Problem Statement  
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 xaxis 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.  
Definition  
 
Constraints  
  Each element of points will be formatted as a list of x,y pairs "<x_{1}> <y_{1}> <x_{2}> <y_{2}> <x_{3}> <y_{3}> ...", where there is exactly one space between every two terms, and both <x_{i}> and <y_{i}> are integers.  
  <x_{i}> and <y_{i}> will both be between 10,000 and 10,000, inclusive.  
  Each point will be unique.  
  There will be between 2 and 200 points, inclusive.  
Examples  
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