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 Lua (Lua 5.3.5) (judge verdict: Accepted)

k = io.read("*n")

if k % 2 == 0 then
  print(-1)
  return
end

sevens = 7
step = 1

while sevens % k ~= 0 do
  if step > 10 ^ 6 then
    step = -1
    break
  end

  sevens = sevens * 10 + 7
  sevens = sevens % k
  step = step + 1
end

print(step)