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.to_i
dp = Array.new(100001, 100000)
dp[0], dp[1] = 0, 1
list = [1]
(1...10000).each do |i|
  break if 6 ** i > 100000
  list.push(6 ** i)
end
(1...10000).each do |i|
  break if 9 ** i > 100000
  list.push(9 ** i)
end
(2..n).each do |i|
  list.each do |j|
    dp[i] = [dp[i - j] + 1, dp[i]].min if i - j >= 0
  end
end
puts dp[n]