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)

use std::io::{BufRead, Write};
use std::io;

fn digit_sum(mut x: usize) -> usize {
    let mut sum = 0;
    while x > 0 {
        sum += x % 10;
        x /= 10;
    }
    sum
}

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut buf = String::new();
    input.read_line(&mut buf).unwrap();
    let k: usize = buf.trim_right().parse().unwrap();
    // Thanks!!! http://www.sjsu.edu/faculty/watkins/Digitsum0.htm
    let result: usize = (1..10).map(|x| digit_sum(k * x)).min().unwrap();
    writeln!(output, "{}", result).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test(
            "6
",
            "3\n",
        );
    }

    #[test]
    fn case2() {
        test(
            "41
",
            "5\n",
        );
    }

    #[test]
    fn case3() {
        test(
            "79992
",
            "36\n",
        );
    }
}