#include <bits/stdc++.h>
using namespace std;
inline char nc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline void Read(int& x) {
  char c = nc();
  for (; c < '0' || c > '9'; c = nc())
    ;
  for (x = 0; c >= '0' && c <= '9'; x = (x << 3) + (x << 1) + c - 48, c = nc())
    ;
}
int n, i, j, q;
int main() {
  scanf("%d", &q);
  while (q--) {
    scanf("%d", &n);
    if (!(n % 4)) {
      printf("%d\n", n / 4);
    } else if (n % 4 == 1) {
      if (n / 4 >= 2)
        printf("%d\n", n / 4 - 1);
      else
        puts("-1");
    } else if (n % 4 == 2) {
      if (n / 4 >= 1)
        printf("%d\n", n / 4);
      else
        puts("-1");
    } else {
      if (n / 4 >= 3)
        printf("%d\n", n / 4 - 1);
      else
        puts("-1");
    }
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline char nc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline void Read(int& x) {
  char c = nc();
  for (; c < '0' || c > '9'; c = nc())
    ;
  for (x = 0; c >= '0' && c <= '9'; x = (x << 3) + (x << 1) + c - 48, c = nc())
    ;
}
int n, i, j, q;
int main() {
  scanf("%d", &q);
  while (q--) {
    scanf("%d", &n);
    if (!(n % 4)) {
      printf("%d\n", n / 4);
    } else if (n % 4 == 1) {
      if (n / 4 >= 2)
        printf("%d\n", n / 4 - 1);
      else
        puts("-1");
    } else if (n % 4 == 2) {
      if (n / 4 >= 1)
        printf("%d\n", n / 4);
      else
        puts("-1");
    } else {
      if (n / 4 >= 3)
        printf("%d\n", n / 4 - 1);
      else
        puts("-1");
    }
  }
  return 0;
}

```