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 		__lowerCamelCase							(UpperCAmelCase__   :							Tuple					,       UpperCAmelCase__   :							Optional[Any]     ):



					if isinstance(UpperCAmelCase__					,       (list, tuple)     ):
										return honor_type(UpperCAmelCase__					,       (move_to_device(UpperCAmelCase__					,       UpperCAmelCase__     ) for t in state)     )
					elif isinstance(UpperCAmelCase__					,       UpperCAmelCase__     ):
										return type(UpperCAmelCase__     )({k: move_to_device(UpperCAmelCase__					,       UpperCAmelCase__     ) for k, v in state.items()}     )
					elif isinstance(UpperCAmelCase__					,       torch.Tensor     ):
										return state.to(UpperCAmelCase__     )
					return state


class   lowercase			(   torch.optim.Optimizer   ):




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



												'''simple docstring'''

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

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




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



												'''simple docstring'''

												return self.optimizer.state




							@state.setter
							def 		__snake_case(  self      :    Optional[Any]		,							_UpperCamelCase      :    Union[str, Any]					)    -> Any:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				state




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



												'''simple docstring'''

												return self.optimizer.param_groups




							@param_groups.setter
							def 		__snake_case(  self      :    List[str]		,							_UpperCamelCase      :    Union[str, Any]					)    -> Optional[Any]:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				param_groups




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



												'''simple docstring'''

												return self.optimizer.defaults




							@defaults.setter
							def 		__snake_case(  self      :    Any		,							_UpperCamelCase      :    int					)    -> int:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				defaults




							def 		__snake_case(  self      :    List[Any]		,							_UpperCamelCase      :    List[str]					)    -> Union[str, Any]:



												'''simple docstring'''

												self.optimizer.add_param_group(snake_case__					)




							def 		__snake_case(  self      :    str		,							_UpperCamelCase      :    List[Any]					)    -> Optional[int]:



												'''simple docstring'''

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




							def 		__snake_case(  self      :    int					)    -> Any:



												'''simple docstring'''

												return self.optimizer.state_dict()




							def 		__snake_case(  self      :    Any		,							_UpperCamelCase      :    Dict=None					)    -> List[Any]:



												'''simple docstring'''

												if self.gradient_state.sync_gradients:
																	SCREAMING_SNAKE_CASE				=				"set_to_none" in inspect.signature(self.optimizer.zero_grad					).parameters
																	if accept_arg:
																						if set_to_none is None:
																											SCREAMING_SNAKE_CASE				=				False
																						self.optimizer.zero_grad(set_to_none=snake_case__					)
																	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 		__snake_case(  self      :    Dict		,							_UpperCamelCase      :    Optional[Any]=None					)    -> List[str]:



												'''simple docstring'''

												if self.gradient_state.sync_gradients:
																	if self.accelerator_state.distributed_type == DistributedType.TPU:
																						SCREAMING_SNAKE_CASE				=				{"closure": closure} if closure is not None else {}
																						xm.optimizer_step(self.optimizer		,							optimizer_args=snake_case__					)
																	elif self.scaler is not None:
																						SCREAMING_SNAKE_CASE				=				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
																											SCREAMING_SNAKE_CASE				=				self.scaler.get_scale()
																											SCREAMING_SNAKE_CASE				=				True
																						self.scaler.step(self.optimizer		,							snake_case__					)
																						self.scaler.update()
																						SCREAMING_SNAKE_CASE				=				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.
																											SCREAMING_SNAKE_CASE				=				scale_after < self._last_scale
																						SCREAMING_SNAKE_CASE				=				scale_after

																	else:
																						self.optimizer.step(snake_case__					)




							def 		__snake_case(  self      :    Optional[int]		,							_UpperCamelCase      :    int					)    -> Tuple:



												'''simple docstring'''

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




							@property
							def 		__snake_case(  self      :    List[Any]					)    -> 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."		,							snake_case__		,							)
												return self._is_overflow




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



												'''simple docstring'''

												return self._is_overflow




							def __getstate__(  self      :    List[str]					)    -> int:



												'''simple docstring'''

												return self.__dict__.copy()





							def __setstate__(  self      :    Optional[Any]		,							_UpperCamelCase      :    List[str]					)    -> Any:



												'''simple docstring'''

												self.__dict__.update(snake_case__					)












"""simple docstring"""







import math
from decimal import Decimal, getcontext





def 						lowercase__(A = 4_000_000						)				->int:




						"""simple docstring"""



						try:
												lowercase__				:      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."						)
						lowercase__				:      Dict=       100
						lowercase__				:      Optional[Any]=       (Decimal(5						) ** Decimal(0.5						) + 1) / Decimal(2						)

						lowercase__				:      str=       (math.floor(math.log(n * (phi + 2)					,		A						) - 1						) // 3) * 3 + 2
						lowercase__				:      Optional[Any]=       Decimal(round(phi ** Decimal(index + 1						)						)						) / (phi + 2)
						lowercase__				:      Tuple=       num // 2
						return int(A						)


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






