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: Accepted)

{-# LANGUAGE FlexibleContexts #-}
main :: IO ()
main = do
  n <- readLn :: IO Int
  let count6 = map (count 6) [0..n]
      count9 = map (count 9) [n,n-1..0]
  print $ minimum $ zipWith (+) count6 count9


count :: Int -> Int -> Int
count unit money = let idx = ceiling $ 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)