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 PyPy3 (7.3.0) (judge verdict: Accepted)

N = int(input())
inf = float("inf")
dp = [inf for _ in range(N+1)]
l6 = 7
l9 = 6
dp[0] = 0

# DP
for i in range(1, N+1):
    # 1円を引き出す
    dp[i] = min(dp[i], dp[i-1] + 1)
    
    # 6の累乗円を引き出す
    for j in range(1, l6):
        if i - 6**j >= 0:
            dp[i] = min(dp[i], dp[i - 6**j] + 1)
        
    # 9の累乗円を引き出す
    for j in range(1, l9):
        if i - 9**j >= 0:
            dp[i] = min(dp[i], dp[i - 9**j] + 1)

print(dp[N])