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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $n);
for ($p = 0; $p <= log($n + 0.1, 9); $p++) {
	$es[] = 9 ** $p;
}
for ($p = 1; $p <= log($n + 0.1, 6); $p++) {
	$es[] = 6 ** $p;
}
rsort($es);
$q = new SplMaxHeap();
$q->insert(0);
for ($t = 1; $t <= $n; $t++) {
	$q2 = new SplMaxHeap();
	while (!$q->isEmpty()) {
		$i = $q->extract();
		foreach ($es as $e) {
			$x = $i + $e;
			if ($x > $n || isset($f[$x])) continue;
			if ($x == $n) exit("$t");
			$q2->insert($x);
			$f[$x] = 1;
		}
	}
	$q = $q2;
}