#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:10034217728")
using namespace std;
const int N = 210;
bool non_prime[N];
int min_steps[N];
const int inf = 2e9;
int main() {
  for (int i = 2; i < N; i++) {
    for (int j = i * 2; j < N; j += i) {
      non_prime[j] = 1;
    }
  }
  vector<int> np;
  for (int i = 0; i < N; i++) {
    if (non_prime[i]) np.push_back(i);
  }
  for (int i = 0; i < N; i++) min_steps[i] = -inf;
  min_steps[0] = 0;
  for (int i = 0; i < N; i++) {
    if (min_steps[i] == -inf) continue;
    for (int j = 0; j < np.size(); j++) {
      int v = np[j];
      int nxt_i = v + i;
      if (nxt_i >= N) continue;
      min_steps[nxt_i] = max(min_steps[nxt_i], min_steps[i] + 1);
    }
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int x;
    cin >> x;
    int ans = 0;
    if (x >= 180) {
      int fours = x / 4;
      ans += fours - 40;
      x %= 4;
      x += 160;
    }
    if (min_steps[x] == -inf) {
      cout << -1 << endl;
      continue;
    }
    cout << min_steps[x] + ans << endl;
  }
  return 0;
}

### 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>
#pragma comment(linker, "/STACK:10034217728")
using namespace std;
const int N = 210;
bool non_prime[N];
int min_steps[N];
const int inf = 2e9;
int main() {
  for (int i = 2; i < N; i++) {
    for (int j = i * 2; j < N; j += i) {
      non_prime[j] = 1;
    }
  }
  vector<int> np;
  for (int i = 0; i < N; i++) {
    if (non_prime[i]) np.push_back(i);
  }
  for (int i = 0; i < N; i++) min_steps[i] = -inf;
  min_steps[0] = 0;
  for (int i = 0; i < N; i++) {
    if (min_steps[i] == -inf) continue;
    for (int j = 0; j < np.size(); j++) {
      int v = np[j];
      int nxt_i = v + i;
      if (nxt_i >= N) continue;
      min_steps[nxt_i] = max(min_steps[nxt_i], min_steps[i] + 1);
    }
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int x;
    cin >> x;
    int ans = 0;
    if (x >= 180) {
      int fours = x / 4;
      ans += fours - 40;
      x %= 4;
      x += 160;
    }
    if (min_steps[x] == -inf) {
      cout << -1 << endl;
      continue;
    }
    cout << min_steps[x] + ans << endl;
  }
  return 0;
}

```