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)

n = gets.to_i
num_list = [1]
i = 1
while true
  if 6**i <= n
    num_list << 6**i
  else
    break
  end
  i += 1
end
j = 1
while true
  if 9**j <= n
    num_list << 9**j
  else
    break
  end
  j += 1
end
num_list.sort!
dp = Array.new(n,nil)
dp[0] = 0
k = 0
while k <= n
  if dp[k]
    num_list.each do |num|
      if !dp[k+num]
        dp[k+num] = dp[k] + 1
      else
        dp[k+num] = [dp[k+num],dp[k]+1].min
      end
    end
  end
  k += 1
end
puts dp[n]