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: Wrong Answer)

from collections import deque
import math

n = int(input())

#引き出せる金額の準備
a1 = set([1])
a6 = set([6**x for x in range(1, int(math.log(n, 6))+1)])
a9 = set([9**x for x in range(1, int(math.log(n, 9))+1)])
a = a1 | a6 | a9
b = list(a)
b.sort()

# n円引き出すための引き出し回数
dp = [-1] *(n+1)
dp[0]  = 0

# 探索キューを初期値ゼロで用意
d = deque([0])

# キューがなくなるまでループ
for _ in range(10**7):
    # キューが無いなら終了
    if len(d) == 0:
        break
        
    # キューから取り出し
    tmp = d.pop()
    
    # +1回で引き出せる範囲をDPにメモ
    for x in b:
        if tmp+x > n:
            break
        if dp[tmp+x] != -1:
            continue
        dp[tmp+x] = dp[tmp]+1
        d.appendleft(tmp+x)

print(dp[n])