



'''simple docstring'''






def    lowerCamelCase__ (		_A = 100_0000       ):
  a		:      List[str]       =  [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				,    _A       ):
        phi[j] -= phi[j] // i

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


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




'''simple docstring'''






from ..utils import DummyObject, requires_backends

class 							a__(      metaclass=lowerCamelCase__			):
    lowercase__				=					["""torch""", """torchsde"""]







    def __init__(   self				:						Any		,    *__snake_case				:						List[str]		,    **__snake_case				:						Tuple			):
      requires_backends(self		,    ['torch', 'torchsde']			)







    @classmethod
    def     lowercase_ (   cls				:						List[Any]		,    *__snake_case				:						str		,    **__snake_case				:						List[Any]			):
      requires_backends(cls		,    ['torch', 'torchsde']			)







    @classmethod
    def     lowercase_ (   cls				:						Dict		,    *__snake_case				:						Optional[Any]		,    **__snake_case				:						str			):
      requires_backends(cls		,    ['torch', 'torchsde']			)