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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass
{
    static void Main()
    {
        int N = int.Parse(ReadLine());

        var dp = Enumerable.Repeat(int.MaxValue, N + 1).ToArray() ;
        dp[0] = 0;
        for (int i = 0; i < N; i++)
        {
            if (dp[i] == int.MaxValue) continue;
            int num = 1;
            while (i + num <= N) num *= 9;
            num /= 9;
            int v = 1;
            int index = i;
            while (num > 1)
            {
                if (index + num <= N) index += num;
                dp[ index] = Min(dp[index],dp[i]+v);
                v++;
                num/=9;
            }
        }
        for (int i = 0; i < N; i++)
        {
            if (dp[i] == int.MaxValue) continue;
            int num = 1;
            while (i + num <= N) num *= 6;
            num /= 6;
            int v = 1;
            int index = i;
            while (num > 1)
            {
                if (index + num <= N) index += num;
                dp[index] = Min(dp[index], dp[i]+v);
                v++;
                num /= 6;
            }

        }
        int ans = int.MaxValue;
        for (int i = N; i >= 0; i--)
        {
            if (dp[i] == int.MaxValue) continue;
            ans = Min(ans, dp[i] + N - i);
        }
        WriteLine(ans);
    }
}