Problem:
Score : 300 points

Problem Statement

Takahashi loves the number 7 and multiples of K.

Where is the first occurrence of a multiple of K in the sequence 7,77,777,\ldots? (Also see Output and Sample Input/Output below.)

If the sequence contains no multiples of K, print -1 instead.

Constraints

1 \leq K \leq 10^6

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4.)

Sample Input 1

101

Sample Output 1

4

None of 7, 77, and 777 is a multiple of 101, but 7777 is.

Sample Input 2

2

Sample Output 2

-1

All elements in the sequence are odd numbers; there are no multiples of 2.

Sample Input 3

999983

Sample Output 3

999982

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import qualified Data.ByteString.Char8 as BS
import Data.Maybe

main = do
    k <- fst . fromJust . BS.readInt <$> BS.getLine
    print $ answer k

answer k
    | even k = -1
    | mod k 7 == 0 = fst.head $ filter (judge k') $ nines k'
    | otherwise = fst.head $ filter (judge k'') $ nines k''
    where
        k' = 9*div k 7
        k'' = 9*k

judge k (_,nine) = mod nine k == 0

nines k = zip [1..] . scanl1 (\a b -> mod (a*10+b) k) $ repeat 9