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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Solution
{
    static void Main()
    {
        long k = int.Parse(Console.ReadLine());
        var min = long.MaxValue;

        for (int i = 1; i < 100000; i++)
        {
            var m = k*i;
            var sum = m.ToString().Select(c => c - '0').Sum();
            min = Math.Min(sum, min);
        }

        Console.WriteLine(min);
    }
}