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.chomp.to_i
def log9(x)
  i = 0
  while x - 9 ** i >= 0
    i += 1
  end
  i-1
end
def log6(x)
  i = 0
  while x - 6 ** i >= 0
    i += 1
  end
  i-1
end
$dfs_hash = {0 => 0}
def dfs(n)
  return $dfs_hash[n] if $dfs_hash[n]
  pow9 = log9(n)
  pow6 = log6(n)
  return n if pow9 == 0 && pow6 == 0
  if pow9 > 0 && pow6 > 0
    $dfs_hash[n] = [dfs(n-9**pow9),dfs(n-6**pow6)].min + 1
  elsif pow9 > 0
    $dfs_hash[n] = dfs(n-9**pow9) + 1
  else
    $dfs_hash[n] = dfs(n-6**pow6) + 1
  end
end
puts dfs(n)