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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>

int min(int a, int b)
{
    return a <= b ? a : b;
}

int main()
{
    int N;
    scanf("%d", &N);

    int dp[N+1];
    dp[0] = 0;
    for (int i = 1; i < N+1; ++i)
    {
        dp[i] = dp[i-1] + 1;
        for (int j = 1; j < i+1; ++j)
        {
            for (int k = 1; k < 7; ++k)
            {
                if (j % (int)pow(6, k) == 0)
                {
                    if (j / pow(6, k) == 1)
                    {
                        dp[i] = min(dp[i], dp[i-j]+1);
                        break;
                    }
                }
                else break;
            }
            for (int k = 1; k < 6; ++k)
            {
                if (j % (int)pow(9, k) == 0)
                {
                    if (j / pow(9, k) == 1)
                    {
                        dp[i] = min(dp[i], dp[i-j]+1);
                        break;
                    }
                }
                else break;
            }
        }
    }

    printf("%d", dp[N]);

    return 0;
}