Statement

Luca decided to enter the art business, and is opening a new modern art gallery in Milan. As soon as he opened a call for young emerging artists, his e-mail was flooded by pictures of paintings! In fact, too much to be selected by hand: he needs an algorithm to extract the most promising among them. Following blindly his profound artistic sense, developed in years studying engineering, Luca believes that the most beautiful paintings are those featuring subjects arranged symmetrically with respect to a vertical axis. Given a description of a painting, picturing N main subjects, each of them on a specific coordinate (X_i, Y_i), help Luca determine whether there exists a vertical axis of symmetry for the given points.