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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
public class Main {
    static long mod = (long) Math.pow(10, 9) + 7;
    public static void main(String[] args) {
        FastScanner f = new FastScanner(System.in);
        long n = f.nextLong();
        long ans = 0;
        if(n % 2 == 1)
            pn(0);
        else
        {
            long copy = n;
            long i = 1;
            long dis = 0;
            long temp = 0;
            while(true){
                temp =  (copy / (50 * i));
                dis += temp;
                if(temp <= 0)
                    break;
                i *= 5;
            }
            ans = (n / 10) + dis;
        }
        pn(ans);
    }
        
/******************************END OF MAIN PROGRAM*******************************************/
    // Fast Scanner Alternative of Scanner 
    // Uses Implementation of BufferedReader Class
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new
                    InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    
    // Print in console
    static void pn(Object o){System.out.println(o);}
    static void p(Object o){System.out.print(o);}
    static void pni(Object o){System.out.println(o);System.out.flush();}

    //GCD of two integers
    static int gcd(int a, int b) {
        if(b == 0) return a;
        else {
            return gcd(b, a % b);
        }
    }

    // GCD of a array of integers
    static int gcdarray(int a[]) {
        int res = a[0];
        for(int i = 1; i < a.length; i++) {
            res = gcd(a[i] , res);
        }
        return res;
    }
    
    // Return boolean sieve of first n prime nos.
    static boolean[] sieve(int n) {
        boolean isprime[] = new boolean[n + 1];
        for(int i = 0; i <= n;++i) {
            isprime[i] = true;
        }
        isprime[0] = false;
        isprime[1] = false;
        for(int i = 2; i * i <= n; ++i) {
             if(isprime[i] == true) {               
                 for(int j = i * i; j <= n;j += i)
                     isprime[j] = false;
            }
        }
        return isprime;
    }

    // Return HashSet of factors of a number
    static HashSet<Long> factors(long n) {
        HashSet<Long> hs = new HashSet<Long>();
        for(long i = 1; i <= (long)Math.sqrt(n); i++) {
            if(n % i == 0) {
                hs.add(i);
                hs.add(n / i);
            }
        }
        return hs;
    }

    //Is n prime ?
    static boolean isPrime(int n) {
        if(n == 1) return false;
        int i = 2;
        while((i * i) <= n) {
            if(n % i == 0) return false;
            i += 1;
        }
        return true;
    }
}