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.Linq;
using System.Numerics;
using System.Text;
using System.Threading;
using System.Threading.Tasks;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine())+1;
            var memo = new List<int>(Enumerable.Range(0, N).Select(s => int.MaxValue));
            var t6 = new List<int>();
            var t9 = new List<int>();
            for (var i = 1; i < N; i++)
            {
                var tmp = (int)Math.Pow(6, i);
                if (N < tmp) break;
                t6.Add(tmp);
            }
            for (var i = 1; i < N; i++)
            {
                var tmp = (int)Math.Pow(9, i);
                if (N < tmp) break;
                t9.Add(tmp);
            }
            Action<List<int>, int, int> chmin =
                (ls, index, val) =>
                {
                    if (val < ls[index]) ls[index] = val;
                };
            memo[0] = 0;
            for (var i = 1; i < N; i++)
            {
                chmin(memo, i, memo[i-1]+1);
                for (var k = 0; k<t6.Count; k++)
                {
                    if (i - t6[k] < 0) continue;
                    chmin(memo, i, memo[i - t6[k]] + 1);
                }
                for (var k = 0; k < t9.Count; k++)
                {
                    if (i - t9[k] < 0) continue;
                    chmin(memo, i, memo[i - t9[k]] + 1);
                }
            }
            Console.WriteLine(memo[N - 1]);
        }
    }
}