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: Accepted)


import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static final int INF=9999999;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N=sc.nextInt();
		
		
		List<Integer> money = new ArrayList<>();
		money.add(1);
		{
			int x=6;
			while(x<=100000){
				money.add(x);
				x*=6;
			}
			x=9;
			while(x<=100000){
				money.add(x);
				x*=9;
			}
			Collections.sort(money);
		}

		int[] a=new int[100001];
		Arrays.fill(a, INF);
		
		int step=0;
		List<Integer> stepList = new ArrayList<>();
		List<Integer> nextStepList = new ArrayList<>();
		stepList.add(0);
		
		while(a[N]==INF){
			for(int x:stepList){
				for(int m:money){
					if(x+m>N) break;
					if(a[x+m]>step+1){
						a[x+m]=step+1;
						nextStepList.add(x+m);
					}
				}
			}
			step++;
			stepList=new ArrayList<>(nextStepList);
			nextStepList.clear();
		}
		
		System.out.println(a[N]);
		
	}
}