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
a = [1, 6, 9, 36, 81, 216, 729, 1296, 6561, 7776, 59049, 46656, 531441].freeze

m, dp = gets.to_s.to_i, [0]
(1..m).each {|i|
  cans = a.select {|j| i - j >= 0 }.map{|j| i - j }.uniq
  dp.push(cans.map{|j| dp[j] }.min + 1)
}
p dp.last