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)


// Problem : E - Double Factorial
// Contest : AtCoder - AtCoder Beginner Contest 148
// URL : https://atcoder.jp/contests/abc148/tasks/abc148_e
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

//Macros

#define ll long long
#define db long double
#define pb push_back
#define eb emplace_back
#define pii pair<int,int>
#define vi vector<int>
#define vii vector<pii>
#define mi map<int,int>
#define mii map<pii,int>
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define sz(x) (int)x.size()
#define mod 1000000007
#define EPS 1e-9
#define io ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define inf 1e10
#define PI acos(-1.0)
#define int long long
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define N 100005

//Solution

void solve(){
    int n;
    cin>>n;
    if(n%2) cout<<0<<endl;
    else{
        int ans = 0;
        int cur = 10;
        while(n/cur > 0){
            ans += n/cur;
            cur *= 5;
        }
        cout<<ans<<endl;
    }
}

signed main(){
    io;
    //freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
    int tests;
    //cin>>tests;
    tests = 1;
    while(tests--){
        solve();
    }
    return 0;
}