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)

object Main {
  def main(args: Array[String]): Unit = {
    solve
  }

  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val patterns = Seq(1, 36, 216, 1296, 7776, 46656, 9, 81, 729, 6561, 59049).sorted


    // hiまでにかかるコスト
    val dp = Array.fill[Int](100001)(Int.MaxValue)
    dp(0) = 0
    for (i <- 0 until n) {
      for (pat <- patterns) {
        if (i + pat <= n) {
          dp(i + pat) = math.min(dp(i + pat), dp(i) + 1)
        }
      }
    }
    println(dp(n))
  }
}