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 solve_coin_change(coins, value):
    table = [None for x in range(value + 1)]
    table[0] = []
    for i in range(1, value + 1):
        for coin in coins:
            if coin > i: 
                continue
            elif not table[i] or len(table[i - coin]) + 1 < len(table[i]):
                if table[i - coin] != None:
                    table[i] = table[i - coin][:]
                    table[i].append(coin)

    if table[-1] != None:
        return len(table[-1])
    else:
        return -1      

# Driver program to test above function
coins1 = [1]
coins6 = [6]
coins9 = [9]

maximum = 100000
i = 1
while True:
    new = coins6[i-1] * coins6[0]
    if new <= maximum:
        coins6.append(new)
        i += 1
    else:
        break
i = 1
while True:
    new = coins9[i-1] * coins9[0]
    if new <= maximum:
        coins9.append(new)
        i += 1
    else:
        break

n = int(input())
print(solve_coin_change(coins1 + coins6 + coins9, n))