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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)


import java.util.*;
import java.util.concurrent.ConcurrentHashMap;

/**
 * Created by oka on 2018/06/10.
 */
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        int[] temp = {1, 6, 9, 36, 81, 216, 729, 1296, 6561, 7776, 46656, 59049};
        List<Integer> list = new ArrayList<Integer>();
        ConcurrentHashMap map = new ConcurrentHashMap();
        for (int i = 0; i < 12; i++) {
            if (temp[i] <= n) {
                if (n == temp[i]) {
                    System.out.println(1);
                    return;
                }
                list.add(temp[i]);
                map.put(temp[i], true);
            }
        }

        int retCounter = 1;
        while (true) {
            retCounter++;
            List<Integer> tmp = new ArrayList<Integer>();
            synchronized (map) {
                for (Iterator<Integer> i = map.keySet().iterator(); i.hasNext(); ) {
                    tmp.add(i.next());
                }
            }
            synchronized (map) {
                for (int key: tmp) {
                    synchronized (map) {
                        map.remove(key);
                    }
                    for (int j = 0; j < list.size(); j++) {
                        int newKey = key + list.get(j);
                        if (newKey == n) {
                            System.out.println(retCounter);
                            return;
                        }
                        synchronized (map) {
                            map.put(newKey, true);
                        }
                    }
                }
            }
        }
    }
}