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
INF = N + 1
dp = Array.new(N+1,INF)
dp[0] = 0
n = N
a = 1
b = 1
ans = 0
stack = [1]
# binding.pry
while n / (a * 9) >= 1
  stack << a *= 9
end
# p a
while n / (b * 6) >= 1
  stack << b *= 6
end
stack.sort_by!{|x|x}
# p stack
stack.size.times do |i|
  stack[i].upto(N) do |j|
    dp[j] = [dp[j], dp[j - stack[i]] + 1].min
  end
end
puts dp[N]