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)

import sys
from math import log, floor

n = int(sys.stdin.readline().rstrip())

def main():
    cand = set()
    for i in range(floor(log(n, 6)) + 1):
        if 6 ** i <= n:
            cand.add(6 ** i)
        if 9 ** i <= n:
            cand.add(9 ** i)
    cand = sorted(cand)

    res = set([0])
    cnt = 0
    while True:
        nex = set()
        for val in res:
            for c in cand:
                if val + c <= n:
                    nex.add(val + c)
                else:
                    break
        cnt += 1
        if n in nex:
            return cnt
        res = nex
    
if __name__ == '__main__':
    ans = main()
    print(ans)