


"""simple docstring"""







from __future__ import annotations




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					if len(lowerCAmelCase_   ) == 0:
										raise ValueError("find_max() arg is an empty sequence"   )
					if (
					    left >= len(lowerCAmelCase_   )
					    or left < -len(lowerCAmelCase_   )
					    or right >= len(lowerCAmelCase_   )
					    or right < -len(lowerCAmelCase_   )
					):
										raise IndexError("list index out of range"   )
					if left == right:
										return nums[left]
					__SCREAMING_SNAKE_CASE						   =				(left + right) >> 1  # the middle
					__SCREAMING_SNAKE_CASE						   =				find_max(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )  # find max in range[left, mid]
					__SCREAMING_SNAKE_CASE						   =				find_max(lowerCAmelCase_  ,						mid + 1  ,						lowerCAmelCase_   )  # find max in range[mid + 1, right]

					return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)




"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_ = 100_0000   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				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_   )   )   )

					__SCREAMING_SNAKE_CASE						   =				[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() = }")
