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.

Examples

Input

6

Output

3

Input

41

Output

5

Input

79992

Output

36

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