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.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long k = long.Parse(Console.ReadLine());//int.Parseは文字列を整数に変換。
		long answer = long.MaxValue;
    long num = 0;
    for(long i = 0; i<2000000; i++)
    {
      num += k;
      answer = Math.Min(answer, findSumOfDigits(num));
    }

		Console.WriteLine(answer);//WriteLineをWriteとすると、改行なしで出力。
	}

  static long findSumOfDigits(long n) 
  {//引数をnとして、nの各桁の数の和を求める
    long sum = 0;
    while (n > 0) 
    { // n が 0 になるまで
      sum += n % 10;//一の位から順に数をたす
      n /= 10;//10なら次は１、9なら終了になる
      }
  return sum;
  }
  
}