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 (2.3.3) (judge verdict: Accepted)

n = gets.to_i

counts = Array.new(n + 1)
counts[0] = 0
counts[1] = 1
available = [1]
max_six = 1
max_nine = 1
(1..n).each do |num|
  new_six = max_six * 6
  if new_six <= num
    available << new_six
    max_six = new_six
  end

  new_nine = max_nine * 9
  if new_nine <= num
    available << new_nine
    max_nine = new_nine
  end

  counts[num] = available.map { |a| counts[num - a] }.min + 1
end

puts counts[n]