Sophia writes an algorithm to solve the graph isomorphism problem. Given a graph G=(V, E), her algorithm iterates through all permutations of the set \left\{v_{1}, \ldots, v_{|V|}\right\}, each time examining all ordered pairs \left(v_{i}, v_{j}\right) \in V \times V to see if an edge exists. When |V|=8, her algorithm makes N such examinations. What is the largest power of two that divides N?