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.Linq;
using System.Collections.Generic;

namespace lineAralgebra
{
	class Program
	{
		public static void Main(String[] args)
		{
			var n = int.Parse(Console.ReadLine());

			var dp = new int[n + 1];

			for (var i = 0; i <= n; i++)
			{
				dp[i] = int.MaxValue;
			}
			dp[0] = 0;

			for (var i = 1; i <= n; i++)
			{
				for (var power9 = 1; power9 <= i; power9 *= 9)
				{
					dp[i] = Math.Min(dp[i], dp[i - power9] + 1);
				}

				for (var power6 = 1; power6 <= i; power6 *= 6)
				{
					dp[i] = Math.Min(dp[i], dp[i - power6] + 1);
				}
			}

			System.Console.WriteLine(dp[n]);
		}
	}
}