






"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					int			):
			"""simple docstring"""
			lowerCamelCase__	:	Dict				=int(snake_case_			)
			if decimal in (0, 1):  # Exit cases for the recursion
						return str(snake_case_			)
			lowerCamelCase__	:	Dict				=divmod(snake_case_							,	2			)
			return binary_recursive(snake_case_			) + str(snake_case_			)






def   snake_case__     (	__lowerCamelCase       :					str			):
			"""simple docstring"""
			lowerCamelCase__	:	Union[str, Any]				=str(snake_case_			).strip()
			if not number:
						raise ValueError('''No input value was provided'''			)
			lowerCamelCase__	:	Optional[int]				="-" if number.startswith('''-'''			) else ""
			lowerCamelCase__	:	Optional[Any]				=number.lstrip('''-'''			)
			if not number.isnumeric():
						raise ValueError('''Input value is not an integer'''			)
			return f'''{negative}0b{binary_recursive(int(snake_case_			)			)}'''


if __name__ == "__main__":
		from doctest import testmod

		testmod()









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					list[int]			):
			"""simple docstring"""
			if not numbers:
						return 0

			if not isinstance(__lowerCamelCase							,	(list, tuple)			) or not all(
			    isinstance(__lowerCamelCase							,	__lowerCamelCase			) for number in numbers			):
						raise ValueError('''numbers must be an iterable of integers'''			)

			lowerCamelCase__	:	Any				=numbers[0]

			for i in range(1							,	len(__lowerCamelCase			)			):
						# update the maximum and minimum subarray products
						lowerCamelCase__	:	Dict				=numbers[i]
						if number < 0:
									lowerCamelCase__			,     lowerCamelCase__	:	List[Any]				=min_till_now, max_till_now
						lowerCamelCase__	:	Optional[int]				=max(__lowerCamelCase							,	max_till_now * number			)
						lowerCamelCase__	:	Dict				=min(__lowerCamelCase							,	min_till_now * number			)

						# update the maximum product found till now
						lowerCamelCase__	:	Tuple				=max(__lowerCamelCase							,	__lowerCamelCase			)

			return max_prod




