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 8.8.3) (judge verdict: Wrong Answer)

{-# LANGUAGE BangPatterns     #-}
{-# LANGUAGE FlexibleContexts #-}
import           Control.Monad
import           Control.Monad.ST
import           Control.Monad.State
import           Control.Monad.Trans.State
import           Data.Array.IArray
import           Data.Array.ST
import           Data.Array.Unboxed        (UArray)
import qualified Data.Array.Unboxed        as U
import           Data.Bits
import           Data.ByteString.Char8     (ByteString)
import qualified Data.ByteString.Char8     as BS
import           Data.Char
import           Data.Graph
import           Data.Int                  (Int64)
import           Data.List
import           Data.Maybe
import           Data.Proxy
import           Data.Sequence             (Seq, (<|), (><), (|>))
import qualified Data.Sequence             as Seq
import qualified Data.Set                  as S
import           Data.STRef
import qualified Data.Vector               as V
import qualified Data.Vector.Unboxed       as VU
import           Numeric

main :: IO ()
main = do
  n <- readLn :: IO Int
  let count6 = V.map (count 6) $ V.enumFromStepN 0 1 (n+1)
      count9 = V.map (count 9) $ V.enumFromStepN n (-1) (n+1)
  print $ V.minimum $ V.zipWith (+) count6 count9

  return ()

count :: Int -> Int -> Int
count unit money = let idx = floor $ logBase (fromIntegral unit) $ fromIntegral money
                   in  go (map (unit^) [idx,idx-1..0]) money 0
  where go _ 0 c      = c
        go (x:xs) m c = go xs (m`mod`x) (c + m`div`x)

unconsChar :: StateT BS.ByteString Maybe Char
unconsChar = StateT BS.uncons

unconsInt :: StateT BS.ByteString Maybe Int
unconsInt = StateT $ BS.readInt . BS.dropWhile isSpace

readLnAsVecNWith :: VU.Unbox a => Int -> StateT BS.ByteString Maybe a -> IO (VU.Vector a)
readLnAsVecNWith n st = VU.unfoldrN n (runStateT st) <$> BS.getLine

getAsString :: IO [String]
getAsString = map BS.unpack . BS.words <$> BS.getLine

getAsCharArray1DWithLength :: IO (Int, UArray Int Char)
getAsCharArray1DWithLength = BS.getLine >>= \ !cs ->
  let !n = BS.length cs
      !ary = (U.listArray (1,n) $ unfoldr BS.uncons cs) :: UArray Int Char
  in return (n, ary)

-- n: number of lines
-- m: number of chars per a line
getAsCharArray2D :: Int -> Int -> IO (UArray (Int,Int) Char)
getAsCharArray2D !n !m = U.listArray ((1,1),(n,m)) . unfoldr BS.uncons . BS.concat <$> replicateM n BS.getLine