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;
using Int = long long;
bool isprime(int x) {
  for (int i = 2; i * i <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
const int MAX = 500;
signed main() {
  int dp[MAX], used[MAX];
  memset(used, 0, sizeof(used));
  function<int(int)> dfs = [&](int x) {
    if (x == 0) return 0;
    if (used[x]) return dp[x];
    used[x] = 1;
    int res = -1;
    for (int i = 2; i <= x; i++) {
      if (!isprime(i) && dfs(x - i) >= 0) {
        res = max(res, dfs(x - i) + 1);
      }
    }
    return dp[x] = res;
  };
  int q;
  cin >> q;
  while (q--) {
    int n;
    cin >> n;
    if (n < MAX)
      cout << dfs(n) << endl;
    else
      cout << (n / 4) - (n & 1) << endl;
  }
  return 0;
}
