





'''simple docstring'''






from math import ceil, sqrt






def      __A						(							a_						:  int = 1_0_0_0_0_0_0	):
		lowerCAmelCase     :    int						=   0

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










'''simple docstring'''






def      __A						(							a_						:  int	):
		assert (
		    isinstance(a_      ,a_	) and number_of_steps > 0
		), f'''number_of_steps needs to be positive integer, your input {number_of_steps}'''
		if number_of_steps == 1:
				return 1
		lowerCAmelCase	,		lowerCAmelCase     :    int						=   1, 1
		for _ in range(number_of_steps - 1	):
				lowerCAmelCase	,		lowerCAmelCase     :    Union[str, Any]						=   current + previous, current
		return current


if __name__ == "__main__":
					import doctest

					doctest.testmod()



