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: Runtime Error)

n = int(input())
coins = []
for i in range(7):
    if 6**i <= 10**5:
        coins.append(6**i)
    if 9**i <= 10**5:
        coins.append(9**i)
dp = [10**5]*(n+1)

def f(i):
    if i==0:
        return 0
    if dp[i] != 10**5:
        return dp[i]
    candidates = [f(i-coin)+1 for coin in coins if i-coin >= 0]
    dp[i] = min(candidates)
    return dp[i]

print(f(n))