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 main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  vector<int> isPrime(100, 1), composites;
  for (long long i = 2; i < 100; i++) {
    if (isPrime[i]) {
      for (long long j = i * i; j < 100; j += i) isPrime[j] = 0;
    } else
      composites.push_back(i);
  }
  vector<int> count(100);
  for (int i = 4; i < 100; i++) {
    count[i] = !isPrime[i];
    for (int c : composites) {
      if (i - c <= 0) break;
      if (count[i - c]) count[i] = max(count[i], 1 + count[i - c]);
    }
  }
  int N;
  cin >> N;
  for (int i = 0; i < N; i++) {
    int ai;
    cin >> ai;
    if (ai < 100) {
      if (count[ai])
        cout << count[ai] << endl;
      else
        cout << "-1\n";
    } else {
      int ans = ai / 4;
      ai -= ans * 4;
      while (!count[ai]) {
        ai += 4;
        ans--;
      }
      cout << ans + count[ai] << endl;
    }
  }
  return 0;
}
