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: Accepted)

import qualified Data.IntSet as S

main :: IO ()
main = print =<< solve <$> readLn

solve :: Int -> Int
solve n = go (S.singleton 0)
  where
    go s
      | n `S.member` s = 0
      | otherwise      = 1 + go s'
      where
        s' = S.filter (<= n) $ S.unions [ S.map (+w) s | w <- ws ]

    ws = 1 : [ 6 ^ p | p <- [1..6] ] ++ [ 9 ^ p | p <- [1..7] ]