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D - Small Multiple

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 $K$.

6

3

$12=6×2$ yields the smallest sum.

41

5

$11111=41×271$ yields the smallest sum.

79992

36