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++14 (GCC 5.4.1) (judge verdict: Accepted)


#include<bits/stdc++.h>

using namespace std;

#define FOR(i, j, k, in) for (int i=j ; i<k ; i+=in)
#define RFOR(i, j, k, in) for (int i=j ; i>=k ; i-=in)
#define REP(i, j) FOR(i, 0, j, 1)
#define FOREACH(it, l) for (auto it = l.begin(); it != l.end(); it++)
#define MP make_pair
#define PB push_back
#define PI 3.1415926535897932384626433832795
#define MOD 1000000007
const double pi=acos(-1.0);
typedef pair<int, int> PII;
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int  uint64;

#define int long long
#define trace(x) cerr << #x << ": " << x << " " << endl;


inline int add(int a, int b){a += b; if(a >= MOD)a -= MOD; return a;}
inline int sub(int a, int b){a -= b; if(a < 0)a += MOD; return a;}
inline int mul(int a, int b){return (int)((int) a * b %MOD);}


#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);

int dp[20][2];

signed main()
{
    IOS
    #define int unsigned long long
    int n;
    cin >> n;
    if(n&1)
    {
        cout << 0;
        return 0;
    }
    n = n/2;
   int ct = 0;
   while(n)
   {
       ct+=n/5;
       n=n/5;
   }
   cout << ct;
}