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: Time Limit Exceeded)

K = gets.chomp.to_i

a = 1

unless [1, 3, 7, 9].include?(K % 10)
  puts -1
  exit
end

tmp = 0
ichi = K % 10
while true
  tmp_mod_10 = tmp % 10
  kakeru = if tmp_mod_10 <= 7
             (0..9).find{ |n| (n * ichi % 10) == (7 - tmp_mod_10) }
           else
             (0..9).find{ |n| (n * ichi % 10) == (17 - tmp_mod_10) }
           end
  kaketa = K * kakeru
  tmp = (tmp + kaketa) / 10
  break if tmp.to_s.each_char.all?{ |c| c == "7" }
  a += 1
end

puts (a + tmp.to_s.length)