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)

import math
inf = 10 ** 9
n = int(input())
dp = [inf] * (n+1)
dp[1] = 1
for i in range(1, n+1):
    d6 = math.floor(math.log(i)/math.log(6))
    d9 = math.floor(math.log(i)/math.log(9))
    dp[i] = min(dp[i - 6 ** d6] + 1, dp[i])
    dp[i] = min(dp[i - 9 ** d9] + 1, dp[i])
    dp[i] = min(dp[i-1] + 1, dp[i])
print(dp[-1])