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: Wrong Answer)

<?php
$n=intval(fgets(STDIN));
$list = new SplFixedArray($n+1);
for($i = 0; $i < $n + 1; $i++) {
  $list[$i] = $n;
}
$list[0] = 0;

$six_pow = new SplFixedArray(8);
for($i = 1; $i < 8; $i++) {
  $six_pow[$i] = 6 ** ($i + 1);
}

$nine_pow = new SplFixedArray(8);
for($i = 0; $i < 8; $i++) {
  $nine_pow[$i] = 9 ** ($i + 1);
}

for($i = 0; $i < $n; $i++) {
  $list[$i+1] = min($list[$i+1], $list[$i]+1);
  for($j = 0; $j < 8; $j++) {
    if ($i + $six_pow[$j] <= $n) {
       $list[$i+$six_pow[$j]] = min($list[$i+$six_pow[$j]], $list[$i]+1);
    }
  }
  for($j = 0; $j < 8; $j++) {
    if ($i + $nine_pow[$j] <= $n) {
       $list[$i+$nine_pow[$j]] = min($list[$i+$nine_pow[$j]], $list[$i]+1);
    }
  }
}
echo $list[$n];