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;

namespace Practice
{
    static class StrangeBank
    {
        static void Main()
        {
            int N;
            N = int.Parse(Console.ReadLine());
            int[] a = { 6, 9, 36, 81, 216, 729, 1296, 6561, 7776, 46656, 59049 };
            
            int[] MinCount = Enumerable.Range(0, N+1).ToArray();
            for(int i = 6; i <= N; i++)
            {
                // 各i <= Nについて「i-a[k]を作ってa[k]を1回加える」で最小を更新するか判定
                foreach(int val in a)
                {
                    if(val <= i)
                        MinCount[i] = Math.Min(MinCount[i - val] + 1, MinCount[i]);
                }
            }

            Console.WriteLine($"{MinCount[N]}");
        }
    }
}