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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# OPTIONS_GHC -O #-}
import Control.Monad
import Data.List

sp n p b
    | n < p*b = p
    | otherwise = sp n (p*b) b

s69 n
    | n == 0 = Nothing
    | otherwise = Just ((max (sp n 1 9) (sp n 1 6)), n - (max (sp n 1 9) (sp n 1 6)))

main=do
    n<-readLn :: IO Int
    let r = takeWhile (>1) $ unfoldr s69 n
    print $ case n-(sum r) of
        0 -> length r
        1 -> length r + 1
        2 -> length r + 2
        3 -> length r + 1
        4 -> length r + 2
        5 -> length r + 3