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

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var dp = Enumerable.Repeat(int.MaxValue, n + 1).ToArray();
            dp[0] = 0;

            for (var i = 1; i <= n; i++)
            {
                dp[i] = dp[i - 1] + 1;
                var six = 6;
                var multiple = 1;
                while (i - six >= 0)
                {
                    dp[i] = Math.Min(dp[i], dp[i - six] + 1);
                    six = (int)Math.Pow(6, ++multiple);
                }

                var nine = 9;
                multiple = 1;
                while  (i - nine >= 0)
                {
                    dp[i] = Math.Min(dp[i], dp[i - nine] + 1);
                    nine = (int)Math.Pow(9, ++multiple);
                }
            }

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