100773: [AtCoder]ABC077 D - Small Multiple

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