"""simple docstring"""


# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue





def       lowerCamelCase_			( __lowerCAmelCase    )							-> Union[str, Any]:




						'''simple docstring'''



						lowerCamelCase__ =Queue()
						lowerCamelCase__ =[False] * len(__lowerCAmelCase    )
						lowerCamelCase__ =[-1] * len(__lowerCAmelCase    )

						def bfs():
												while not queue.empty():
																		lowerCamelCase__ =queue.get()
																		lowerCamelCase__ =True

																		for neighbour in graph[u]:
																								if neighbour == u:
																														return False

																								if color[neighbour] == -1:
																														lowerCamelCase__ =1 - color[u]
																														queue.put(__lowerCAmelCase    )

																								elif color[neighbour] == color[u]:
																														return False

												return True

						for i in range(len(__lowerCAmelCase    )    ):
												if not visited[i]:
																		queue.put(__lowerCAmelCase    )
																		lowerCamelCase__ =0
																		if bfs() is False:
																								return False

						return True


if __name__ == "__main__":
	# Adjacency List of graph
	print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))



"""simple docstring"""


def       lowerCamelCase_			( __lowerCAmelCase    )							-> bool:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						if len(__lowerCAmelCase    ) == 1:
												return True
						try:
												lowerCamelCase__ =series[1] / series[0]
												for index in range(len(__lowerCAmelCase    ) - 1    ):
																		if series[index + 1] / series[index] != common_ratio:
																								return False
						except ZeroDivisionError:
												return False
						return True





def       lowerCamelCase_			( __lowerCAmelCase    )							-> float:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						lowerCamelCase__ =1
						for value in series:
												answer *= value
						return pow(__lowerCAmelCase       ,   1 / len(__lowerCAmelCase    )    )


if __name__ == "__main__":
	import doctest

	doctest.testmod()


