There are n chords on a circle with radius 1. Assume that endpoints are known {a1,a2,...}, {b1,b2,...}. Write an algorithm that finds the number of intersections between these lines and runs in O(nlogn) and prove that its correct. Proof should be formal or give clear arguments why it works (Induction/contradiction maybe used). Algorithm can be in pseudo code or clear English or an actual code in a programming language.