"""simple docstring"""
from ..utils import DummyObject, requires_backends



class      lowerCAmelCase_			(	metaclass=__lowerCamelCase    ):



				"""simple docstring"""
				_lowerCAmelCase   :			Dict	     =  ["""speech"""]

				def __init__( self						,			*lowerCAmelCase						,			**lowerCAmelCase			):






										"""simple docstring"""

										requires_backends(self						,			['speech']			)





class      lowerCAmelCase_			(	metaclass=__lowerCamelCase    ):



				"""simple docstring"""
				_lowerCAmelCase   :			int	     =  ["""speech"""]

				def __init__( self						,			*lowerCAmelCase						,			**lowerCAmelCase			):






										"""simple docstring"""

										requires_backends(self						,			['speech']			)







from math import ceil, sqrt



def 			_lowerCAmelCase       (					__lowerCAmelCase = 1000000      )   ->					int:


				"""simple docstring"""

				snake_case__	:      Dict     		=	0

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

