#include <bits/stdc++.h>
using namespace std;
bool arr[31623];
int b[3401];
void e() {
  for (int i = 0; i < 31623; i++) {
    arr[i] = true;
  }
  for (int i = 2; i <= pow(31623, 0.5); i++) {
    if (arr[i]) {
      for (int j = i * i; j <= 31623; j += i) {
        arr[j] = false;
      }
    }
  }
  int index = 0;
  for (int i = 2; i < 31623; i++) {
    if (arr[i]) {
      b[index] = i;
      index++;
    }
  }
}
int main() {
  e();
  int q, n;
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> n;
    if ((n % 4 == 1) and (n / 4 >= 2)) {
      cout << (n / 4) - 1 << endl;
    } else if ((n % 4 == 2) and (n / 4 >= 1)) {
      cout << (n / 4) << endl;
    } else if ((n % 4 == 3) and (n / 4 >= 3)) {
      cout << (n / 4) - 1 << endl;
    } else if (n % 4 == 0) {
      cout << n / 4 << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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;
bool arr[31623];
int b[3401];
void e() {
  for (int i = 0; i < 31623; i++) {
    arr[i] = true;
  }
  for (int i = 2; i <= pow(31623, 0.5); i++) {
    if (arr[i]) {
      for (int j = i * i; j <= 31623; j += i) {
        arr[j] = false;
      }
    }
  }
  int index = 0;
  for (int i = 2; i < 31623; i++) {
    if (arr[i]) {
      b[index] = i;
      index++;
    }
  }
}
int main() {
  e();
  int q, n;
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> n;
    if ((n % 4 == 1) and (n / 4 >= 2)) {
      cout << (n / 4) - 1 << endl;
    } else if ((n % 4 == 2) and (n / 4 >= 1)) {
      cout << (n / 4) << endl;
    } else if ((n % 4 == 3) and (n / 4 >= 3)) {
      cout << (n / 4) - 1 << endl;
    } else if (n % 4 == 0) {
      cout << n / 4 << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}

```