#include <bits/stdc++.h>
using namespace std;
template <typename T>
using vc = vector<T>;
template <typename T, typename X>
using pr = pair<T, X>;
const long long int MOD = 1e9 + 7;
const long double PI = 3.14159265;
long long int powerWithMod(long long int base, long long int exponent,
                           long long int modulus = LLONG_MAX) {
  long long int result = 1;
  base %= modulus;
  while (exponent > 0) {
    if (exponent % 2 == 1) result = (result * base) % modulus;
    exponent >>= 1;
    base = (base * base) % modulus;
  }
  return result;
}
long long int modInverse(long long int a, long long int m = MOD) {
  return powerWithMod(a, m - 2, m);
}
int q;
long long int n;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> q;
  while (q--) {
    long long int ans = 0;
    cin >> n;
    if (n & 1) {
      n -= 9;
      ans++;
    }
    if (n < 0) {
      cout << "-1\n";
      continue;
    }
    if (n % 4) {
      ans++;
      n -= 6;
    }
    if (n < 0) {
      cout << "-1\n";
      continue;
    }
    cout << ans + n / 4 << "\n";
  }
  return 0;
}

### Prompt

Your challenge is to write 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 vc = vector<T>;
template <typename T, typename X>
using pr = pair<T, X>;
const long long int MOD = 1e9 + 7;
const long double PI = 3.14159265;
long long int powerWithMod(long long int base, long long int exponent,
                           long long int modulus = LLONG_MAX) {
  long long int result = 1;
  base %= modulus;
  while (exponent > 0) {
    if (exponent % 2 == 1) result = (result * base) % modulus;
    exponent >>= 1;
    base = (base * base) % modulus;
  }
  return result;
}
long long int modInverse(long long int a, long long int m = MOD) {
  return powerWithMod(a, m - 2, m);
}
int q;
long long int n;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> q;
  while (q--) {
    long long int ans = 0;
    cin >> n;
    if (n & 1) {
      n -= 9;
      ans++;
    }
    if (n < 0) {
      cout << "-1\n";
      continue;
    }
    if (n % 4) {
      ans++;
      n -= 6;
    }
    if (n < 0) {
      cout << "-1\n";
      continue;
    }
    cout << ans + n / 4 << "\n";
  }
  return 0;
}

```