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: Wrong Answer)

#!/usr/bin/env ruby
# require 'pry'

# dpテンプレ
# 最小化
# dp = Hash.new{ Float::INFINITY }
# dp[i] = [dp[i], dp[i-1] + hoge].min
# dp[0] = 0
# 最大化
dp = Hash.new{Float::INFINITY}
dp[0] = 0
n = gets.to_i
ary=[]
1.upto(10) do |num|
  break if (6**num) > 10**5
  ary << 6**num
  ary << 9**num
  dp[num] = num
end
dp[6]=1
dp[7]=2
dp[8]=3
dp[9]=1
10.upto(n) do |i|
  ary.each do |ele|
    break if ele > i
    dp[i] = [(dp[i-ele] + 1), (dp[i-1] + 1), dp[i]].min
  end
end

puts dp[n]