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 <bits/stdc++.h>
using namespace std;
const int maxn = 3e5 + 123;
#define int long long 
int n, m;
pair <int, int> a[maxn];
string s, t;
main () { 
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> n;

    int cur = 1;
    if(n % 2) {
    	cout << 0;
    	exit(0);
    }

    int ans = 0;
    for(int i = 1; i; i++) {
		if(cur * 5. > n * 1.) break;
		cur *= 5;
	
		int res = n / cur;
		int rem = res % 2;
		res /= 2;
		//res -= rem;
		ans += res;
    }
    cout << ans;
}