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)

n = gets.to_i

# require 'irb'
nums = [1,6,9,36,81,216,729,1296,6561,7776,46656,59049]
dp = []

12.times do |i|
  dp[i] = []
  n.times do |j|
    if i == 0
      dp[i][j] = j+1
    else
      if (j+1) >= nums[i]
        div = (j+1) / nums[i]
        mod = (j+1) % nums[i]

        if mod == 0
          dp[i][j] = [div, dp[i-1][j]].min
        else
          dp[i][j] = [(div + dp[i][mod-1]), dp[i-1][j]].min
        end
      else
        dp[i][j] = dp[i-1][j]
      end
    end
  end
end

puts dp[-1][-1]