AtCoder ARC 084 D - Small Multiple (AtCoder 3621)

D - Small Multiple

题目传送门
Time limit : 2sec / Memory limit : 256MB
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≤K≤105
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×