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;

public class AtCoder
{
    public static void Main()
    {
        //問題
        //0以上の整数nに対し、f(n)を次のように定義します。
        //f(n)=1 (n<2のとき)
        //f(n)=nf(n−2) (n≥2のとき)
        //整数Nが与えられます。
        //f(N)を10進法で表記した時に末尾に何個の0が続くかを求めてください。
        //0≤N≤10^18

        //解法
        //Nが0もしくは奇数の場合、2が素因数に現れないので計算するまでもなく答えは0
        //Nが0より大きい偶数の場合、5の倍数の方が圧倒的に少ないので5の素因数の個数が答え
        var N = long.Parse(Console.ReadLine());
        if(N==0 || N % 2 == 1)
        {
            Console.WriteLine(0);
        }
        else
        {
            long count = 0;
            long ten = 10;
            while (N >= ten)
            {
                count += N / ten;
                ten *= 5;
            }
            Console.WriteLine(count);
        }
    }
}