



"""simple docstring"""

from math import loga




def __lowercase    (							_a					):
				if a < 0:
								raise ValueError('''Input value must be a positive integer'''					)
				elif isinstance(_A	,    _A					):
								raise TypeError('''Input value must be a \'int\' type'''					)
				return 0 if (a == 0) else int(loga(a & -a					)					)


if __name__ == "__main__":
					import doctest

					doctest.testmod()










"""simple docstring"""

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




def __lowercase    (							_a					):
    snake_case_				:  Dict       =			str(_a					).strip()
    if not number:
        raise ValueError('''No input value was provided'''					)
    snake_case_				:  List[str]       =			'''-''' if number.startswith('''-'''					) else ''''''
    snake_case_				:  Optional[Any]       =			number.lstrip('''-'''					)
    if not number.isnumeric():
        raise ValueError('''Input value is not an integer'''					)
    return f"{negative}0b{binary_recursive(int(_a					)					)}"


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

     testmod()





