Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn readln<T>() -> T
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().parse().unwrap()
}

use std::collections::VecDeque;

fn main() {
    let k = readln();

    let mut xs = vec![vec![vec![]; 2]; k];

    for i in 0..k {
        let j = (i + 1) % k;
        let h = (i * 10) % k;

        xs[i][0].push(h);
        xs[i][1].push(j);
    }

    let mut ds = vec![None; k];
    let mut q = VecDeque::new();
    ds[1] = Some(1);
    q.push_back(1);

    while let Some(u) = q.pop_front() {
        for &v in &xs[u][0] {
            if let None = ds[v] {
                ds[v] = ds[u];
                q.push_front(v);
            }
        }
        for &v in &xs[u][1] {
            if let None = ds[v] {
                ds[v] = Some(ds[u].unwrap() + 1);
                q.push_back(v);
            }
        }
    }

    println!("{}", ds[0].unwrap());
}