




def 	_a      (						SCREAMING_SNAKE_CASE_							:				float     ):

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







def 	_a      (						SCREAMING_SNAKE_CASE_							:				float     ):

					if edge <= 0 or not isinstance(SCREAMING_SNAKE_CASE_      ,      SCREAMING_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()










def 	_a      (						SCREAMING_SNAKE_CASE_							:				int = 1_00_00_00     ):
					__lowerCAmelCase				   =       [i - 1 for i in range(limit + 1     )]

					for i in range(2      ,      limit + 1     ):
										if phi[i] == i - 1:
															for j in range(2 * i      ,      limit + 1      ,      SCREAMING_SNAKE_CASE_     ):
																				phi[j] -= phi[j] // i

					return sum(phi[2 : limit + 1]     )


if __name__ == "__main__":
					print(solution())




