





from __future__ import annotations





def      lowerCAmelCase_ (       __a	,    __a	,    __a		)     ->		tuple[float, list[float]]:







  """simple docstring"""





  lowerCamelCase__:      Any			  =list(range(len(__a		)		)		)
  lowerCamelCase__:      Optional[Any]			  =[v / w for v, w in zip(__a	,    __a		)]
  index.sort(key=lambda __a		: ratio[i]	,    reverse=__a		)

  lowerCamelCase__:      float			  =0
  lowerCamelCase__:      list[float]			  =[0] * len(__a		)
  for i in index:
    if weight[i] <= capacity:
      lowerCamelCase__:      Optional[int]			  =1
      max_value += value[i]
      capacity -= weight[i]
    else:
      lowerCamelCase__:      Optional[int]			  =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      lowerCAmelCase_ (       __a = 1000000		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =0

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

