#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000000 + 7;
int addm(int& a, int b) { return (a += b) < mod ? a : a -= mod; }
template <class T, class U>
bool smin(T& a, U b) {
  return a > b ? (a = b, 1) : 0;
}
template <class T, class U>
bool smax(T& a, U b) {
  return a < b ? (a = b, 1) : 0;
}
int comp[]{4, 6, 8, 9, 15, 21, 22, 24, 25, 27, 33};
int dp[101];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  fill(dp, dp + 101, INT_MIN / 2);
  dp[0] = 0;
  for (int i = 0; i < 100; i++)
    for (int j = 0; j < 11; j++)
      for (int k = 0; comp[j] + k <= 100; k++)
        dp[k + comp[j]] = max(dp[k + comp[j]], dp[k] + 1);
  long long q, n;
  cin >> q;
  while (q--) {
    cin >> n;
    long long num4 = 0;
    if (n > 100) num4 = (n - 100) / 4;
    n -= num4 * 4;
    long long bans = -1;
    while (n > 0) {
      bans = max(bans, num4 + dp[n]);
      num4++;
      n -= 4;
    }
    if (bans == -1)
      cout << -1 << '\n';
    else
      cout << bans << '\n';
  }
}

### Prompt

Create a solution in cpp for 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;
const int mod = 1000000000 + 7;
int addm(int& a, int b) { return (a += b) < mod ? a : a -= mod; }
template <class T, class U>
bool smin(T& a, U b) {
  return a > b ? (a = b, 1) : 0;
}
template <class T, class U>
bool smax(T& a, U b) {
  return a < b ? (a = b, 1) : 0;
}
int comp[]{4, 6, 8, 9, 15, 21, 22, 24, 25, 27, 33};
int dp[101];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  fill(dp, dp + 101, INT_MIN / 2);
  dp[0] = 0;
  for (int i = 0; i < 100; i++)
    for (int j = 0; j < 11; j++)
      for (int k = 0; comp[j] + k <= 100; k++)
        dp[k + comp[j]] = max(dp[k + comp[j]], dp[k] + 1);
  long long q, n;
  cin >> q;
  while (q--) {
    cin >> n;
    long long num4 = 0;
    if (n > 100) num4 = (n - 100) / 4;
    n -= num4 * 4;
    long long bans = -1;
    while (n > 0) {
      bans = max(bans, num4 + dp[n]);
      num4++;
      n -= 4;
    }
    if (bans == -1)
      cout << -1 << '\n';
    else
      cout << bans << '\n';
  }
}

```