Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in PHP (5.6.30) (judge verdict: Wrong Answer)

<?php

$input_data = trim(fgets(STDIN));

$result = 0;
$multiplication = 1;
$sum = 99999999;
while (true)
{
	$mul = $input_data * $multiplication;

	if ($sum < strlen($mul) || $sum <= strlen($mul) || strlen($mul) > strlen($input_data) * 2)
	{
		$result = $sum;
		break;
	}

	$sum_tmp = 0;
	$mul_tmp = $mul;
	for ($i = 0; $i < strlen($mul); $i++)
	{
		$sum_tmp += $mul_tmp % 10;
		$mul_tmp = $mul_tmp / 10;
	}

	$sum = min($sum_tmp, $sum);
	$multiplication++;
}

echo $result;