






# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("ignore", category=UserWarning, module="torch.optim.lr_scheduler")






class 		lowercase_					:






      '''simple docstring'''




      def __init__(      self      :						Union[str, Any] ,					__UpperCAmelCase      :						Any ,					__UpperCAmelCase      :						Any ,					__UpperCAmelCase      :						bool = True ,					__UpperCAmelCase      :						bool = False  )    ->Dict:




       """simple docstring"""


       a		  =      scheduler
       a		  =      optimizers if isinstance(__UpperCAmelCase ,					(list, tuple)  ) else [optimizers]
       a		  =      split_batches
       a		  =      step_with_optimizer
       a		  =      GradientState()







      def       __lowerCAmelCase					(      self      :						int ,					*__UpperCAmelCase      :						List[str] ,					**__UpperCAmelCase      :						str  )    ->str:




       """simple docstring"""


       if not self.step_with_optimizer:
        # No link between scheduler and optimizer -> just step
        self.scheduler.step(*__UpperCAmelCase ,					**__UpperCAmelCase  )
        return

       # Otherwise, first make sure the optimizer was stepped.
       if not self.gradient_state.sync_gradients:
        if self.gradient_state.adjust_scheduler:
         self.scheduler._step_count += 1
        return

       for opt in self.optimizers:
        if opt.step_was_skipped:
         return
       if self.split_batches:
        # Split batches -> the training dataloader batch size is not changed so one step per training step
        self.scheduler.step(*__UpperCAmelCase ,					**__UpperCAmelCase  )
       else:
        # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
        # num_processes steps per training step
        a		  =      AcceleratorState().num_processes
        for _ in range(__UpperCAmelCase  ):
         # Special case when using OneCycle and `drop_last` was not used
         if hasattr(self.scheduler ,					'''total_steps'''  ):
          if self.scheduler._step_count <= self.scheduler.total_steps:
           self.scheduler.step(*__UpperCAmelCase ,					**__UpperCAmelCase  )
         else:
          self.scheduler.step(*__UpperCAmelCase ,					**__UpperCAmelCase  )







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




       """simple docstring"""


       return self.scheduler.get_last_lr()







      def       __lowerCAmelCase					(      self      :						Tuple  )    ->Optional[Any]:




       """simple docstring"""


       return self.scheduler.state_dict()







      def       __lowerCAmelCase					(      self      :						Optional[int] ,					__UpperCAmelCase      :						Tuple  )    ->Optional[int]:




       """simple docstring"""


       self.scheduler.load_state_dict(__UpperCAmelCase  )







      def       __lowerCAmelCase					(      self      :						Any  )    ->Dict:




       """simple docstring"""


       return self.scheduler.get_lr()







      def       __lowerCAmelCase					(      self      :						Union[str, Any] ,					*__UpperCAmelCase      :						str ,					**__UpperCAmelCase      :						Any  )    ->Union[str, Any]:




       """simple docstring"""


       return self.scheduler.print_lr(*__UpperCAmelCase ,					**__UpperCAmelCase  )










def 						_a    (      a :int = 100 )							->			int:
 a		  =      n * (n + 1) * (2 * n + 1) / 6
 a		  =      (n * (n + 1) / 2) ** 2
 return int(square_of_sum - sum_of_squares )


if __name__ == "__main__":
     print(f"""{solution() = }""")


