Annie would like to visit as many restaurants as possible in the shortest amount of time. To do so, she plots all the restaurants as an undirected graph to get a visual overview of every place she wants to eat. Surprisingly enough, all the restaurants that are connected by an edge in the graph are exactly 1 mile apart. Annie can only stay from Monday to Friday (5 days) and would like to visit a different set of restaurants each day. She doesnt want to eat at restaurants connected by an edge on the same day, and she doesnt want to eat at any restaurant multiple times throughout the week. Prove that if Annie cannot find a way to eat at every restaurant while satisfying these restrictions, there are at least two cycles of restaurants such that the total distance around each cycle is an odd number of miles and that the two cycles dont share any restaurants.