






"""simple docstring"""



from __future__ import annotations

def  _snake_case				(     lowerCamelCase__	:    list				,						lowerCamelCase__	:    int | None = None				,						lowerCamelCase__	:    int | None = None  )				->	Optional[Any]:





							if start is None:
														lowerCamelCase_       :							Dict									=0

							if end is None:
														lowerCamelCase_       :							List[Any]									=len(__SCREAMING_SNAKE_CASE  ) - 1

							if start >= end:
														return

							lowerCamelCase_       :							Tuple									=(start + end) // 2

							slowsort(__SCREAMING_SNAKE_CASE				,						__SCREAMING_SNAKE_CASE				,						__SCREAMING_SNAKE_CASE  )
							slowsort(__SCREAMING_SNAKE_CASE				,						mid + 1				,						__SCREAMING_SNAKE_CASE  )

							if sequence[end] < sequence[mid]:
														lowerCamelCase_       :							List[str]									=sequence[mid], sequence[end]

							slowsort(__SCREAMING_SNAKE_CASE				,						__SCREAMING_SNAKE_CASE				,						end - 1  )


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

						testmod()





'''simple docstring'''







def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: int							):



						"""simple docstring"""





						lowercase_	:     Optional[int]													=       int(__SCREAMING_SNAKE_CASE							)
						if decimal in (0, 1):  # Exit cases for the recursion
												return str(__SCREAMING_SNAKE_CASE							)
						lowercase_						, lowercase_	:     List[str]													=       divmod(__SCREAMING_SNAKE_CASE      ,      2							)
						return binary_recursive(__SCREAMING_SNAKE_CASE							) + str(__SCREAMING_SNAKE_CASE							)
def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: str							):



						"""simple docstring"""





						lowercase_	:     str													=       str(__SCREAMING_SNAKE_CASE							).strip()
						if not number:
												raise ValueError('''No input value was provided'''							)
						lowercase_	:     Optional[int]													=       '''-''' if number.startswith('''-'''							) else ''''''
						lowercase_	:     Union[str, Any]													=       number.lstrip('''-'''							)
						if not number.isnumeric():
												raise ValueError('''Input value is not an integer'''							)
						return F'''{negative}0b{binary_recursive(int(__SCREAMING_SNAKE_CASE							)							)}'''


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

							testmod()



