Kids like cakes. It’s obvious. In this problem, we consider only cakes having the form of a convex polygon, as viewed from above.
Every cake needs to be split into pieces. In this problem, every piece should have a form of a nondegenerate triangle with vertices at original cake’s vertices. The pieces may not intersect, and their union should form the original cake.
Some kids also like fairness. Let’s call the unfairness number of a cake the maximal possible difference between the areas of the largest and the smallest pieces of it.
Your task is to find the unfairness number of a given cake.