#include <bits/stdc++.h>
using namespace std;
template <typename T>
using pq_gt = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using pq_lt = priority_queue<T, vector<T>, less<T>>;
vector<int> compo;
int ans[1000];
bool isPrime(int x) {
  for (int i = 2; i <= sqrt(x); ++i) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
void solve(int x) {
  for (int i = 0; i < compo.size() && compo[i] <= x; ++i) {
    if (ans[x - compo[i]] != -1) ans[x] = max(ans[x], 1 + ans[x - compo[i]]);
  }
}
int main() {
  ios::sync_with_stdio(false);
  for (int i = 4; i < 1000; ++i) {
    if (!isPrime(i)) {
      compo.push_back(i);
    }
  }
  for (int i = 1; i < 1000; i++) {
    ans[i] = -1;
  }
  for (int i = 1; i < 1000; ++i) {
    solve(i);
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int t;
    cin >> t;
    if (t < 1000) {
      cout << ans[t] << endl;
    } else {
      int temp = (t - 996) / 4;
      cout << temp + ans[t - 4 * temp] << endl;
      ;
    }
  }
}

### Prompt

Your task is to create a Cpp solution 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;
template <typename T>
using pq_gt = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using pq_lt = priority_queue<T, vector<T>, less<T>>;
vector<int> compo;
int ans[1000];
bool isPrime(int x) {
  for (int i = 2; i <= sqrt(x); ++i) {
    if (x % i == 0) {
      return false;
    }
  }
  return true;
}
void solve(int x) {
  for (int i = 0; i < compo.size() && compo[i] <= x; ++i) {
    if (ans[x - compo[i]] != -1) ans[x] = max(ans[x], 1 + ans[x - compo[i]]);
  }
}
int main() {
  ios::sync_with_stdio(false);
  for (int i = 4; i < 1000; ++i) {
    if (!isPrime(i)) {
      compo.push_back(i);
    }
  }
  for (int i = 1; i < 1000; i++) {
    ans[i] = -1;
  }
  for (int i = 1; i < 1000; ++i) {
    solve(i);
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int t;
    cin >> t;
    if (t < 1000) {
      cout << ans[t] << endl;
    } else {
      int temp = (t - 996) / 4;
      cout << temp + ans[t - 4 * temp] << endl;
      ;
    }
  }
}

```