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)

N = int(input())

def factorial(n, p):
    if n == 0: return 1
    return n/p + factorial(n/p, p)

def duble_factorial(n, p):
    if n%2 == 1:
        return factorial(n,p) - duble_factorial(n-1, p) # n!! = n!/(n-1)!!だからpで割ると引き算で表せるよね
    else:
        res = factorial(n/2, p)
        if p == 2: 
            res += n/2
        return res

ans = min(duble_factorial(N,2), duble_factorial(N,5))
print(ans)