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: Wrong Answer)

def strange_bank(N: int) -> int:
    prices = [1] + \
        [9 ** i for i in range(1, 6)] + \
        [6 ** i for i in range(1, 7)]
    dp = [float('inf')] * (N + 1)
    dp[N] = 0

    for n in range(N, 1, -1):
        for p in prices:
            if p <= N:
                dp[n-p] = min(dp[n] + 1, dp[n-p])

    return dp[0]


if __name__ == "__main__":
    N = int(input())
    ans = strange_bank(N)
    print(ans)