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

a = [1]

[6,9].each do |m|
  u = 1
  while u * m <= n do
    u *= m
    a << u
  end
end

a.sort!.reverse!

dp = Array.new(n+1, 0)

1.upto(n) do |i|
  b = a.bsearch_index {|x| x <= i}
  min = 10**9
  b.upto(a.length-1) do |j|
    tmp = dp[i-a[j]]
    min = tmp if tmp < min
  end

  dp[i] = min + 1
end
puts dp[n]