Problem:
Score : 500 points

Problem Statement

For an integer n not less than 0, let us define f(n) as follows:

f(n) = 1 (if n < 2)

f(n) = n f(n-2) (if n \geq 2)

Given is an integer N. Find the number of trailing zeros in the decimal notation of f(N).

Constraints

0 \leq N \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of trailing zeros in the decimal notation of f(N).

Sample Input 1

12

Sample Output 1

1

f(12) = 12 × 10 × 8 × 6 × 4 × 2 = 46080, which has one trailing zero.

Sample Input 2

5

Sample Output 2

0

f(5) = 5 × 3 × 1 = 15, which has no trailing zeros.

Sample Input 3

1000000000000000000

Sample Output 3

124999999999999995

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>

// Acknowledgement: Special thanks to kyomukyomupurin, who developed this
// template.
template <class T, class U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
  return os << '(' << p.first << ", " << p.second << ')';
}

template <class T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
  int n = 0;
  for (auto e : vec) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T>
std::ostream& operator<<(std::ostream& os, const std::set<T>& st) {
  int n = 0;
  for (auto e : st) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T, class U>
std::ostream& operator<<(std::ostream& os, const std::map<T, U>& mp) {
  int n = 0;
  for (auto e : mp) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T>
std::istream& operator>>(std::istream& is, std::vector<T>& vec) {
  for (T& e : vec) is >> e;
  return is;
}

#ifdef LOCAL
#define debug(...) \
  std::cerr << "[" << #__VA_ARGS__ << "]: ", debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() { std::cerr << '\n'; }

template <class Head, class... Tail>
void debug_out(Head&& head, Tail&&... tail) {
  std::cerr << head;
  if (sizeof...(Tail) != 0) std::cerr << ", ";
  debug_out(std::forward<Tail>(tail)...);
}
using namespace std;
using int64 = long long;

int main() {
  int64 N;
  cin >> N;
  if (N % 2 == 1) {
    cout << 0 << endl;
    return 0;
  }
  int64 divide_by = 10;
  int64 ans = 0;
  while (divide_by <= N) {
    ans += N / divide_by;
    divide_by *= 5;
  }
  cout << ans << endl;
  return 0;
}