from math import ceil, sqrt





def  _lowerCamelCase					(   a_				: int = 1_00_00_00):
			lowerCamelCase						:Tuple						  =     0

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




import os
from math import logaa





def  _lowerCamelCase					(   a_				: str = "base_exp.txt"):
			lowerCamelCase						:float						  =     0
			lowerCamelCase						:Optional[int]						  =     0
			for i, line in enumerate(open(os.path.join(os.path.dirname(a_)						,			a_))):
						lowerCamelCase  ,    lowerCamelCase						:Optional[int]						  =     list(map(a_						,			line.split(''',''')))
						if x * logaa(a_) > largest:
									lowerCamelCase						:List[Any]						  =     x * logaa(a_)
									lowerCamelCase						:Any						  =     i + 1
			return result


if __name__ == "__main__":
			print(solution())



