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 ans[100];
bool bpr[100];
int main() {
  for (int i = 0; i < 100; i++) bpr[i] = 1;
  for (int i = 2; i < 100; i++) {
    if (!bpr[i]) continue;
    for (int j = 2; j * i < 100; j++) bpr[i * j] = 0;
  }
  ans[0] = 0;
  for (int i = 1; i < 100; i++) {
    ans[i] = -100005;
    for (int j = 2; j <= i; j++) {
      if (bpr[j]) continue;
      ans[i] = max(ans[i], ans[i - j] + 1);
    }
  }
  int q;
  scanf("%d", &q);
  for (int i = 1; i <= q; i++) {
    int a;
    scanf("%d", &a);
    if (a < 100) {
      if (ans[a] >= 0)
        printf("%d\n", ans[a]);
      else
        printf("-1\n");
    } else {
      int nst = (a - 100) / 4;
      nst++;
      a -= nst * 4;
      printf("%d\n", ans[a] + nst);
    }
  }
  return 0;
}
