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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

module Main where
import Data.List

int = read::String -> Int
main = interact $ printer . solver . parser

printer = unlines . (:[]) . show
parser = int

solver :: Int -> Int
solver k = minimum $ take 100 $ map target [k,(k*2)..]

target 0 = 0 
target n = r + target q
  where
    (q,r) = divMod n 10