




def  lowerCAmelCase  (	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					if not isinstance(UpperCAmelCase,	UpperCAmelCase       ) or number < 0:
										raise ValueError('''Input must be a non-negative integer'''       )

					__magic_name__					:							int		   =							number & ~(number - 1)
					__magic_name__					:							Optional[int]		   =							0
					while intermediate:
										intermediate >>= 1
										index += 1
					return index - 1


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)









def  lowerCAmelCase  (	UpperCAmelCase       )  ->int:






					"""simple docstring"""






					return n * (2 * n - 1)







def  lowerCAmelCase  (	UpperCAmelCase       )  ->bool:






					"""simple docstring"""






					__magic_name__					:							Any		   =							(1 + 24 * n) ** 0.5
					return ((1 + root) / 6) % 1 == 0







def  lowerCAmelCase  (	UpperCAmelCase = 144       )  ->int:






					"""simple docstring"""






					__magic_name__					:							Optional[int]		   =							start
					__magic_name__					:							int		   =							hexagonal_num(UpperCAmelCase       )
					while not is_pentagonal(UpperCAmelCase       ):
										n += 1
										__magic_name__					:							Optional[int]		   =							hexagonal_num(UpperCAmelCase       )
					return num


if __name__ == "__main__":
				print(f"{solution()} = ")



