USACO 3.2 Factorials

Do pre-processing steps to remove the pairs of factor 2 and 5 (which combines together can generate a 0). Then do factorial calculation against preprocessed numbers, and only keep a single digit at each step.
Why not just keep a single digit without pre-processing step? Because even if a digit is not zero, it could become zero after multiplying - so we need make sure kill those factors (2 and 5) first.

int N;
int main() {
  ifstream fin("fact4.in");
  ofstream fout("fact4.out");
  fin >> N;
  vector<int> num(N, 0);
  for (int i = 0; i < N; ++i) {
    num[i] = i + 1;
  }
  int cnt = 0;
  for (auto &i : num) {
    while (i % 5 == 0) {
      i = i / 5;
      ++cnt;
    }
  }
  for (auto &i : num) {
    while (i % 2 == 0) {
      if (cnt == 0) break;
      i = i / 2;
      --cnt;
    }
    if (cnt == 0) break;
  }
  long long r = 1;
  for (int i = 0; i < N; ++i) {
    r = (r * num[i]) % 10;
  }
  cout << r << endl;
  fout << r << endl;
}