






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       ):

					'''simple docstring'''







					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   SCREAMING_SNAKE_CASE (       torch.optim.Optimizer    ):





							"""simple docstring"""

							def __init__(     self:      List[Any]						,   __A:      Union[str, Any]						,   __A:      str=True						,   __A:      List[str]=None      )			-> Optional[Any]:
												_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:      str      )			-> int:
												return self.optimizer.state

							@state.setter
							def 					__A       (     self:      Any						,   __A:      Tuple      )			-> str:
												_A									=       state

							@property
							def 					__A       (     self:      str      )			-> List[Any]:
												return self.optimizer.param_groups

							@param_groups.setter
							def 					__A       (     self:      List[str]						,   __A:      int      )			-> Dict:
												_A									=       param_groups

							@property
							def 					__A       (     self:      Optional[int]      )			-> Dict:
												return self.optimizer.defaults

							@defaults.setter
							def 					__A       (     self:      Optional[Any]						,   __A:      Optional[int]      )			-> List[Any]:
												_A									=       defaults

							def 					__A       (     self:      Optional[Any]						,   __A:      str      )			-> Dict:
												self.optimizer.add_param_group(__A      )

							def 					__A       (     self:      Tuple						,   __A:      List[str]      )			-> Union[str, Any]:
												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]      )			-> Any:
												return self.optimizer.state_dict()

							def 					__A       (     self:      Union[str, Any]						,   __A:      Optional[int]=None      )			-> int:
												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:      Dict						,   __A:      Optional[Any]=None      )			-> Dict:
												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:      Dict						,   __A:      Tuple      )			-> Optional[int]:
												for param_group in self.optimizer.param_groups:
																	_A									=       [parameters_map.get(__A						,   __A      ) for p in param_group['''params''']]

							@property
							def 					__A       (     self:      Union[str, Any]      )			-> str:
												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:      List[Any]      )			-> str:
												return self._is_overflow

							def __getstate__(     self:      str      )			-> Optional[Any]:
												return self.__dict__.copy()



							def __setstate__(     self:      Optional[int]						,   __A:      int      )			-> Optional[int]:
												self.__dict__.update(__A      )











import math

def    lowerCAmelCase__		(			_a				:	int			):

		if 1 < number < 4:
				# 2 and 3 are primes
				return True
		elif number < 2 or number % 2 == 0 or number % 3 == 0:
				# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
				return False

		# All primes number are in format of 6k +/- 1
		for i in range(5     ,					int(math.sqrt(_a			) + 1			)     ,					6			):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True

def    lowerCAmelCase__		(			_a				:	int = 60_08_51_47_51_43			):

		try:
				snake_case_ :							int         =				int(_a			)
		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."			)
		snake_case_ :							Dict         =				0
		if is_prime(_a			):
				return n
		while n % 2 == 0:
				n //= 2
		if is_prime(_a			):
				return n
		for i in range(3     ,					int(math.sqrt(_a			)			) + 1     ,					2			):
				if n % i == 0:
						if is_prime(n // i			):
								snake_case_ :							List[Any]         =				n // i
								break
						elif is_prime(_a			):
								snake_case_ :							str         =				i
		return max_number


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