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 (2.7.1) (judge verdict: Accepted)

n = gets.to_i
dp = Array.new(10**6 + 100, 10**8)
dp[0] = 0


(0..100000).each do |i|
  pow6 = 1
  pow9 = 1
  while pow6 + i <= n do
    dp[i + pow6] = [dp[i]+1, dp[i+pow6]].min
    pow6 *= 6
  end
  while pow9 + i <= n do
    dp[i + pow9] = [dp[i]+1, dp[i+pow9]].min
    pow9 *= 9
  end
end

puts dp[n]