#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int b[5000 + 5], num = 0, s[5000 + 5], h[5000 + 5], cnt = 0, f[5000 + 5];
int main() {
  for (int i = 2; i <= 5000; ++i) {
    if (!b[i])
      s[++num] = i;
    else
      h[++cnt] = i;
    for (int j = 1; s[j] * i <= 5000; ++j) {
      b[s[j] * i] = 1;
      if (i % s[j] == 0) break;
    }
  }
  memset(f, 200, sizeof(f));
  f[0] = 0;
  for (int i = 1; i <= 5000; ++i)
    for (int j = 1; j <= cnt; ++j)
      if (i >= h[j]) f[i] = max(f[i], f[i - h[j]] + 1);
  for (int T = read(); T; --T) {
    int x = read();
    if (x <= 5000)
      printf("%d\n", f[x] < 0 ? -1 : f[x]);
    else {
      int t = (x - 5000 + 3) / 4;
      printf("%d\n", f[x - t * 4] + t);
    }
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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 int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int b[5000 + 5], num = 0, s[5000 + 5], h[5000 + 5], cnt = 0, f[5000 + 5];
int main() {
  for (int i = 2; i <= 5000; ++i) {
    if (!b[i])
      s[++num] = i;
    else
      h[++cnt] = i;
    for (int j = 1; s[j] * i <= 5000; ++j) {
      b[s[j] * i] = 1;
      if (i % s[j] == 0) break;
    }
  }
  memset(f, 200, sizeof(f));
  f[0] = 0;
  for (int i = 1; i <= 5000; ++i)
    for (int j = 1; j <= cnt; ++j)
      if (i >= h[j]) f[i] = max(f[i], f[i - h[j]] + 1);
  for (int T = read(); T; --T) {
    int x = read();
    if (x <= 5000)
      printf("%d\n", f[x] < 0 ? -1 : f[x]);
    else {
      int t = (x - 5000 + 3) / 4;
      printf("%d\n", f[x - t * 4] + t);
    }
  }
  return 0;
}

```