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
NN=100000

min_withdraw_num = []
min_withdraw_num[0] = 0

can_withdraw_moneys = []
can_withdraw_moneys[0] = [0]

sixes = (1..99).map {|i| 6**i }
nines = (1..99).map {|i| 9**i }

for i in 1..N
  moneys = can_withdraw_moneys[i-1]

  a = []

  moneys.each do |m|
    b = [1]
    b += sixes.take_while {|s| s+m<=NN }
    b += nines.take_while {|s| s+m<=NN }
    b.each do |bb|
      new_money = m+bb
      unless min_withdraw_num[new_money]
        min_withdraw_num[new_money] = i
        a << new_money
      end
    end
  end

  can_withdraw_moneys[i] = a
end

puts min_withdraw_num[N]