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

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

        var cnt = Repeat(int.MaxValue, 100_001).ToArray();

        var units = new[] { 1 }
            .Concat(Range(1, 6).Select(i => (int)Math.Pow(6, i)))
            .Concat(Range(1, 5).Select(i => (int)Math.Pow(9, i)))
            .Where(x => x < cnt.Length).OrderBy(x => x).ToArray();

        var q = new Queue<(int v, int c)>(units.Select(x => (x, 1)));

        foreach (var (v, c) in q)
            cnt[v] = c;

        while(0 < q.Count)
        {
            var (v, c) = q.Dequeue();
            var nextC = c + 1;

            foreach (var nextV in units.Select(x => v + x).Where(x => x < cnt.Length))
            {
                if (cnt[nextV] == int.MaxValue)
                {
                    cnt[nextV] = nextC;
                    q.Enqueue((nextV, nextC));
                }
            }
        }

        WriteLine(cnt[N]);
    }
}

static class ArrayDeconstructExtensions
{
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2) => (i1, i2) = (a[0], a[1]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3) => (i1, i2, i3) = (a[0], a[1], a[2]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4) => (i1, i2, i3, i4) = (a[0], a[1], a[2], a[3]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4, out T i5) => (i1, i2, i3, i4, i5) = (a[0], a[1], a[2], a[3], a[4]);
}