Count Number of Trapezoids II

Count the number of 4-point subsets that form a trapezoid — i.e., a convex quadrilateral with at least one pair of parallel sides — from up to 500 distinct points. The core challenge is combinatorially counting pairs of disjoint point-segments with the same slope (parallel sides) while excluding degenerate/overlapping cases, typically done by grouping point-pairs by reduced slope in O(n^2) time.