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 Ruby (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor :a, :b, :n, :m, :h, :w, :dp

  def initialize
    @n = gets.to_s.to_i
    @dp = Array.new(n+1, -1)
    @dp[0] = 0
  end

  def solve
    rec(n)
  end

  def rec(n)
    return @dp[n] if @dp[n] != -1
    ans = 1 + rec(n-1)
    1.upto(7) do |j|
      d = 6 ** j
      1.upto(5) do |k|
        next if n < d * k
        cnt = k + rec(n - d * k)
        ans = cnt if cnt < ans
      end
    end
   
    1.upto(6) do |j|
      d = 9 ** j
      1.upto(8) do |k|
        next if n < d * k
        cnt = k + rec(n - d * k)
        ans = cnt if cnt < ans
      end
    end

    @dp[n] = ans
  end

  def show(ans)
    puts ans
  end
end

Problem.new.instance_eval do
  show(solve)
end