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 OCaml (4.02.3) (judge verdict: Accepted)

let rec take_while pred = function
    [] -> []
  | (x::xs) -> if pred x then x :: take_while pred xs else []

let rec scan_n n f v = if n <= 0 then [] else v :: scan_n (n-1) f (f v)

let arr = Array.init 101010 (fun i -> i)
let () = Scanf.scanf "%d" (fun n ->
  Array.init (n+1) (fun i ->
    [6; 9] |> List.iter (fun m ->
      scan_n 20 (( * ) m) 1 |> take_while ((>=) i) |> List.iter (fun j ->
        arr.(i) <- min arr.(i) (arr.(i - j) + 1)))) |> ignore;
  Printf.printf "%d\n" arr.(n))