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;
using System.Collections.Generic;
using System.Text;


public class C
{
	public static void Main()
	{	
		int N = Int32.Parse(Console.ReadLine());
		
		List<int> option = new List<int>();

		option.Add(1);

		for(int i = 1; ; i++)
		{
			if(Math.Pow(6,i) > N)
				break;
			option.Add((int)Math.Pow(6,i));
		}

		for(int i = 1; ; i++)
		{
			if(Math.Pow(9,i) > N)
				break;
			option.Add((int)Math.Pow(9,i));
		}

		option.Sort();
		
		int[] dp = new int[N+1];  // dp[0] = 0;
		for(int i = 1; i <= N; i++)
		{
			int tmp = Int32.MaxValue;
			for(int j = 0; j < option.Count; j++)
			{
				if(option[j] > i)
					break;
				tmp = Math.Min(tmp, dp[i - option[j]]);
			}
			dp[i] = tmp + 1;
		}

		Console.WriteLine(dp[N]); 
	}	
}