





import numpy as np





def     _UpperCamelCase     (a__   :np.array       ):






							"""simple docstring"""





							return 1 / (1 + np.exp(-vector       ))





def     _UpperCamelCase     (a__   :np.array       ):






							"""simple docstring"""





							return vector * sigmoid(1.702 * vector       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()











from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

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




