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 static Input;
using NX = System.Int64;


public class Prog
{
    public static void Solve()
    {
        long N = NextLong();
        //Console.WriteLine(f(N));
        //return;
        if (N % 2 == 0)
        {
            long[] box = new long[100];
            box[0] = 10;
            box[1] = 50;
            for (int i = 2; i <= 25; i++) box[i] = box[i - 1] * 5;
            //for (int i = 2; i <= 25; i++) Console.WriteLine(i + " : " + box[i]);
            long ans = 0;
            for (int i = 25; i >= 0; i--)
            {
                ans += N / box[i];
            }
            Console.WriteLine(ans);

        }
        else Console.WriteLine(0);
    }

    public static long f(long n)
    {
        if (n < 2) { return 1; }
        else return n * f(n - 2);
    }

    public static long RepPow(long x, long p, long m = 1000000007)
    {
        if (p == 0) return 1;
        if (p == 1) return x % m;
        long b = RepPow(x, p / 2, m) % m;
        if (p % 2 == 0) { return (b * b) % m; }
        else { return (x * ((b * b) % m)) % m; }
    }
    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
        return;
    }
    public static long GCD(long a, long b)
    {
        if (a < b) GCD(b, a);
        long d = a % b;
        while (b != 0)
        {
            d = a % b;
            a = b;
            b = d;
        }
        return a;
    }
    public static long LCM(long a, long b)
    {
        return a / GCD(a, b) * b;
    }
}
public class Input
{
    public const long MOD = 1000000007;
    public const int INF = 1000000007;
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
    public long Abs(long a, long b) => Math.Abs(a - b);
}