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
// define('DEBUG', true);
define('DEBUG', false);

fscanf(STDIN, "%d", $N);

$answer = PHP_INT_MAX;

$max9 = floor($N / 9);
for ($i = $max9; $i >= 0; $i--) {
    $newN = $N;
    $newN -= 9 * $i;
    $ret9 = getLog($i * 9, 9);
    $num6 = floor($newN / 6);
    $ret6 = getLog($num6 * 6, 6);
    $newN -= 6 * $num6;
    $ret1 = $newN;
    $sum = $ret9 + $ret6 + $ret1;
    $answer = min($sum, $answer);
    if (DEBUG) printf("9:%d 6:%d 1:%d sum:%d\n", $ret9, $ret6, $ret1, $sum);
}
echo $answer . PHP_EOL;

function getLog($n, $base) {
    $tmp = floor(log($n, $base));

    $ret = 0;
    for ($i = $tmp; $i >= 1; $i--) {
        $num = floor($n / pow($base, $i));
        $n -= $num * pow($base, $i);
        if (DEBUG) printf("base:%d number:%d proc:%d rest:%d\n", $base, pow($base, $i), $num, $n);
        $ret += $num;
    }
    return $ret;
}