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)

class Integer
    def price_playable
        [1, 6, 9].each_with_object([]){|i, arr| 
            next arr << i if i == 1
            
            power = 1
            while i ** power <= self do
                arr << i ** power
                power += 1
            end
        }.sort
    end
end


def count_dp(n, price_playable) #dp法
    c_dp = Array.new(n+1, n)
    c_dp[0] = 0 
    
    (1..n).each{|i| 
        (0...price_playable.size).each{|j| 
            break if i < price_playable[j]
            #puts "#{i}, #{j}, #{c_dp[i]}, #{c_dp[i-price_playable[j]] + 1} , #{i-price_playable[j]}"
            c_dp[i] = c_dp[i-price_playable[j]] + 1 if c_dp[i] > c_dp[i-price_playable[j]] + 1
        }
    }
    
    c_dp[n]
end

n = gets.to_i
price_playable = n.price_playable
#p price_playable
x = count_dp(n, price_playable)
p x