			}
			System.out.println();
			return true;
		}
		for (int o : off) {
			if (cur + o >= 1 && cur + o <= n && !vis[cur+o]) {
				if (dfs(cur+o, i+1)) return true;
			}
		}
		vis[cur] = false;
		order[i] = -1;
		return false;
	}
}
