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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long k = sc.nextLong();
        sc.close();
        long min = Long.MAX_VALUE;
        for (long i = 1; i < 10000000; i++) {
            long l = k*i;
            long sum = 0;
            while (l > 0) {
                sum += l % 10;
                l /= 10;
            }
            min = Math.min(min, sum);
        }
        System.out.println(min);
    }

}