Problem:
Score : 300 points

Problem Statement

To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:

1 yen (the currency of Japan)

6 yen, 6^2(=36) yen, 6^3(=216) yen, ...

9 yen, 9^2(=81) yen, 9^3(=729) yen, ...

At least how many operations are required to withdraw exactly N yen in total?

It is not allowed to re-deposit the money you withdrew.

Constraints

1 \leq N \leq 100000

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If at least x operations are required to withdraw exactly N yen in total, print x.

Sample Input 1

127

Sample Output 1

4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.

Sample Input 2

3

Sample Output 2

3

By withdrawing 1 yen three times, we can withdraw 3 yen in three operations.

Sample Input 3

44852

Sample Output 3

16

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
namespace Q3
{
    class Program
    {
        static void Main(string[] args)
        {
            string r = Console.ReadLine();
            int N = int.Parse(r);
            var list = new List<int>();

            list.Add(1);
            
            for(int i = 1; (int)System.Math.Pow(6, i) <= N; i++)
            {
                list.Add((int)System.Math.Pow(6, i));
            }
            for (int i = 1; (int)System.Math.Pow(9, i) <= N; i++)
            {
                list.Add((int)System.Math.Pow(9, i));
            }

            list.Sort((a, b) => b - a);
            int result = 0;
            result = Calc(N, list, 0);
            //for (int i = 0; N > 0; )
            //{
            //    if (N >= list[i])
            //    {
            //        N -= list[i];
            //        result++;
            //    }
            //    else
            //    {
            //        i++;
            //    }
            //}
            
            Console.Write(result);
            r = Console.ReadLine();
        }


        static int Calc(int N, List<int> list, int limit)
        {
            if (N == 0) return 0;
            int result = 100000;
            int kouho = 0;
            for (int i = limit; i < list.Count; i++)
            {
                if (list[i] * 9 < N) continue;
                for(int j = 1; j <= 8; j++)
                {
                    if (N >= list[i] * j)
                    {
                        kouho = Calc(N - list[i] * j, list, i + 1) + j;
                        if (kouho < result) result = kouho;
                    }
                }
            }

            return result;
        }
    }
}