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: Wrong Answer)

N = int(input())
ans = 0

def check_ten(N):
    count = 0
    i = 10
    exp = 1
    while True:
        divided = N // i
        if divided == 0:
            break
        count += divided
        exp += 1
        i = i ** exp
    print("check_ten", count)
    return count
        
def check_five(N):
    count = 0
    i = 5
    exp = 1
    while True:
        divided = N // i
        if divided == 0:
            break
        count += divided
        exp += 1
        i = i ** exp
    print("check_five", count)
    return count

if N % 2 == 0:
    ans = check_ten(N)
else:
    ans = check_five(N) - check_ten(N)

if N < 9:
    ans = 0

print(ans)
# if N % 2 == 1:
#     multiply_list = [(2*i - 1) for i in range(1, int(N/2)+2)]
# else:
#     multiply_list = [(2*i) for i in range(1, int(N/2)+1)]