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.ArrayList;
import java.util.Scanner;

public class max_split {

    private static int max = 0;
    private static int[] cache;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] nums = new int[n];
        for (int i=0;i<n;i++) {
            nums[i] = in.nextInt();
        }
        max = 11;
        cache = new int[max+1];
        in.close();
        primes();
        for (int i : nums) {
            if (i<12) {
                int r = f(i);
                if (r<1) r = -1;
                System.out.printf("%d\n",r);
            } else {
                System.out.printf("%d\n",(i/4)-(i%2));
            }
        }
    }

    private static int f(int x) {
        if (x < 4) {
            if (x==0)
                return 0;
            return Integer.MIN_VALUE/5;
        }
        if (cache[x]!=0) return cache[x];
        int res = -1;
        for (int i : composite_numbers) {
            if (i>x) break;
            res = Math.max(res, f(x-i)+1);
        }
        cache[x] = res;
        return res;
    }


    private static ArrayList<Integer> composite_numbers = new ArrayList<>();

    private static void primes() {
        boolean sieve[] = new boolean[max+1];
        int K = max;
        for (int i=2; i<=K; i++) {
            if (sieve[i]) {
                continue;
            }
            for (int j=i*i; j<=K; j+=i) {
                sieve[j] = true;
            }

        }
        for (int i=3; i<K; i++) {
            if (sieve[i]) {
                composite_numbers.add(i);
            }
        }
    }
}
