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.Text;
using System.IO;
using System.Linq;
using System.Diagnostics;
using System.Globalization;
using static System.Console;
using static System.Math;

namespace abc_99.c
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            const int nmax = 100001;
            var list = new List<int>();
            list.Add(1);

            /* 100000を超えない6の累乗の数を入れてく */
            int tmp=6;
            int cnt=1;
            while(Pow(tmp,cnt)<=100000){
                list.Add((int)Pow(tmp,cnt));
                cnt++;
            }

            /* 100000を超えない9の累乗の数を入れてく */
            tmp=9;
            cnt=1;
            while(Pow(tmp,cnt)<=100000){
                list.Add((int)Pow(tmp,cnt));
                cnt++;
            }

            //コイン問題dp
            int[] dp = new int[nmax];
            for(int i=0; i<nmax; i++)dp[i] = int.MaxValue;
            dp[0] = 0;

            for(int i=0; i<list.Count; i++){
                for(int j=0; j+list[i] <= n; j++){
                    dp[j+list[i]] = Min(dp[j+list[i]], dp[j]+1);
                }
            }
            WriteLine(dp[n]);
        }

        /// 値のスワップ
        static void Swap<T>(ref T lhs, ref T rhs)
        {
            T temp;
            temp = lhs;
            lhs = rhs;
            rhs = temp;
        }


    }
}