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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(defun solve (K)
  (defvar r (mod 7 K))
  (defvar ht (make-hash-table))

  (loop for i from 1
        
        if (zerop r) return i
        if #1=(gethash r ht) return -1
        do (setf #1# t
                 r (mod (+ (* 10 r) 7) K))))

(princ (solve (read)))