



"""simple docstring"""


def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int = 100_0000				):






				'''simple docstring'''



				_UpperCAmelCase					=    [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())








"""simple docstring"""


class 			_a :
			"""simple docstring"""



			def __init__(		self     :    Tuple				,   __UpperCamelCase     :    list[int]   )->None:
							_UpperCAmelCase					=    len(__UpperCamelCase   )
							_UpperCAmelCase					=    [0] * len_array

							if len_array > 0:
											_UpperCAmelCase					=    array[0]

							for i in range(1				,   __UpperCamelCase   ):
											_UpperCAmelCase					=    self.prefix_sum[i - 1] + array[i]



			def  lowercase__						(		self     :    str				,   __UpperCamelCase     :    int				,   __UpperCamelCase     :    int   )->int:
							if start == 0:
											return self.prefix_sum[end]

							return self.prefix_sum[end] - self.prefix_sum[start - 1]



			def  lowercase__						(		self     :    Any				,   __UpperCamelCase     :    int   )->bool:
							_UpperCAmelCase					=    {0}
							for sum_item in self.prefix_sum:
											if sum_item - target_sum in sums:
															return True

											sums.add(__UpperCamelCase   )

							return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()



