def     A__	(       __A						):







    '''simple docstring'''
    if not isinstance(__A ,			__A						):
        raise ValueError("""Input series is not valid, valid series - [1, 2/3, 2]"""						)
    if len(__A						) == 0:
        raise ValueError("""Input list must be a non empty list"""						)
    if len(__A						) == 1 and series[0] != 0:
        return True
    _lowerCamelCase  :		Tuple			    =    []
    _lowerCamelCase  :		Union[str, Any]			    =    len(__A						)
    for i in range(0 ,			__A						):
        if series[i] == 0:
            raise ValueError("""Input series cannot have 0 as an element"""						)
        rec_series.append(1 / series[i]						)
    _lowerCamelCase  :		Any			    =    rec_series[1] - rec_series[0]
    for index in range(2 ,			__A						):
        if rec_series[index] - rec_series[index - 1] != common_diff:
            return False
    return True







def     A__	(       __A						):







    '''simple docstring'''
    if not isinstance(__A ,			__A						):
        raise ValueError("""Input series is not valid, valid series - [2, 4, 6]"""						)
    if len(__A						) == 0:
        raise ValueError("""Input list must be a non empty list"""						)
    _lowerCamelCase  :		Optional[Any]			    =    0
    for val in series:
        answer += 1 / val
    return len(__A						) / answer


if __name__ == "__main__":
    import doctest

    doctest.testmod()





import torch

from accelerate import Accelerator, DistributedType




class 						__snake_case						:





      '''simple docstring'''






      def __enter__(       self  :					Union[str, Any])					->Dict:


          """simple docstring"""


          if self.enabled:
              _lowerCamelCase  :		str			    =    self.model.no_sync()
              self.model_sync_obj.__enter__()

          return self



      def __exit__(       self  :					List[str]     ,	_UpperCamelCase  :					Any     ,	_UpperCamelCase  :					Union[str, Any]     ,	_UpperCamelCase  :					int)					->Optional[Any]:


          """simple docstring"""


          if self.enabled:
              # Average all models on exit
              self._sync_and_avg_model_params()
              self.model_sync_obj.__exit__(_UpperCamelCase     ,	_UpperCamelCase     ,	_UpperCamelCase)



      def __init__(       self  :					Union[str, Any]     ,	_UpperCamelCase  :					Accelerator     ,	_UpperCamelCase  :					torch.nn.Module     ,	_UpperCamelCase  :					int     ,	_UpperCamelCase  :					bool = True)					->int:


          """simple docstring"""


          if accelerator.distributed_type not in [
              DistributedType.NO,
              DistributedType.MULTI_CPU,
              DistributedType.MULTI_GPU,
          ]:
              raise NotImplementedError("""LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)""")
          _lowerCamelCase  :		str			    =    enabled and accelerator.distributed_type != DistributedType.NO
          _lowerCamelCase  :		Optional[int]			    =    0
          if self.enabled:
              _lowerCamelCase  :		Union[str, Any]			    =    accelerator
              _lowerCamelCase  :		int			    =    model
              _lowerCamelCase  :		int			    =    local_sgd_steps



      def 						_SCREAMING_SNAKE_CASE     (       self  :					Union[str, Any])					->Union[str, Any]:


          """simple docstring"""


          self.num_steps += 1
          if not self.enabled:
              return

          if self.num_steps % self.local_sgd_steps == 0:
              self._sync_and_avg_model_params()




      def 						_SCREAMING_SNAKE_CASE     (       self  :					Optional[Any])					->List[str]:


          """simple docstring"""


          self.accelerator.wait_for_everyone()
          with self.accelerator.autocast():
              for param in self.model.parameters():
                  _lowerCamelCase  :		Union[str, Any]			    =    self.accelerator.reduce(param.data     ,	reduction="""mean""")




