


"""simple docstring"""


import inspect
import warnings

import torch

from .state import AcceleratorState, GradientState
from .utils import DistributedType, honor_type, is_tpu_available


if is_tpu_available(check_device=False):
		import torch_xla.core.xla_model as xm






def    a__       ( __lowercase   ,	__lowercase      )		->		Optional[int]:
				if isinstance(__lowercase   ,	(list, tuple)      ):
								return honor_type(__lowercase   ,	(move_to_device(__lowercase   ,	__lowercase      ) for t in state)      )
				elif isinstance(__lowercase   ,	__lowercase      ):
								return type(__lowercase      )({k: move_to_device(__lowercase   ,	__lowercase      ) for k, v in state.items()}      )
				elif isinstance(__lowercase   ,	torch.Tensor      ):
								return state.to(__lowercase      )
				return state




class snake_case					(     torch.optim.Optimizer):







		def __init__(    self					:				str			,      a__					:				List[Any]			,      a__					:				Optional[int]=True			,      a__					:				Dict=None						)				->  Union[str, Any]:





						'''simple docstring'''







						_A         =	optimizer
						_A         =	scaler
						_A         =	AcceleratorState()
						_A         =	GradientState()
						_A         =	device_placement
						_A         =	False
						_A         =	None

						# Handle device placement
						if device_placement:
										_A         =	self.optimizer.state_dict()
										if self.accelerator_state.distributed_type == DistributedType.TPU:
														xm.send_cpu_data_to_device(a__			,      self.accelerator_state.device						)
										else:
														_A         =	move_to_device(a__			,      self.accelerator_state.device						)
										self.optimizer.load_state_dict(a__						)







		@property
		def        a_       (    self					:				Optional[Any]						)				->  Tuple:





						'''simple docstring'''







						return self.optimizer.state







		@state.setter
		def        a_       (    self					:				Dict			,      a__					:				Any						)				->  Dict:





						'''simple docstring'''







						_A         =	state







		@property
		def        a_       (    self					:				List[Any]						)				->  Any:





						'''simple docstring'''







						return self.optimizer.param_groups







		@param_groups.setter
		def        a_       (    self					:				Any			,      a__					:				Tuple						)				->  str:





						'''simple docstring'''







						_A         =	param_groups







		@property
		def        a_       (    self					:				List[str]						)				->  List[Any]:





						'''simple docstring'''







						return self.optimizer.defaults







		@defaults.setter
		def        a_       (    self					:				int			,      a__					:				List[str]						)				->  Optional[int]:





						'''simple docstring'''







						_A         =	defaults







		def        a_       (    self					:				Tuple			,      a__					:				List[Any]						)				->  str:





						'''simple docstring'''







						self.optimizer.add_param_group(a__						)







		def        a_       (    self					:				Any			,      a__					:				Any						)				->  List[str]:





						'''simple docstring'''







						if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
										xm.send_cpu_data_to_device(a__			,      self.accelerator_state.device						)
						self.optimizer.load_state_dict(a__						)







		def        a_       (    self					:				Optional[Any]						)				->  Dict:





						'''simple docstring'''







						return self.optimizer.state_dict()







		def        a_       (    self					:				Any			,      a__					:				List[str]=None						)				->  str:





						'''simple docstring'''







						if self.gradient_state.sync_gradients:
										_A         =	"set_to_none" in inspect.signature(self.optimizer.zero_grad						).parameters
										if accept_arg:
														if set_to_none is None:
																		_A         =	False
														self.optimizer.zero_grad(set_to_none=a__						)
										else:
														if set_to_none is not None:
																		raise ValueError("`set_to_none` for Optimizer.zero_grad` is not supported by this optimizer."						)
														self.optimizer.zero_grad()







		def        a_       (    self					:				Union[str, Any]			,      a__					:				int=None						)				->  List[Any]:





						'''simple docstring'''







						if self.gradient_state.sync_gradients:
										if self.accelerator_state.distributed_type == DistributedType.TPU:
														_A         =	{"closure": closure} if closure is not None else {}
														xm.optimizer_step(self.optimizer			,      optimizer_args=a__						)
										elif self.scaler is not None:
														_A         =	False
														if self._last_scale is None:
																		# `get_scale` is an async operation requiring full synchronization
																		# on CPU and GPUs before finishing. As a result, we store away
																		# the prior one to reduce the call overhead
																		_A         =	self.scaler.get_scale()
																		_A         =	True
														self.scaler.step(self.optimizer			,      a__						)
														self.scaler.update()
														_A         =	self.scaler.get_scale()
														if not new_scale:
																		# If we reduced the loss scale, it means the optimizer step was skipped because of gradient overflow.
																		_A         =	scale_after < self._last_scale
														_A         =	scale_after

										else:
														self.optimizer.step(a__						)







		def        a_       (    self					:				Optional[int]			,      a__					:				Dict						)				->  Tuple:





						'''simple docstring'''







						for param_group in self.optimizer.param_groups:
										_A         =	[parameters_map.get(a__			,      a__						) for p in param_group["params"]]







		@property
		def        a_       (    self					:				Optional[int]						)				->  Union[str, Any]:





						'''simple docstring'''







						warnings.warn(
						    "The `is_overflow` property is deprecated and will be removed in version 1.0 of Accelerate use "
						    "`optimizer.step_was_skipped` instead."			,      a__			,      )
						return self._is_overflow







		@property
		def        a_       (    self					:				Any						)				->  Any:





						'''simple docstring'''







						return self._is_overflow







		def __getstate__(    self					:				str						)				->  int:





						'''simple docstring'''







						return self.__dict__.copy()







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





						'''simple docstring'''







						self.__dict__.update(a__						)



"""simple docstring"""


def    a__       ( __lowercase = 20      )		->		int:

				try:
								_A         =	int(__lowercase      )
				except (TypeError, ValueError):
								raise TypeError("Parameter n must be int or castable to int."      )
				if n <= 0:
								raise ValueError("Parameter n must be greater than or equal to one."      )
				_A         =	0
				while 1:
								i += n * (n - 1)
								_A         =	0
								for j in range(2   ,	__lowercase      ):
												if i % j != 0:
																_A         =	1
																break
								if nfound == 0:
												if i == 0:
																_A         =	1
												return i
				return None


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