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.Arrays;
import java.util.Scanner;

class Main{
	static int N;

	static int[] memo;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		N = sc.nextInt();

		memo = new int[N + 1];
		Arrays.fill(memo, -1);
		memo[0] = 0;

		System.out.println(dp(N));
		sc.close();
	}

	static int dp(int n){
		if(memo[n] == -1) {
			int min = Integer.MAX_VALUE;
			for(int i = 9; i <= n; i *= 9) {
				if(dp(n - i) < min)
					min = dp(n - i);
			}
			for(int i = 6; i <= n; i *= 6) {
				if(dp(n - i) < min)
					min = dp(n - i);
			}
			if(min == Integer.MAX_VALUE)
				min = dp(n - 1);
			memo[n] = min + 1;
		}
		return memo[n];
	}
}