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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.to_i
f = [1]
if n%2 == 0
  [*1..n/2].each{|i|
    f << 2*i*f[i-1]
  }
else
  [*1..n/2+1].each{|i|
    f << (2*i-1)*f[i-1]
  }
end
fn = f.pop
ans = 0
while fn%10 == 0
  ans += 1
  fn /= 10
end
p ans