"""simple docstring"""


def       lowerCamelCase_			( __lowerCAmelCase    )							-> int:




      '''simple docstring'''



      if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
            raise ValueError("double_factorial() only accepts integral values"    )
      if num < 0:
            raise ValueError("double_factorial() not defined for negative values"    )
      lowerCamelCase__ =1
      for i in range(__lowerCAmelCase       ,   0       ,   -2    ):
            value *= i
      return value


if __name__ == "__main__":
 import doctest

 doctest.testmod()



"""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()


