def _lowerCamelCase  (		snake_case  ):

							if edge <= 0 or not isinstance(snake_case     , snake_case  ):
														raise ValueError('Length must be a positive.'  )
							return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)






def _lowerCamelCase  (		snake_case  ):

							if edge <= 0 or not isinstance(snake_case     , snake_case  ):
														raise ValueError('Length must be a positive.'  )
							return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
				import doctest

				doctest.testmod()







from math import ceil, sqrt






def _lowerCamelCase  (		snake_case = 1_000_000  ):
							_lowerCAmelCase							=							0

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






