






from math import ceil, sqrt






def   a			(						lowerCamelCase_ = 100_0000				):






				'''simple docstring'''
				lowercase__    =			0

				for outer_width in range(3		,   (limit // 4) + 2				):
								if outer_width**2 > limit:
												lowercase__    =			max(ceil(sqrt(outer_width**2 - limit				)				)		,   1				)
								else:
												lowercase__    =			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() = }")












from math import asin, atan, cos, radians, sin, sqrt, tan

A__	:			Optional[int]			   = 637_8137.0
A__	:			List[str]			   = 635_6752.31_4245
A__	:			Union[str, Any]			   = 6_37_81_37






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_				):






				'''simple docstring'''
				lowercase__    =			(AXIS_A - AXIS_B) / AXIS_A
				lowercase__    =			atan((1 - flattening) * tan(radians(lowerCamelCase_				)				)				)
				lowercase__    =			atan((1 - flattening) * tan(radians(lowerCamelCase_				)				)				)
				lowercase__    =			radians(lowerCamelCase_				)
				lowercase__    =			radians(lowerCamelCase_				)
				# Equation
				lowercase__    =			sin((phi_a - phi_a) / 2				)
				lowercase__    =			sin((lambda_a - lambda_a) / 2				)
				# Square both values
				sin_sq_phi *= sin_sq_phi
				sin_sq_lambda *= sin_sq_lambda
				lowercase__    =			sqrt(sin_sq_phi + (cos(lowerCamelCase_				) * cos(lowerCamelCase_				) * sin_sq_lambda)				)
				return 2 * RADIUS * asin(lowerCamelCase_				)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




