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)

N = int(input())
list6 = [6**x for x in range(0,7) ]
list9 = [9**x for x in range(0,6) ]
result = {}

def f(x):
    if x < 6:
        return x
    elif x in result:
        return result[x] 
    else:
        max6 = max(y for y in list6 if y <= x)
        max9 = max(y for y in list9 if y <= x)
        x6 = x - max6
        x9 = x - max9
        result[x] = min(f(x6)+ 1,f(x9)+ 1)
        return result[x]

print(f(N))