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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
 
fscanf(STDIN, "%d", $n);

$counter = 0;
while ($n != 0) {
  if ($n >= 12 && $n <= 14) {
    $max = 6;
  }
  else {
    $max = 1;

    $i = 1;
    while (($m = pow(6, $i)) < $n) {
      if ($m > $max) $max = $m;
      ++$i;
    }

    $i = 1;
    while (($m = pow(9, $i)) < $n) {
      if ($m > $max) $max = $m;
      ++$i;
    }
  }
  
  ++$counter;
  echo "[{$counter}] {$n} - {$max}\n";
  $n -= $max;
}

echo $counter;