





"""simple docstring"""


def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						UpperCamelCase				:		List[Any]				   =			""""""
						for word_or_phrase in separated:
												if not isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
																		raise Exception("""join() accepts only strings to be joined"""     )
												joined += word_or_phrase + separator
						return joined.strip(SCREAMING_SNAKE_CASE     )


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

		testmod()










"""simple docstring"""


from math import ceil, sqrt

def      UpperCamelCase							(SCREAMING_SNAKE_CASE = 100_0000     ):
						UpperCamelCase				:		int				   =			0

						for outer_width in range(3							,     (limit // 4) + 2     ):
												if outer_width**2 > limit:
																		UpperCamelCase				:		Optional[Any]				   =			max(ceil(sqrt(outer_width**2 - limit     )     )							,     1     )
												else:
																		UpperCamelCase				:		str				   =			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() = }''')



