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;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] dp = new int[n + 2];

        dp[0] = 0;
        for(int i = 1; i <= n; i++)
        {
            int power = 1;
            dp[i] = 100100;
            while(power <= i)
            {
                dp[i] = Math.Min(dp[i], dp[i - power] + 1);
                power *= 6;
            }
        }
        for (int i = 1; i <= n; i++)
        {
            int power = 1;
            while (power <= i)
            {
                dp[i] = Math.Min(dp[i], dp[i - power] + 1);
                power *= 9;
            }
        }
        Console.WriteLine(dp[n]);
    }
}