





def      lowerCAmelCase_ (       __a = 10**9		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      str			  =1
  lowerCamelCase__:      Optional[int]			  =2

  lowerCamelCase__:      List[str]			  =0
  lowerCamelCase__:      Dict			  =0
  lowerCamelCase__:      Any			  =0
  while perimeter <= max_perimeter:
    perimeters_sum += perimeter

    prev_value += 2 * value
    value += prev_value

    lowerCamelCase__:      Optional[Any]			  =2 * value + 2 if i % 2 == 0 else 2 * value - 2
    i += 1

  return perimeters_sum


if __name__ == "__main__":
     print(f'{solution() = }')








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() = }')

