



from math import ceil, sqrt



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	int = 1_000_000				)  ->     int:
 _snake_case    :  Tuple					=					0

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





from math import ceil, sqrt



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	int = 1_000_000				)  ->     int:
 _snake_case    :  Tuple					=					0

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