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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn f1(a:usize, b:usize) -> usize {
  if a == 0 {
    0
  } else {
    a/b + f1(a/b, b)
  }
}

fn f2(a:usize, b:usize) -> usize {
  if a % 2 == 1 {
    return f1(a, b) - f2(a-1, b);
  }
  let mut result = f1(a/2, b);
  if b == 2 {
    result += a/2;
  }
  result
}

fn main() {
  input!{
    mut n: usize,
  }
    
  println!("{}", std::cmp::min(f2(n, 2), f2(n, 5)));
}