#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void chkmax(T &x, const T &y) {
  if (x < y) x = y;
}
template <class T>
inline void chkmin(T &x, const T &y) {
  if (x > y) x = y;
}
const int MAXN = (1 << 20);
int q;
void read() { cin >> q; }
void solve() {
  while (q--) {
    int n;
    cin >> n;
    if (n < 9 && n % 2 == 1) {
      cout << -1 << '\n';
      continue;
    }
    if (n < 4) {
      cout << -1 << '\n';
      continue;
    }
    int answer = n / 4;
    if (n % 4 == 1) {
      answer -= 2;
      if (answer < 0) {
        cout << -1 << '\n';
        continue;
      }
      answer += 1;
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 0) {
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 2) {
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 3) {
      answer -= 3;
      if (answer < 0) {
        cout << -1 << '\n';
        continue;
      }
      answer += 2;
      cout << answer << '\n';
      continue;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  read();
  solve();
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void chkmax(T &x, const T &y) {
  if (x < y) x = y;
}
template <class T>
inline void chkmin(T &x, const T &y) {
  if (x > y) x = y;
}
const int MAXN = (1 << 20);
int q;
void read() { cin >> q; }
void solve() {
  while (q--) {
    int n;
    cin >> n;
    if (n < 9 && n % 2 == 1) {
      cout << -1 << '\n';
      continue;
    }
    if (n < 4) {
      cout << -1 << '\n';
      continue;
    }
    int answer = n / 4;
    if (n % 4 == 1) {
      answer -= 2;
      if (answer < 0) {
        cout << -1 << '\n';
        continue;
      }
      answer += 1;
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 0) {
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 2) {
      cout << answer << '\n';
      continue;
    }
    if (n % 4 == 3) {
      answer -= 3;
      if (answer < 0) {
        cout << -1 << '\n';
        continue;
      }
      answer += 2;
      cout << answer << '\n';
      continue;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  read();
  solve();
  return 0;
}

```