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: Wrong Answer)

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

public class Hello
{
    public static void Main()
    {
        var a = new List<int>();
        for (int i = 1; i <= 6; i++) a.Add((int)Math.Pow(6, i));
        for (int i = 1; i <= 5; i++) a.Add((int)Math.Pow(9, i));
        var b = a.OrderByDescending(x => x).ToArray();
        var n = int.Parse(Console.ReadLine().Trim());
        var dp = new int[n + 1];
        for (int i = 1; i <= n; i++) dp[i] = i;
        for (int i = 1; i <= n; i++)
        {
            foreach (var x in b)
            {
                var p = 1;
                while (true)
                {
                    var t = x * p;
                    if (t + i > n) break;
                    if (p + dp[i] < dp[t + i]) dp[t + i] = p + dp[i];
                    p++;
                }
            }
        }
        Console.WriteLine(dp[n]);
    }
}