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: Accepted)

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::BinaryHeap;
use std::cmp::Ordering;

#[derive(Clone, Copy, Eq, PartialEq)]
struct E {
    v: usize,
    d: usize,
}

impl Ord for E {
    fn cmp(&self, other: &Self) -> Ordering {
        other.d.cmp(&self.d)
    }
}

impl PartialOrd for E {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

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

    let mut bs = vec![true; k];
    let mut q = BinaryHeap::new();
    q.push(E{
        v: 1,
        d: 1,
    });

    let mut res = 0;

    while let Some(e) = q.pop() {
        if e.v == 0 {
            res = e.d;
            break;
        }

        bs[e.v] = false;

        let j = (e.v * 10) % k;
        if bs[j] {
            q.push(E{
                v: j,
                d: e.d,
            });
        }
        let j = (e.v + 1) % k;
        if bs[j] {
            q.push(E {
                v: j,
                d: e.d + 1,
            });
        }
    }

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