
def 						UpperCAmelCase			(	a_ = 1_0_0_0_0_0_0						)		->	int:







				"""simple docstring"""



				__A   			= set(range(3		,   a_		,   2						)						)
				primes.add(2						)
				for p in range(3		,   a_		,   2						):
								if p not in primes:
												continue
								primes.difference_update(set(range(p * p		,   a_		,   a_						)						)						)

				__A   			= [float(a_						) for n in range(limit + 1						)]

				for p in primes:
								for n in range(a_		,   limit + 1		,   a_						):
												phi[n] *= 1 - 1 / p

				return int(sum(phi[2:]						)						)


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






def __UpperCamelCase			(       _A  ):
						if not numbers:
												return 0

						if not isinstance(_A ,  (list, tuple)  ) or not all(
						    isinstance(_A ,  _A  ) for number in numbers  ):
												raise ValueError('''numbers must be an iterable of integers'''  )

						lowerCAmelCase_      			=  lowerCAmelCase_      			=  lowerCAmelCase_      			=  numbers[0]

						for i in range(1 ,  len(_A  )  ):
												# update the maximum and minimum subarray products
												lowerCAmelCase_      			=  numbers[i]
												if number < 0:
																		lowerCAmelCase_			,					lowerCAmelCase_      			=  min_till_now, max_till_now
												lowerCAmelCase_      			=  max(_A ,  max_till_now * number  )
												lowerCAmelCase_      			=  min(_A ,  min_till_now * number  )

												# update the maximum product found till now
												lowerCAmelCase_      			=  max(_A ,  _A  )

						return max_prod




