



from __future__ import annotations



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	list[int]				,       SCREAMING_SNAKE_CASE__       :	list[int]				,       SCREAMING_SNAKE_CASE__       :	int				)  ->     tuple[float, list[float]]:
 _snake_case    :  Tuple					=					list(range(len(SCREAMING_SNAKE_CASE__				)				)				)
 _snake_case    :  Optional[int]					=					[v / w for v, w in zip(SCREAMING_SNAKE_CASE__				,       SCREAMING_SNAKE_CASE__				)]
 index.sort(key=lambda SCREAMING_SNAKE_CASE__				: ratio[i]				,       reverse=SCREAMING_SNAKE_CASE__				)

 _snake_case    :  float					=					0
 _snake_case    :  list[float]					=					[0] * len(SCREAMING_SNAKE_CASE__				)
 for i in index:
  if weight[i] <= capacity:
   _snake_case    :  List[Any]					=					1
   max_value += value[i]
   capacity -= weight[i]
  else:
   _snake_case    :  List[Any]					=					capacity / weight[i]
   max_value += value[i] * capacity / weight[i]
   break

 return max_value, fractions


if __name__ == "__main__":
  import doctest

  doctest.testmod()










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() = }''')
