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: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
public class Main { //Prime FACTORIZE!
//1e18 = 5^18*2^18 (Simply consider 5s since all factors are even anyway)
	public static void main(String[] args) { 
		Scanner input = new Scanner(System.in);
		long N = input.nextLong();
		if (N%2==1) System.out.println(0);
		else {
			long cnt = 0;
			long div = 5;
			cnt+=N/div/2;
			while (div<N) {
				div*=5;
				cnt+=(N/div)/2; //Odd multiples of 5 are excluded
			}
			System.out.println(cnt);
		}
	}
}