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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.math.pow

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt
  
  def from(b: Int, n: Int): Stream[Int] = Stream.cons(pow(b, n).toInt, from(b, n + 1))
   
  val po9 = from(9, 1).takeWhile(_ <= n).toList
  val po6  = from(6, 1).takeWhile(_ <= n).toList
  val list =  (po9 ::: po6).sorted.reverse
  
  println(solve(0, n, list))
  
  
  def solve(count: Int, yen: Int, list: List[Int]): Int = {
    if (list.isEmpty) {
      count + yen
    } else if (yen >= list.head) {
      solve(count + 1, yen - list.head, list)
    } else {
      solve(count, yen, list.tail)
    }
  }
  
}