Problem Statement  
A parallelogram is a quadrilateral with two sets of parallel sides. You are given three distinct points A(xA,yA), B(xB,yB) and C(xC,yC) in the plane. Consider all nondegenerate parallelograms such that A, B, and C are three of its vertices. Your method should return the difference between the largest and the smallest possible perimeter of such a parallelogram. If there is no such parallelogram, return 1 instead.  
Definition  
 
Constraints  
  xA, yA, xB, yB, xC and yC will be between 5,000 and 5,000, inclusive.  
  A, B, and C will be three different points.  
Examples  
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