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 extends App {
  import scala.math._
  
  val n = readInt
  val dp = Array.fill[Int](n+1)(Int.MaxValue)
  dp(0) = 0
  
  for (i <- 0 until n) {
    dp(i+1) = min(dp(i+1),dp(i)+1) //1円引き出す
    for (j <- 0 to ((log((n-i).toDouble)/log(6.0)).toInt)) dp(i+pow(6,j).toInt) = min(dp(i+pow(6,j).toInt),dp(i)+1) //6のべき乗円引き出す
    for (j <- 0 to ((log((n-i).toDouble)/log(9.0)).toInt)) dp(i+pow(9,j).toInt) = min(dp(i+pow(9,j).toInt),dp(i)+1) //9のべき乗円引き出す
  }
  
  println(dp(n))
}