


from math import factorial




def    a   (							A__ = 2_0							)	-> int:




      '''simple docstring'''

      SCREAMING_SNAKE_CASE__       :  Tuple						     =		2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
      # 2, 3,...
      SCREAMING_SNAKE_CASE__       :  Dict						     =		n // 2

      return int(factorial(A__							) / (factorial(A__							) * factorial(n - k							))							)


if __name__ == "__main__":
    import sys

    if len(sys.argv) == 1:
        print(solution(20))
    else:
        try:
            a_ :str  							=			int(sys.argv[1])
            print(solution(n))
        except ValueError:
            print('Invalid entry - please enter a number.')












'''simple docstring'''







# 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 					_a :





     '''simple docstring'''



     def __init__(				self							,__a							,__a							,__a = True							,__a = False							)      ->				Dict:
          snake_case			:      List[Any]        =			scheduler
          snake_case			:      List[Any]        =			optimizers if isinstance(__a							,(list, tuple)							) else [optimizers]
          snake_case			:      List[str]        =			split_batches
          snake_case			:      List[str]        =			step_with_optimizer
          snake_case			:      int        =			GradientState()







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







     def 			snake_case_      (				self							)      ->				Dict:
          return self.scheduler.get_last_lr()







     def 			snake_case_      (				self							)      ->				int:
          return self.scheduler.state_dict()







     def 			snake_case_      (				self							,__a							)      ->				Any:
          self.scheduler.load_state_dict(__a							)







     def 			snake_case_      (				self							)      ->				Any:
          return self.scheduler.get_lr()







     def 			snake_case_      (				self							,*__a							,**__a							)      ->				Optional[Any]:
          return self.scheduler.print_lr(*__a							,**__a							)



