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)

require "set"
MAX = 100_000
n = gets.chomp.to_i
dp = Hash.new{MAX}

6.times do |i|
  dp[i + 1] = i + 1
end
dp[7], dp[8] = 2, 3

set_for_once = Set.new({})
(Math.log(MAX, 6).ceil).times.reduce(set_for_once){|memo, attr| memo.add 6 ** attr}
(Math.log(MAX, 9).ceil).times.reduce(set_for_once){|memo, attr| memo.add 9 ** attr}
set_for_once = set_for_once.sort
set_for_once.each{|attr| dp[attr] = 1}

10.upto(n) do |i|
  next if dp[i] != MAX
  idx = set_for_once.index{|attr| attr > i} || set_for_once.size - 1
  idx.times do |j|
    dp[i] = [dp[i - set_for_once[j]] + 1, dp[i]].min
  end
end
puts dp[n]