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)

N = int(input())

prices = [1]
idx = 1
while 6 ** idx <= N:
    prices.append(6 ** idx)
    idx += 1
idx = 1
while 9 ** idx <= N:
    prices.append(9 ** idx)
    idx += 1

prices.sort()

dp = [float('inf') for _ in range(N + 1)]
dp[0] = 0
for n in range(N + 1):
    for price in prices:
        dp[n] = min(dp[n], dp[n - price] + 1)

print(dp[-1])