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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N = in.nextInt

  val dp = Array.tabulate(N + 1)(identity)

  def seq(i: Int): LazyList[Int] = i #:: seq(i).map(_ * i)

  def doDp(i: Int): Unit = {
    for {
      u <- seq(i).takeWhile(_ <= N)
      n <- 1 to i
      i <- 0 to (N - n * u)
    } {
      dp(i + n * u) = dp(i + n * u) min (dp(i) + n)
    }
  }

  doDp(6)
  doDp(9)
  println(dp(N))
}