





import random







def        __lowerCamelCase (							__a       :int   ,					__a       :float   ,					__a       :bool = False   )		->    dict:






		"""simple docstring"""

		A__  				=       {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 (							__a       :int   )		->    dict:






		"""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()








from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def        __lowerCamelCase (							__a       :int   )		->    int:






		"""simple docstring"""

		A__  				=       prime_factors(__a   )
		if is_square_free(__a   ):
				return -1 if len(__a   ) % 2 else 1
		return 0


if __name__ == "__main__":
					import doctest

					doctest.testmod()



