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)

# BFS
from collections import deque

N=int(input())

dp = [-1] * 200005;
q = deque()

g = [1]
a = 6
while a <= 100000:
  g.append(a)
  a *= 6
a = 9
while a <= 100000:
  g.append(a)
  a *= 9
g.sort(reverse=True)

dp[0] = 0
q.append(0)

while len(q) > 0:
  v = q.popleft()
  if v == N: break
  for j in g:
    if dp[v+j] != -1: continue
    if v+j > N: continue
    dp[v+j] = dp[v] + 1
    q.append(v+j)

print(dp[N])