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)

n = int(input())


def dfs(remain, count):
    if 6 > remain:
        return count + remain
    count9 = dfs(remain - 9, count + 1) if remain - 9 > 0 else count + remain
    count6 = dfs(remain - 6, count + 1) if remain - 6 > 0 else count + remain
    return count9 if count9 < count6 else count6


count = 0
while n >= 6:
    m_9 = 1
    while 9 ** m_9 <= n:
        m_9 += 1
    m_6 = 1
    while 6 ** m_6 <= n:
        m_6 += 1
    if 2 == m_9 and 2 == m_6:
        count += dfs(n, 0)
        n = 0
    else:
        candidates = [9 ** (m_9 - 1), 6 ** (m_6 - 1)]
        n -= max(candidates)
        count += 1
print(count + n)