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: Wrong Answer)

import java.util.*;

public class Main {
    static int modP = 1000000007;
    static int inf  = 1<<29;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n    = in.nextInt();
        int[] dp = new int[100001];
        Arrays.fill(dp, inf);
        dp[0] = 0;
        Queue<Integer> q = new PriorityQueue<>();
        q.add(1);
        for(int i = 6; i < 1000000; i *= 6) q.add(i);
        for(int i = 9; i < 1000000; i *= 9) q.add(i);

        Object[] a = q.toArray();
        for(int i = 0; i < dp.length; i++) {
            for(int j = 0; j < a.length; j++) {
                int aj = (int)a[j];
                if(i - aj >= 0) {
                    dp[i] = Math.min(dp[i], dp[i-aj] + 1);
                }
            }
        }
    }

    static void print(String s) {
        System.out.println(s);
    }

    static void print(int i) {
        System.out.println(i);
    }
}