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.
#include <bits/stdc++.h>
using namespace std;
int foo[30];
int comp[] = {4,  6,  8,  9,  10, 12, 14, 15, 16, 18,
              20, 21, 22, 24, 25, 26, 27, 28, 30, 32};
int main() {
  foo[0] = 0;
  for (int i = 1; i < 30; ++i) {
    int mx = -1;
    for (int j = 0; comp[j] <= i; j++) {
      if (foo[i - comp[j]] != -1) mx = max(mx, foo[i - comp[j]] + 1);
    }
    foo[i] = mx;
  }
  int q;
  scanf("%d", &q);
  while (q--) {
    int a;
    scanf("%d", &a);
    if (a < 30) {
      cout << foo[a] << "\n";
      continue;
    }
    int res = -1;
    for (int i = 12; i <= 15; ++i) {
      int b = a - i;
      if (b % 4 == 0) res = max(res, foo[i] + b / 4);
    }
    printf("%d\n", res);
  }
}
