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: Time Limit Exceeded)

N=int(input())
dp=[-1]*(N+1)
dp[0]=0
que=[0]
while len(que)!=0:
    v=que[0]
    que=que[1:]
    pow6=1
    while v+pow6<=N:
        if dp[v+pow6]==-1:
            dp[v+pow6]=dp[v]+1
            que.append(v+pow6)
        pow6*=6
    pow9=1
    while v+pow9<=N:
        if dp[v+pow9]==-1:
            dp[v+pow9]=dp[v]+1
            que.append(v+pow9)
        pow9*=9
print(dp[N])