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: Wrong Answer)

k = gets.to_i
x = 7
if k % 2 == 0 or k % 5 == 0
  puts "-1"
  exit
end

require "prime"
ps = Prime.prime_division k
qs = ps.map do |(q, e)|
  next 999982**e if q == 999983
  y = 7
  cnt = 1
  until y % q == 0
    cnt += 1
    y = y * 10 + 7
  end
  cnt ** e
end


p qs.inject(&:*)