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)

# p (0..6).to_a.map{|j| [6 ** j, 9 ** j] }.flatten.uniq.sort
a = [1, 6, 9, 36, 81, 216, 729, 1296, 6561, 7776, 46656, 59049, 531441]
 
m, dp = gets.to_s.to_i, [0]
(1..m).each {|i|
  t = 987654321
  idx = (a.bsearch_index{|j| i < j } || a.size ) - 1
  (a[0..idx]).map{|j| i - j }.each{|c| t = dp[c] if t > dp[c] }
  dp.push(t + 1)
}
puts dp[-1]