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;
const int MAXN = 100;
bool pr[MAXN];
int dp[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  memset(pr, true, sizeof(pr));
  pr[0] = false;
  for (int i = 2; i < MAXN; i++) {
    if (pr[i]) {
      for (int j = 2; j * i < MAXN; j++) {
        pr[j * i] = false;
      }
    }
  }
  memset(dp, 255, sizeof(dp));
  dp[0] = 0;
  for (int i = 4; i < MAXN; i++) {
    if (!pr[i]) {
      dp[i] = 1;
    }
    for (int j = 1; j < i; j++) {
      if ((!pr[j]) && (!pr[i - j])) {
        dp[i] = max(dp[i], dp[i - j] + dp[j]);
      }
    }
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int x;
    cin >> x;
    if (x < MAXN) {
      cout << dp[x] << "\n";
      continue;
    }
    int ans = 0;
    int ost = x % 4;
    for (int j = 0; j < 5; j++) {
      if (pr[4 * j + ost]) continue;
      ans = max(ans, dp[4 * j + ost] + (x - 4 * j - ost) / 4);
    }
    cout << ans << "\n";
  }
  return 0;
}
