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 PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
    n = int(input())
    dp = [n] * 200000
    dp[0] = 0
    
    for i in range(n):
        p6 = 1
        while True:
            if i + p6 > n:
                break
            dp[i + p6] = min(dp[i + p6], dp[i] + 1)
            p6 *= 6
        p9 = 1
        while True:
            if i + p9 > n:
                break
            dp[i + p9] = min(dp[i + p9], dp[i] + 1)
            p9 *= 9
    print(dp[n])


if __name__ == "__main__":
    main()