"""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()



"""simple docstring"""


from __future__ import annotations

from collections.abc import Generator





def       lowerCamelCase_			( __lowerCAmelCase    )							-> Generator[int, None, None]:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ) or n < 1:
												raise Exception("Sequence only defined for positive integers"    )

						yield n
						while n != 1:
												if n % 2 == 0:
																		n //= 2
												else:
																		lowerCamelCase__ =3 * n + 1
												yield n





def       lowerCamelCase_			( )							-> List[str]:




						'''simple docstring'''



						lowerCamelCase__ =43
						lowerCamelCase__ =tuple(collatz_sequence(__lowerCAmelCase    )    )
						print(__lowerCAmelCase    )
						print(F'''Collatz sequence from {n} took {len(__lowerCAmelCase    )} steps.'''    )


if __name__ == "__main__":
	main()


