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 Python (3.4.3) (judge verdict: Runtime Error)

import sys

def double_factorial(args):
    for n in args:
        if n % 2 == 0 or n < 1:
            error = 'Must enter an odd number greater than or equal to one.'
            raise ValueError(error)

    max_arg = max(args)
    total = 1
    results = []
    for arg in args:
        for i in [x for x in range(1, max_arg + 1) if x % 2 != 0]:
            if i <= arg:
                total *= i
        results.append(total)
        total = 1
    return results


if __name__ == '__main__':
    if len(sys.argv) > 1:
        if sys.argv[1] == '-n':
            arg = int(sys.argv[2])
            args = []
            for i in range(1, arg + 1):
                args.append(2 * i - 1)
            results = double_factorial(args)
        else:
            args = [int(x) for x in sys.argv[1:]]
            results = double_factorial(args)
        for result in results:
            print result
    else:
        Exception('At least one integer is expected.')