




def  lowerCAmelCase  (	UpperCAmelCase       )  ->bool:






					"""simple docstring"""






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







def  lowerCAmelCase  (	UpperCAmelCase       )  ->float:






					"""simple docstring"""






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


if __name__ == "__main__":
				import doctest

				doctest.testmod()









def  lowerCAmelCase  (	UpperCAmelCase       )  ->str:






					"""simple docstring"""






					return " ".join(sorted(set(sentence.split()       )       )       )


if __name__ == "__main__":
				import doctest

				doctest.testmod()



