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 N3_15_10 {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int q=scanner.nextInt();
        int n[]=new int[q];
        for (int i=0;i<q;i++){
            n[i]=scanner.nextInt();

        }
        for (int i=0;i<q;i++){
            System.out.println(func(n[i]));
        }

    }
    public static int func(int n)
    {

        if (n<4 )
            return -1;
        if (n/4 - n%2 ==1 && prost(n)) {return -1;}
        if (n/4 - n%2 ==0) {
            //if (prost(n))
                return -1;
            //else return (n/4);
        }else return (n/4-n%2);
        //else return -1;
    }
    public static boolean prost(int  n){
        boolean flag=true;
        for (int i=2;i<=n/2;i++) {
            if (n % i == 0) {
            flag = false;
            break;
             }
        }
        return flag;
    }

}
