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)

#region using directives
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
using static System.Convert;
#endregion

namespace for_contests
{
    class Program
    {
        static void Main()
        {
            long k = ToInt64(ReadLine());
            long min = ToInt64(10e6);
            for(long i = 1; i < 10e5; i++)
            {
                long t = k * i;
                long sum = 0;
                while(t > 0)
                {
                    sum += t % 10;
                    t /= 10;
                }
                if (sum < min)
                    min = sum;
            }
            WriteLine(min);
        }
    }
}