




from math import ceil, sqrt





def 		__A		(	__lowerCamelCase = 100_0000    )      ->       int:
	a										=							0

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





def 		__A		(	__lowerCamelCase    )      ->       float:
	if num <= 0:
		raise ValueError("""math domain error"""    )
	if num > 171.5:
		raise OverflowError("""math range error"""    )
	elif num - int(__lowerCamelCase    ) not in (0, 0.5):
		raise NotImplementedError("""num must be an integer or a half-integer"""    )
	elif num == 0.5:
		return sqrt(__lowerCamelCase    )
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1    )





def 		__A		(	)      ->       None:
	assert gamma(0.5    ) == sqrt(__lowerCamelCase    )
	assert gamma(1    ) == 1.0
	assert gamma(2    ) == 1.0


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

		testmod()
		__UpperCamelCase					:       str    					=      1.0
		while num:
				__UpperCamelCase					:       Dict    					=      float(input("Gamma of: "))
				print(F'gamma({num}) = {gamma(num)}')
				print("\nEnter 0 to exit...")

