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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

 (let ((n (read)))
  (labels ((maxpower (n x)
             (labels ((iter (n x c)
                        (if (<= (expt x c) n)
                            (iter n x (1+ c))
                            (expt x (1- c)))))
               (iter n x 1)))
           (f (n n6 n9)
             (let ((nlarge (max n6 n9)))
               (if (= nlarge 1)
                   n
                   (1+ (let ((new-n (- n nlarge)))
                     (f new-n (maxpower new-n 6) (maxpower new-n 9))))))))
    (format t "~A~%" (f n (maxpower n 6) (maxpower n 9)))))