A line of symmetry is a line through the cartesian plane such that if you reflect everything from one side of the line to the other, you still have the same image. For example, if the x-axis is a line of symmetry, it means that for every point (x,y) there is also a point (x,-y).
Your task is, given a list of points, determine how many such lines exist.
|-||Each element of points will be formatted as a list of x,y pairs "<x1> <y1> <x2> <y2> <x3> <y3> ...", where there is exactly one space between every two terms, and both <xi> and <yi> are integers.|
|-||<xi> and <yi> will both be between -10,000 and 10,000, inclusive.|
|-||Each point will be unique.|
|-||There will be between 2 and 200 points, inclusive.|