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.rstrip.to_i

# dp    ; 0~n円の引き出しにかかる回数を全て算出する.
# 初期化; 100000より回数がかかることはないので初期値に設定. 0円は0回なので0.
dp = Array.new(n+1, 100000)
dp[0] = 0

(1..n).each do | i |
  # 1円引出でjumpできる先
  dp[i] = dp[i-1] + 1 < dp[i] ? dp[i-1] + 1 : dp[i]

  # 6円(** x), 9円(** y)引出でjumpできる先
  #   j は 6, 9 のどちらかの元の数字を保持. あとで累乗の計算できるように.
  #   k は累乗の結果を確認していく.
  #   jump元がdp配列の0番目以降になるように, i - k >= 0 を条件にする.
  [6, 9].each do | j |
    k = j
    while i - k >= 0
      dp[i] = dp[i-k] + 1 < dp[i] ? dp[i-k] + 1 : dp[i]
      k *= j
    end
  end
end
p dp[-1]