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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

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

$FR = $K ?? 1;
$SZ = $K ?? 100000;

// echo $FR , " " , $SZ , PHP_EOL;
// exit;

define('FR', $FR);
define('SZ', $SZ);

$arr = array_pad(array(), $SZ + 1, PHP_INT_MAX);
for ($i = $FR; $i <= $SZ; $i++) {
    for ($j = 1; $j <= 100000; $j++) {
        $x = $i * $j;
        $strX = strval($x);
        $num = array_sum(str_split($strX));
        $arr[$i] = min($arr[$i], $num);
        $arr[$j] = min($arr[$j], $num);
    }
}
// var_dump($arr);
// echo $arr[6];
// echo $arr[41];
echo $arr[$K];