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 Control.Arrow
import Control.Monad
import Data.Bits
import qualified Data.ByteString.Char8 as BC
import Data.Char
import Data.List
import Data.Maybe

main :: IO ()
main = do
  n <- getInt
  print . minimum $ [sum (baseConvert 6 x) + sum (baseConvert 9 (n - x)) | x <- [0..n]]

getInt :: IO Int
getInt = readLn

baseConvert :: Int -> Int -> [Int] -- O(log n)
baseConvert b = unfoldr (\n -> if n == 0 then Nothing else Just (n `mod` b, n `div` b))