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 Perl (v5.18.2) (judge verdict: Runtime Error)

$K=<>;
$a+=$_ for$K=~/./g;
if(grep{10**$_%$K==0}0..5){
	print 1,$/
}elsif($K%9==0){
	print$a,$/
}else{
	die;
	($b)=sort{$a-$b}map{eval join'+',($K*$_)=~/./g}1..9;
	if($b<$a){
		if($K%3==0){
			print$b,$/
		}else{
			print 2,$/
		}
	}else{
		print$a,$/
	}
}