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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int a;
    cin >> a;
    int arr[16];
    memset(arr, -1, sizeof(arr));
    int ss[3] = {4, 6, 9};
    arr[0] = 0;
    for (int i = 1; i <= 15; i++)
      for (int j = 0; j < 3; j++) {
        if (i < ss[j] || arr[i - ss[j]] == -1) continue;
        arr[i] = max(arr[i], arr[i - ss[j]] + 1);
      }
    if (a <= 15) {
      cout << arr[a] << endl;
      continue;
      ;
    }
    cout << ((a - 16) / 4 + 1 + arr[a - 4 * ((a - 16) / 4 + 1)]) << endl;
  }
  return 0;
}
