
def 							A__       (    lowerCamelCase    )	->						str:



				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 bin(__a    ).count("""1"""    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()











"""simple docstring"""







from math import ceil, sqrt

def     UpperCAmelCase_					(				__a   :			int = 1_00_00_00						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    0

			for outer_width in range(3      ,							(limit // 4) + 2						):
						if outer_width**2 > limit:
									_lowerCamelCase					:					Optional[int]	       =    max(ceil(sqrt(outer_width**2 - limit						)						)      ,							1						)
						else:
									_lowerCamelCase					:					Any	       =    1
						if (outer_width - hole_width_lower_bound) % 2:
									hole_width_lower_bound += 1

						answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

			return answer


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





