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;
bool IsPrime(int N) {
  for (int i = 2; i * i <= N; ++i) {
    if (N % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  vector<char> is_prime(101, false);
  for (int i = 1; i < is_prime.size(); ++i) {
    is_prime[i] = IsPrime(i);
  }
  vector<int> dp(is_prime.size(), 0);
  for (int i = 1; i < dp.size(); ++i) {
    dp[i] = is_prime[i] ? -1 : 1;
    for (int j = 1; i - j > 0; ++j) {
      if (dp[j] != -1 && dp[i - j] != -1) {
        dp[i] = max(dp[i], dp[j] + dp[i - j]);
      }
    }
  }
  int Q;
  cin >> Q;
  for (int q = 0; q < Q; ++q) {
    int a;
    cin >> a;
    if (a < dp.size()) {
      cout << dp[a] << '\n';
      continue;
    }
    switch (a % 4) {
      case 0: {
        case 2:
          cout << a / 4 << '\n';
          break;
      }
      default: {
        cout << a / 4 - 1 << '\n';
        break;
      }
    }
  }
  return 0;
}
