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.*;
 
public class Maximum_splitting {
    public static boolean prime[] = new boolean[100001];
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int q = scanner.nextInt();
        for (int i = 0; i < 100001; i++) prime[i] = true;
        prime[1] = false;
        for (int i = 2; i < 100001/2; i++) {
            if (prime[i] == true) {
                for (int j = i+i; j < 100001; j += i) {
                    prime[j] = false;
                }
            }
        }
        while (--q >= 0) {
            int n = scanner.nextInt();
            int res = n/4;
            if (n < 4) res = -1;
            else if (n%4 != 0) {
                if (n%4 == 1 && n/4 >= 2) res -= 1;
                else if (n%4 == 3 && n/4 >= 3) res -= 1;
                else if (n%4 != 2) res = -1;
            }
            System.out.println(res);
        }
        scanner.close();
    }
}