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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int q;
  cin >> q;
  while (q--) {
    int n;
    cin >> n;
    int dp[16];
    int a[3] = {4, 6, 9};
    for (int i = 1; i < 16; i++) dp[i] = -1;
    dp[0] = 0;
    for (int i = 1; i < 16; i++) {
      for (int k = 0; k < 3; k++) {
        int j = a[k];
        if (i >= j && dp[i - j] != -1) {
          dp[i] = max(dp[i], dp[i - j] + 1);
        }
      }
    }
    if (n < 16)
      cout << dp[n] << "\n";
    else {
      int t = (n - 16) / 4 + 1;
      cout << t + dp[n - 4 * t] << "\n";
    }
  }
  return 0;
}
