






# 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 							_lowerCAmelCase:





       """simple docstring"""







       def __init__(   self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase = True    ,     _lowerCamelCase = False				):
         UpperCamelCase_:   Optional[int]        =							scheduler
         UpperCamelCase_:   Optional[int]        =							optimizers if isinstance(_lowercase    ,     (list, tuple)				) else [optimizers]
         UpperCamelCase_:   Tuple        =							split_batches
         UpperCamelCase_:   Any        =							step_with_optimizer
         UpperCamelCase_:   int        =							GradientState()





       def      _a       (   self    ,     *_lowerCamelCase    ,     **_lowerCamelCase				):
         if not self.step_with_optimizer:
           # No link between scheduler and optimizer -> just step
           self.scheduler.step(*_lowercase    ,     **_lowercase				)
           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(*_lowercase    ,     **_lowercase				)
         else:
           # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
           # num_processes steps per training step
           UpperCamelCase_:   List[str]        =							AcceleratorState().num_processes
           for _ in range(_lowercase				):
             # 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(*_lowercase    ,     **_lowercase				)
             else:
               self.scheduler.step(*_lowercase    ,     **_lowercase				)





       def      _a       (   self				):
         return self.scheduler.get_last_lr()





       def      _a       (   self				):
         return self.scheduler.state_dict()





       def      _a       (   self    ,     _lowerCamelCase				):
         self.scheduler.load_state_dict(_lowercase				)





       def      _a       (   self				):
         return self.scheduler.get_lr()





       def      _a       (   self    ,     *_lowerCamelCase    ,     **_lowerCamelCase				):
         return self.scheduler.print_lr(*_lowercase    ,     **_lowercase				)


def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0			)->						int:



    """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())
