

'''simple docstring'''



import random
def 						__lowerCamelCase	(       __snake_case					:		Optional[int],		__snake_case					:		Union[str, Any],		__snake_case					:		List[Any] = False	)	->							Union[str, Any]:






						"""simple docstring"""





						A__					:       dict     ={i: [] for i in range(_A	)}

						# if probability is greater or equal than 1, then generate a complete graph
						if probability >= 1:
												return complete_graph(_A	)
						# if probability is lower or equal than 0, then return a graph without edges
						if probability <= 0:
												return graph

						# for each couple of nodes, add an edge from u to v
						# if the number randomly generated is greater than probability probability
						for i in range(_A	):
												for j in range(i + 1,		_A	):
																		if random.random() < probability:
																								graph[i].append(_A	)
																								if not directed:
																														# if the graph is undirected, add an edge in from j to i, either
																														graph[j].append(_A	)
						return graph
def 						__lowerCamelCase	(       __snake_case					:		Optional[Any]	)	->							Any:






						"""simple docstring"""





						return {
						    i: [j for j in range(_A	) if i != j] for i in range(_A	)
						}


if __name__ == "__main__":
						import doctest

						doctest.testmod()




'''simple docstring'''



def 						__lowerCamelCase	(       __snake_case					:		int	)	->							bool:






						"""simple docstring"""





						if p < 2:
												raise ValueError("""p should not be less than 2!"""	)
						elif p == 2:
												return True

						A__					:       Any     =4
						A__					:       int     =(1 << p) - 1
						for _ in range(p - 2	):
												A__					:       Dict     =((s * s) - 2) % m
						return s == 0


if __name__ == "__main__":
		print(lucas_lehmer_test(7))
		print(lucas_lehmer_test(11))

