




'''simple docstring'''





def 					UpperCamelCase_(     snake_case							:	int = 1_0_0_0_0_0_0					):

							'''simple docstring'''






							snake_case_      =				[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							,    snake_case					):
																												phi[j] -= phi[j] // i

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


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










'''simple docstring'''





def 					UpperCamelCase_(     snake_case							:	int = 1_0_0_0_0_0_0					):

							'''simple docstring'''






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

							snake_case_      =				[float(snake_case					) for n in range(limit + 1					)]

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

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


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




