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: Accepted)

/* Coached by Dukkha */
#include <stdio.h>
#include <string.h>

#define N 100000
#define INF 0x3f3f3f3f

int main() {
	static int dp[N + 1];
	int n, a, p, e;

	scanf("%d", &n);
	memset(dp, 0x3f, sizeof dp);
	dp[0] = 0;
	for (a = 0; a <= n; a++)
		if (dp[a] != INF)
			for (e = 6; e <= 9; e += 3)
				for (p = 1; a + p <= n; p *= e)
					if (dp[a + p] > dp[a] + 1)
						dp[a + p] = dp[a] + 1;
	printf("%d\n", dp[n]);
	return 0;
}