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
Lim = 5 * (10 ** 6)

mod10s = []
for i in 1..Lim do
  if i == 1 then
    mod10s[i-1] = (1 % K)
  else
    mod10s[i-1] = (mod10s[i-2] * 10) % K
  end
end

ans = -1
current_mod = 0
for i in 1..Lim do
  current_mod = (current_mod + mod10s[i-1] * 7) % K
  if current_mod == 0 then
    ans = i
    break
  end
end
  
puts ans