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.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class E
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		if(N < 2 || N % 2 == 1)
		{
			WriteLine(0);
			return;
		}

		WriteLine(Min(cntFactor(N / 2, 2) + 1, cntFactor(N / 2, 5)));
	}

	private long cntFactor(long N, long p)
	{
		long K = 0;
		long tmp = N;
		while(tmp > 0)
		{
			K++;
			tmp /= p;
		}
		var pow = new long[K];
		pow[0] = p;
		for(int i = 1; i < K; i++)
			pow[i] = pow[i - 1] * p;

		long res = 0;
		for(int i = 0; i < K; i++)
			res += N / pow[i];

		return res;
	}
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}