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 qualified Data.Set as S
main = do
  k <- readLn :: IO Int
  print $ f k 7 S.empty

f :: Int -> Int -> (S.Set Int) -> Int
f k a s | m == 0 = 1 + S.size s
        | m `S.member` s = -1
        | otherwise = f k (m*10+7) $ S.insert m s
  where
    m = a `mod` k