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)

#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;

const U_INF: usize = 1 << 60;
const I_INF: isize = 1 << 60;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.next_usize();

    if n % 2 == 1 {
        println!("0");
        return;
    }

    let mut ans = 0;
    for m in 1.. {
        if 2 * 5usize.pow(m) > n {
            break;
        }

        ans += n / (2 * 5usize.pow(m));
    }

    println!("{}", ans);
}

pub struct Scanner {
    buf: std::collections::VecDeque<String>,
}

impl Scanner {
    pub fn new() -> Self {
        Self {
            buf: std::collections::VecDeque::new(),
        }
    }

    fn scan_line(&mut self) {
        let mut flag = 0;
        while self.buf.is_empty() {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            let mut iter = s.split_whitespace().peekable();
            if iter.peek().is_none() {
                if flag >= 5 {
                    panic!("There is no input!");
                }
                flag += 1;
                continue;
            }

            for si in iter {
                self.buf.push_back(si.to_string());
            }
        }
    }

    pub fn next<T: std::str::FromStr>(&mut self) -> T {
        self.scan_line();
        self.buf
            .pop_front()
            .unwrap()
            .parse()
            .unwrap_or_else(|_| panic!("Couldn't parse!"))
    }

    pub fn next_usize(&mut self) -> usize {
        self.next()
    }

    pub fn next_isize(&mut self) -> isize {
        self.next()
    }

    pub fn next_chars(&mut self) -> Vec<char> {
        self.next::<String>().chars().collect()
    }

    pub fn next_string(&mut self) -> String {
        self.next()
    }

    pub fn next_char(&mut self) -> char {
        self.next()
    }

    pub fn next_float(&mut self) -> f64 {
        self.next()
    }
}