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)

#include <stdio.h>
#include <stdlib.h>

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

int power(int a, int N){
	if(N == 0){
		return 1;
	}
	else{
		return a * power(a, N - 1);
	}
}

int main(){
	int N, i, j;
	scanf("%d", &N);
	int *dp = (int *)malloc(sizeof(int) * (N + 1));
	dp[0] = 0;
	for(i = 1; i <= N; i++){
		dp[i] = dp[i - 1] + 1;
		for(j = 1; power(6, j) <= i; j++){
			dp[i] = min(dp[i], dp[i - power(6, j)] + 1);
		}
		for(j = 1; power(9, j) <= i; j++){
			dp[i] = min(dp[i], dp[i - power(9, j)] + 1);
		}
	}
	printf("%d\n", dp[N]);
	return 0;
}