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)

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

solve n = do
    a6 <- newListArray (1,6) [6,36,216,1296,7776,46656] :: IO (IOArray Int Int)
    a9 <- newListArray (7,11) [9,81,729,6561,59049] :: IO (IOArray Int Int)
    --
    a <- newArray ((0,0),(n,11)) 0 :: IO (IOUArray (Int,Int) Int)
    forM_ [1..n] $ \j -> writeArray a (j,0) j
    --
    forM_ [(j,i)|i<-[1..6], j<-[0..n]] $ \(j,i) -> do
        p <- readArray a6 i
        m <- liftM minimum $ forM [k|k<-[0..5],k*p<=j] $ \k -> do
            (+k) <$> readArray a (j-k*p,i-1)
        writeArray a (j,i) m
    --
    forM_ [(j,i)|i<-[7..11], j<-[0..n]] $ \(j,i) -> do
        p <- readArray a9 i
        m <- liftM minimum $ forM [k|k<-[0..8],k*p<=j] $ \k -> do
            (+k) <$> readArray a (j-k*p,i-1)
        writeArray a (j,i) m
    --
    readArray a (n,11)

main = do
    n <- readLn :: IO Int
    print =<< solve n