class 			UpperCamelCase					:

     '''simple docstring'''

     def __init__(       self					,					A_    )			->					int:






           """simple docstring"""
           _lowerCamelCase           =					data
           _lowerCamelCase           =					None
           _lowerCamelCase           =					None





     def __str__(       self    )			->					List[str]:






           """simple docstring"""
           return F'{self.data}'





class 			UpperCamelCase					:

     '''simple docstring'''

     def __init__(       self    )			->					int:






           """simple docstring"""
           _lowerCamelCase           =					None
           _lowerCamelCase           =					None



     def __iter__(       self    )			->					Optional[Any]:






           """simple docstring"""
           _lowerCamelCase           =					self.head
           while node:
                 yield node.data
                 _lowerCamelCase           =					node.next



     def __str__(       self    )			->					List[Any]:






           """simple docstring"""
           return "->".join([str(A_    ) for item in self]    )



     def __len__(       self    )			->					int:






           """simple docstring"""
           return sum(1 for _ in self    )



     def 		UpperCamelCase_    (       self					,					A_    )			->					Tuple:






           """simple docstring"""
           self.insert_at_nth(0					,					A_    )



     def 		UpperCamelCase_    (       self					,					A_    )			->					List[str]:






           """simple docstring"""
           self.insert_at_nth(len(self    )					,					A_    )



     def 		UpperCamelCase_    (       self					,					A_					,					A_    )			->					List[str]:






           """simple docstring"""
           _lowerCamelCase           =					len(self    )

           if not 0 <= index <= length:
                 raise IndexError('''list index out of range'''    )
           _lowerCamelCase           =					Node(A_    )
           if self.head is None:
                 _lowerCamelCase           =					_lowerCamelCase           =					new_node
           elif index == 0:
                 _lowerCamelCase           =					new_node
                 _lowerCamelCase           =					self.head
                 _lowerCamelCase           =					new_node
           elif index == length:
                 _lowerCamelCase           =					new_node
                 _lowerCamelCase           =					self.tail
                 _lowerCamelCase           =					new_node
           else:
                 _lowerCamelCase           =					self.head
                 for _ in range(0					,					A_    ):
                       _lowerCamelCase           =					temp.next
                 _lowerCamelCase           =					new_node
                 _lowerCamelCase           =					temp.previous
                 _lowerCamelCase           =					temp
                 _lowerCamelCase           =					new_node



     def 		UpperCamelCase_    (       self    )			->					List[str]:






           """simple docstring"""
           return self.delete_at_nth(0    )



     def 		UpperCamelCase_    (       self    )			->					int:






           """simple docstring"""
           return self.delete_at_nth(len(self    ) - 1    )



     def 		UpperCamelCase_    (       self					,					A_    )			->					Optional[Any]:






           """simple docstring"""
           _lowerCamelCase           =					len(self    )

           if not 0 <= index <= length - 1:
                 raise IndexError('''list index out of range'''    )
           _lowerCamelCase           =					self.head  # default first node
           if length == 1:
                 _lowerCamelCase           =					_lowerCamelCase           =					None
           elif index == 0:
                 _lowerCamelCase           =					self.head.next
                 _lowerCamelCase           =					None
           elif index == length - 1:
                 _lowerCamelCase           =					self.tail
                 _lowerCamelCase           =					self.tail.previous
                 _lowerCamelCase           =					None
           else:
                 _lowerCamelCase           =					self.head
                 for _ in range(0					,					A_    ):
                       _lowerCamelCase           =					temp.next
                 _lowerCamelCase           =					temp
                 _lowerCamelCase           =					temp.previous
                 _lowerCamelCase           =					temp.next
           return delete_node.data



     def 		UpperCamelCase_    (       self					,					A_    )			->					str:






           """simple docstring"""
           _lowerCamelCase           =					self.head

           while current.data != data:  # Find the position to delete
                 if current.next:
                       _lowerCamelCase           =					current.next
                 else:  # We have reached the end an no value matches
                       raise ValueError('''No data matching given value'''    )

           if current == self.head:
                 self.delete_head()

           elif current == self.tail:
                 self.delete_tail()

           else:  # Before: 1 <--> 2(current) <--> 3
                 _lowerCamelCase           =					current.next  # 1 --> 3
                 _lowerCamelCase           =					current.previous  # 1 <--> 3
           return data





     def 		UpperCamelCase_    (       self    )			->					List[Any]:






           """simple docstring"""
           return len(self    ) == 0





def    __magic_name__(	)    ->     None:



      '''simple docstring'''

      _lowerCamelCase           =					DoublyLinkedList()
      assert linked_list.is_empty() is True
      assert str(__UpperCAmelCase		) == ""

      try:
            linked_list.delete_head()
            raise AssertionError  # This should not happen.
      except IndexError:
            assert True  # This should happen.

      try:
            linked_list.delete_tail()
            raise AssertionError  # This should not happen.
      except IndexError:
            assert True  # This should happen.

      for i in range(10		):
            assert len(__UpperCAmelCase		) == i
            linked_list.insert_at_nth(__UpperCAmelCase			,    i + 1		)
      assert str(__UpperCAmelCase		) == "->".join(str(__UpperCAmelCase		) for i in range(1			,    11		)		)

      linked_list.insert_at_head(0		)
      linked_list.insert_at_tail(11		)
      assert str(__UpperCAmelCase		) == "->".join(str(__UpperCAmelCase		) for i in range(0			,    12		)		)

      assert linked_list.delete_head() == 0
      assert linked_list.delete_at_nth(9		) == 10
      assert linked_list.delete_tail() == 11
      assert len(__UpperCAmelCase		) == 9
      assert str(__UpperCAmelCase		) == "->".join(str(__UpperCAmelCase		) for i in range(1			,    10		)		)


if __name__ == "__main__":
     from doctest import testmod

     testmod()
import torch

from accelerate import Accelerator, DistributedType



class 			UpperCamelCase					:

     '''simple docstring'''

     def __enter__(       self    )			->					int:






           """simple docstring"""
           if self.enabled:
                 _lowerCamelCase           =					self.model.no_sync()
                 self.model_sync_obj.__enter__()

           return self



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






           """simple docstring"""
           if self.enabled:
                 # Average all models on exit
                 self._sync_and_avg_model_params()
                 self.model_sync_obj.__exit__(A_					,					A_					,					A_    )



     def __init__(       self					,					A_					,					A_					,					A_					,					A_ = True    )			->					List[str]:






           """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           =					enabled and accelerator.distributed_type != DistributedType.NO
           _lowerCamelCase           =					0
           if self.enabled:
                 _lowerCamelCase           =					accelerator
                 _lowerCamelCase           =					model
                 _lowerCamelCase           =					local_sgd_steps



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






           """simple docstring"""
           self.accelerator.wait_for_everyone()
           with self.accelerator.autocast():
                 for param in self.model.parameters():
                       _lowerCamelCase           =					self.accelerator.reduce(param.data					,					reduction='''mean'''    )