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 Python (3.4.3) (judge verdict: Accepted)

import sys
import math
import collections
import itertools
import array
import inspect

# Set max recursion limit
sys.setrecursionlimit(10000)

# Debug output
def chkprint(*args):
    names = {id(v):k for k,v in inspect.currentframe().f_back.f_locals.items()}
    print(', '.join(names.get(id(arg),'???')+' = '+repr(arg) for arg in args))

# Binary converter
def to_bin(x):
    return bin(x)[2:]

# --------------------------------------------

dp = None
mintime = 9999

def f(current, time, draws):
    global mintime

    if time > mintime:
        return 999999

    if current == 0:
        mintime = min(mintime, time)
        return time

    i = 0
    while draws[i] > current:
        i += 1

    if i + 1 == len(draws):
        return f(current - draws[i], time + 1, draws)
    else:
        return min(f(current-draws[i], time+1, draws), f(current-draws[i+1], time+1, draws))

def main():
    N = int(input())
    draws = [59049, 46656, 7776, 6561, 1296, 729, 216, 81, 36, 9, 6, 1]

    print(f(N, 0, draws))

main()