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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    long gcd(long a, long b)
    {
        return (b != 0) ? gcd(b, a % b) : a;
    }
    long lcm(long a, long b)
    {
        return a / gcd(a, b) * b;
    }
    //ax + by = gcd(a, b)となるx, yを求める
    long extgcd(long a, long b, out long x, out long y)
    {
        long g = a;
        if (b != 0)
        {
            g = extgcd(b, a % b, out y, out x);
            y -= (a / b) * x;
        }
        else
        {
            x = 1;
            y = 0;
        }
        return g;
    }
    void solve()
    {
        var N = cin.nextlong;
        if (N % 2 == 1)
        {
            WriteLine(0);
            return;
        }
        else
        {
            long ans = 0;
            for (long i = 5; i <= N; i *= 5)
            {
                ans += N / lcm(i, 2);
            }
            WriteLine(ans);
        }

    }

    long[][] matpow(long[][] m, long a, long Mod)
    {
        if (a == 0)
        {
            int N = m.Length;
            long[][] ret = new long[N][];
            for (int i = 0; i < N; i++)
            {
                ret[i] = new long[N];
                ret[i][i] = 1;
            }
            return ret;
        }
        if (a % 2 == 0)
        {
            long[][] ret = matpow(m, a / 2, Mod);
            return matmul(ret, ret, Mod);
        }
        else
        {
            return matmul(m, matpow(m, a - 1, Mod), Mod);
        }
    }
    long[][] matmul(long[][] ma, long[][] mb, long Mod)
    {
        int p = ma.Length;
        int q = mb[0].Length;
        int r = ma[0].Length;
        long[][] ret = new long[p][];
        for (int i = 0; i < p; i++)
        {
            ret[i] = new long[q];
            for (int j = 0; j < q; j++)
            {
                for (int k = 0; k < r; k++)
                {
                    ret[i][j] += ma[i][k] * mb[k][j] % Mod;
                }
                ret[i][j] %= Mod;
            }
        }
        return ret;
    }
}


static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}