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 Test01
{
    class Program
    {
        const int INF = 1000000009;
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] dp = (new int[N + 1]).Select(x => INF).ToArray();
            dp[0] = 0;
            int[] six = new int[8];
            int[] nine = new int[8];
            six[0] = 1;
            for (int i = 1; i <= 7; i++) six[i] = six[i - 1] * 6;
            nine[0] = 1;
            for (int i = 1; i <= 7; i++) nine[i] = nine[i - 1] * 9;

            for(int i = 0; i < N; i++)
            {
                dp[i + 1] = Math.Min(dp[i + 1], dp[i] + 1);
                for (int j = 1; j <= 7; j++) if (i + six[j] <= N) dp[i + six[j]] = Math.Min(dp[i + six[j]], dp[i] + 1);
                for (int j = 1; j <= 7; j++) if (i + nine[j] <= N) dp[i + nine[j]] = Math.Min(dp[i + nine[j]], dp[i] + 1);
            }

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