You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.

An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.

Input

The first line contains single integer q (1 ≤ q ≤ 105) — the number of queries.

q lines follow. The (i + 1)-th line contains single integer ni (1 ≤ ni ≤ 109) — the i-th query.

Output

For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.

Examples

Input

1
12


Output

3


Input

2
6
8


Output

1
2


Input

3
1
2
3


Output

-1
-1
-1

Note

12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.

8 = 4 + 4, 6 can't be split into several composite summands.

1, 2, 3 are less than any composite number, so they do not have valid splittings.


import java.util.Scanner;

public class MaximumSplitting {

	public static void main(String[] args) {
		try (Scanner s = new Scanner(System.in)) {
			int n = s.nextInt();
			for (int i = 0; i < n; i++) {
				System.out.println(maxCompositeSplit(s.nextInt()));
			}
		}
	}

	private static int maxCompositeSplit(int num) {
		if (num >= 4) {
			switch (num % 4) {
			case 0:
				return num / 4;
			case 1:
				if (num < 9) {
					return -1;
				}
				return (num - 9) / 4 + 1;
			case 2:
				return (num - 6) / 4 + 1;
			case 3:
				if (num < 15) {
					return -1;
				}
				return (num - 15) / 4 + 2;
			}
		}
		return -1;
	}
}
