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

six_bank = (1..10).map { |i| 6 ** i }
nine_bank = (1..10).map { |i| 9 ** i }

dp = Array.new(N + 1, Float::INFINITY)
dp[N] = 0

N.downto(1) do |i|
  next if dp[i] == Float::INFINITY

  six_bank.each do |s|
    break if i - s < 0

    t = dp[i] + 1
    dp[i - s] = t if dp[i - s] > t
  end

  nine_bank.each do |n|
    break if i - n < 0

    t = dp[i] + 1
    dp[i - n] = t if dp[i - n] > t
  end

  t = dp[i] + 1
  dp[i - 1] = t if dp[i - 1] > t
end

puts dp[0]