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: Time Limit Exceeded)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val N = sc.nextInt()
  val dp = Array.fill(N+1)(Int.MaxValue)
  dp(0) = 0
  for (n <- 1 to N) {
    // 1のパターン
    dp(n) = math.min(dp(n), dp(n-1)+1)
    // 6のi乗のパターン
    var six = 6
    while(six <= n) {
      for (j <- 1 to n / six) {
        dp(n) = math.min(dp(n), dp(n-six*j) + j)
      }
      six = six * 6
    }
    // ９のi乗のパターン
    var nine = 9
    while(nine <= n) {
      for (j <- 1 to n / nine) {
        dp(n) = math.min(dp(n), dp(n-nine*j) + j)
      }
      nine = nine * 9
    }
  }
  println(dp(N))
}