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;
class TaskA {
 public:
  void solve(std::istream& in, std::ostream& out) {
    vector<int> dp(16, -1);
    dp[4] = 1;
    dp[6] = 1;
    dp[8] = 2;
    dp[9] = 1;
    dp[10] = 2;
    dp[12] = 3;
    dp[13] = 2;
    dp[14] = 3;
    dp[15] = 2;
    int q;
    in >> q;
    for (int i = 0; i < q; ++i) {
      int n;
      int count = 0;
      in >> n;
      if (n < 16) {
        out << dp[n] << '\n';
      }
      if (n > 15) {
        int t = (n - 16) / 4 + 1;
        if (dp[n - 4 * t] == -1) {
          out << -1 << '\n';
        } else {
          out << t + dp[n - 4 * t] << '\n';
        }
      }
    }
  }
};
int main() {
  TaskA solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}
