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 Ruby (2.7.1) (judge verdict: Accepted)

k = gets.to_i
s = 10%k
t = 7%k
a = []
a[0] = t
i = 1
while i < k do
  a[i] = (s*a[i-1]+t)%k
  i += 1
end
i = 0
g = 0
while i < k do
  if a[i] == 0
    g = 1
    break
  end
  i += 1
end
if g == 1
  puts i+1
else
  puts "-1"
end