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)

require 'prime'
k = gets.to_i
k_to_s = k.to_s
k_size = k_to_s.size
if k.even? || k_to_s[k_size - 1] == '5' || k_to_s[k_size - 1] == '0'
  puts -1
  exit
end
tmp = 0
ans = -1
mods = [7 % k]
k.times do |i|
  mods[i + 1] = mods[i] * 10 % k
end
1.upto(k) do |i|
  tmp += mods[i]
  tmp %= k
  if tmp == 0
    ans = i
    break
  end
end
puts ans