Eulerian path exists

Given a directed graph with n nodes (0..n-1) and a list of directed edges, return True iff it has an Eulerian path: a walk that uses every edge exactly once (not necessarily returning to the start). The conditions are: at most one vertex with out-degree - in-degree == 1 (the start) and at most one with in-degree - out-degree == 1 (the end), all others balanced, AND all edges lie in a single connected component (ignoring isolated vertices). An empty edge list returns True. Assume 1 <= n <= 10000.