






'''simple docstring'''

from math import ceil, sqrt
def     __lowercase  (_lowercase = 1_000_000     )   ->     int:


     """simple docstring"""
     __lowerCamelCase						:       List[Any]				   =				0

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











'''simple docstring'''

from ..utils import DummyObject, requires_backends







class 	SCREAMING_SNAKE_CASE	(      metaclass=lowerCAmelCase_  ):
       snake_case__    :     Union[str, Any]   		=			['torch', 'torchsde']




       def __init__(					self      : int	,    *A__      : Optional[Any]	,    **A__      : Dict					):


            """simple docstring"""







            requires_backends(self	,    ["""torch""", """torchsde"""]					)




       @classmethod
       def 					a_					(					cls      : Optional[Any]	,    *A__      : str	,    **A__      : Optional[Any]					):


            """simple docstring"""







            requires_backends(cls	,    ["""torch""", """torchsde"""]					)




       @classmethod
       def 					a_					(					cls      : Union[str, Any]	,    *A__      : Any	,    **A__      : Union[str, Any]					):


            """simple docstring"""







            requires_backends(cls	,    ["""torch""", """torchsde"""]					)



