Problem Statement  
Given a set of points, choose the maximal number of them that can be used to form a spiral.
A spiral is formed as follows: 1. Start at point (0, 0). 2. Draw a line segment from the current point to one of the given points (x, y). (x, y) is now the new current point. 3. Repeat step 2 as many times as possible while obeying the following rules:
These three spirals do not satisfy the first, second and third rules: These two do not satisfy the fourth rule: You are given a String[] points, each element of which represents a single point whose coordinates are given as "X Y" (quotes for clarity). Return the maximal number of points that can be used to form a single spiral.  
Definition  
 
Constraints  
  points will contain between 1 and 15 elements, inclusive.  
  Each element of points will be formatted as "X Y" (quotes for clarity), where X and Y are integers with no extra leading zeros.  
  Each X and Y will be between 1000 and 1000, inclusive.  
  All elements in points will be distinct.  
  There will be no "0 0" in points.  
Examples  
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