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: Accepted)

import scala.io.{StdIn => in}

object Main extends App {
  val n = in.readInt
  val dp = Array.fill(n+1)(Int.MaxValue)
  dp(0) = 0

  def loop(i:Int, num:Int, cnt:Int):Unit = {
    val d = math.pow(num,cnt).toInt
    if(d <= i) {
      dp(i) = math.min(dp(i), dp(i-d)+1)
      loop(i, num, cnt+1)
    }
  }

  for(i <- 1 to n) {
    loop(i, 6, 0)
    loop(i, 9, 1)
  }

  println(dp(n))
}