Statement

After decades of research, Giorgio is finally about to solve the mystery of the perfect N-hyperrectangle! This legendary geometrical structure is defined by its lower coordinate L_i and higher coordinate H_i for every axis i = 0 … N-1. In an ancient book, Giorgio has found the coordinates he was looking for. Unfortunately, the book has been shredded over the centuries, mixing up the 2N numbers into a single list V_i for i = 0 … 2N-1, and Giorgio needs to reconstruct the correct arrangement of the 2N numbers into coordinates L_i and H_i. This arrangement has to produce the largest hypervolume, computed as: (H_0 - L_0) × … \time (H_N-1 - L_N-1) Furthermore, among arrangements with the largest hypervolume, the sequence (L_0, …, L_N-1, H_0, …, H_N-1) has to be lexicographically minimum.