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)

def main():
    n = int(input())
    C = [1, ]
    c = 6
    while c < 100000:
        C.append(c)
        c *= 6
    c = 9
    while c < 100000:
        C.append(c)
        c *= 9
    INF = float('inf')
    dp = [INF] * (n + 1)
    dp[0] = 0
    for i in range(1, n + 1):
        C_filtered = [c for c in C if c <= i]
        dp[i] = min([dp[i - c] + 1 for c in C_filtered])
    print(dp[n])
if __name__ == '__main__':
    main()