Statement

Luca is attending a course about graph algorithms but he is a bit bored: the lectures are covering pretty basic topics on graphs, which have been already explained many times. To kill time, Luca starts playing with his imagination and dreams a grasshopper jumping on graph nodes. Everyone knows that dreams are often an exaggeration of the reality: the grasshopper, in this dream, does not jump directly from a vertex on the graph to an adjacent vertex. Instead, it always jumps two vertices at a time: when it passes on the vertex in the middle, it's still "flying"! The lesson is ending and Luca just woke up from the dream. He is still thinking about it, puzzled with an important question: how many vertices could the imaginary grasshopper reach, starting from vertex 0 and jumping however many times it wants?