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())
dp = [100000] * (N + 1)
dp[0] = 0
dp[1] = 1
for i in range(1, N + 1):
    dp[i] = dp[i - 1] + 1
    # 6
    prev = 6
    while i - prev >= 0:
        dp[i] = min(dp[i], dp[i - prev] + 1)
        prev *= 6
    # 9
    prev = 9
    while i - prev >= 0:
        dp[i] = min(dp[i], dp[i - prev] + 1)
        prev *= 9
print(dp[N])