Statement

Giorgio recently became very passionate about Feng Shui, the art of harmonizing everyone with the surrounding environment, and decided to rebuild his home from scratch in order to optimize his harmony with the universe. First, he searched his yard for geomagnetic nodes, producing a list of N points with coordinates (X_i, Y_i). Now, he needs to select four of those points such that together they will form a perfect square whose sides are aligned with the cardinal axes. These points will determine the perimeter of his new home. However, it is not easy to examine such a long list and as of now Giorgio has only found few very small valid squares, not really fit to contain a whole house. Help Giorgio find the largest square that obeys the Feng Shui principles!