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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.ExceptionServices;
using System.Text;

namespace AtCoder.ABC
{
    class QuestionD
	{
		public static void Main(string[] args)
		{
			var scanner = new Scanner();

			var n = scanner.Int();

			var one = 1;
			var six = 6;
			var nine = 9;

			var money = new List<int>();

			money.Add(one);

			while (six <= n) {
				money.Add(six);
				six *= 6;
			}

			while (nine <= n) {
				money.Add(nine);
				nine *= 9;
			}

			var dp = new long[n + 1];

			for (int i = 0; i < n + 1; i++) {
				dp[i] = long.MaxValue;
			}

			dp[0] = 0;

			foreach (var m in money) {
				dp[m] = 1;
			}

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

				foreach (var m in money) {
					var next = i + m;

					if(next <= n) {
						dp[next] = Math.Min(dp[next], dp[i] + 1);
					}
				}
			}

			Console.WriteLine(dp[n]);
		}

		public class Scanner
		{
			private readonly char[] delimiter_ = new char[] { ' ' };
			private readonly string filePath_;
			private readonly Func<string> reader_;
			private string[] buf_;
			private int index_;

			public Scanner(string file = "")
			{
				if (string.IsNullOrWhiteSpace(file)) {
					reader_ = Console.ReadLine;
				} else {
					filePath_ = file;
					var fs = new StreamReader(file);
					reader_ = fs.ReadLine;
				}
				buf_ = new string[0];
				index_ = 0;
			}

			public string NextLine() => reader_();
			public string Next()
			{
				if (index_ < buf_.Length) {
					return buf_[index_++];
				}

				string st = reader_();
				while (st == "") {
					st = reader_();
				}

				buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
				if (buf_.Length == 0) {
					return Next();
				}

				index_ = 0;
				return buf_[index_++];
			}

			public int Int() => int.Parse(Next());
			public long Long() => long.Parse(Next());
			public double Double() => double.Parse(Next());

			public int[] ArrayInt(int N, int add = 0)
			{
				int[] Array = new int[N];
				for (int i = 0; i < N; i++) {
					Array[i] = Int() + add;
				}
				return Array;
			}

			public long[] ArrayLong(int N, long add = 0)
			{
				long[] Array = new long[N];
				for (int i = 0; i < N; i++) {
					Array[i] = Long() + add;
				}
				return Array;
			}

			public double[] ArrayDouble(int N, double add = 0)
			{
				double[] Array = new double[N];
				for (int i = 0; i < N; i++) {
					Array[i] = Double() + add;
				}
				return Array;
			}

			public (int, int) Int2(int add = 0)
			{
				var array = ArrayInt(2, add);
				return (array[0], array[1]);
			}

			public (int, int, int) Int3(int add = 0)
			{
				var array = ArrayInt(3, add);
				return (array[0], array[1], array[2]);
			}

			public (long, long) Long2(int add = 0)
			{
				var array = ArrayLong(2, add);
				return (array[0], array[1]);
			}

			public (long, long, long) Long3(int add = 0)
			{
				var array = ArrayLong(3, add);
				return (array[0], array[1], array[2]);
			}

			public (double, double) Double2(int add = 0)
			{
				var array = ArrayDouble(2, add);
				return (array[0], array[1]);
			}

			public (double, double, double) Double3(int add = 0)
			{
				var array = ArrayDouble(3, add);
				return (array[0], array[1], array[2]);
			}

			public void Save(string text)
			{
				if (string.IsNullOrWhiteSpace(filePath_)) {
					return;
				}

				File.WriteAllText(filePath_ + "_output.txt", text);
			}
		}
	}
}