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())

inf = n + 100
dp = [inf] * (n+1)
dp[0] = 0
for i in range(n):
    if i <= n-1:
        dp[i+1] = min(dp[i+1], dp[i] + 1)

    cnt6 = 6
    while True:
        if i + cnt6 <= n:
            dp[i + cnt6] = min(dp[i + cnt6], dp[i] + 1)
            cnt6 *= 6
        else:
            break

    cnt9 = 9
    while True:
        if i + cnt9 <= n:
            dp[i + cnt9] = min(dp[i + cnt9], dp[i] + 1)
            cnt9 *= 9
        else:
            break

print(dp[n])