




from functools import lru_cache

def       a (_lowerCAmelCase  ):
							SCREAMING_SNAKE_CASE_ 						=     2
							SCREAMING_SNAKE_CASE_ 						=     set()
							while i * i <= n:
														if n % i:
																					i += 1
														else:
																					n //= i
																					factors.add(lowerCAmelCase_  )
							if n > 1:
														factors.add(lowerCAmelCase_  )
							return factors

@lru_cache
def       a (_lowerCAmelCase  ):
							return len(unique_prime_factors(lowerCAmelCase_  )  )

def       a (_lowerCAmelCase  ):
							return len(set(lowerCAmelCase_  )  ) in (0, 1)

def       a (_lowerCAmelCase  ):
							SCREAMING_SNAKE_CASE_ 						=     2

							while True:
														# Increment each value of a generated range
														SCREAMING_SNAKE_CASE_ 						=     [base + i for i in range(lowerCAmelCase_  )]

														# Run elements through out unique_prime_factors function
														# Append our target number to the end.
														SCREAMING_SNAKE_CASE_ 						=     [upf_len(lowerCAmelCase_  ) for x in group]
														checker.append(lowerCAmelCase_  )

														# If all numbers in the list are equal, return the group variable.
														if equality(lowerCAmelCase_  ):
																					return group

														# Increment our base variable by 1
														base += 1

def       a (_lowerCAmelCase = 4  ):
							SCREAMING_SNAKE_CASE_ 						=     run(lowerCAmelCase_  )
							return results[0] if len(lowerCAmelCase_  ) else None


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







'''simple docstring'''

def 	__lowerCamelCase	( lowerCAmelCase_ = 1000000    )     -> int:
		_a	: Optional[int]								=				set(range(3		,     lowerCAmelCase_		,     2    )    )
		primes.add(2    )
		for p in range(3		,     lowerCAmelCase_		,     2    ):
				if p not in primes:
						continue
				primes.difference_update(set(range(p * p		,     lowerCAmelCase_		,     lowerCAmelCase_    )    )    )

		_a	: Tuple								=				[float(lowerCAmelCase_    ) for n in range(limit + 1    )]

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

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


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




