

'''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     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase	)     ->     List[str]:
	if isinstance(__a ,(list, tuple)	):
		return honor_type(__a ,(move_to_device(__a ,__a	) for t in state)	)
	elif isinstance(__a ,__a	):
		return type(__a	)({k: move_to_device(__a ,__a	) for k, v in state.items()}	)
	elif isinstance(__a ,torch.Tensor	):
		return state.to(__a	)
	return state







class        lowercase    (	torch.optim.Optimizer			):


							def __init__(      self     ,      _snake_case     ,      _snake_case=True     ,      _snake_case=None)				->					List[str]:
								UpperCAmelCase_		:   Optional[int]													=       optimizer
								UpperCAmelCase_		:   Optional[Any]													=       scaler
								UpperCAmelCase_		:   Tuple													=       AcceleratorState()
								UpperCAmelCase_		:   List[Any]													=       GradientState()
								UpperCAmelCase_		:   List[Any]													=       device_placement
								UpperCAmelCase_		:   str													=       False
								UpperCAmelCase_		:   Optional[int]													=       None

								# Handle device placement
								if device_placement:
									UpperCAmelCase_		:   Optional[int]													=       self.optimizer.state_dict()
									if self.accelerator_state.distributed_type == DistributedType.TPU:
										xm.send_cpu_data_to_device(a_     ,      self.accelerator_state.device)
									else:
										UpperCAmelCase_		:   List[Any]													=       move_to_device(a_     ,      self.accelerator_state.device)
									self.optimizer.load_state_dict(a_)


							@property
							def     _snake_case				(      self)				->					List[Any]:
								return self.optimizer.state


							@state.setter
							def     _snake_case				(      self     ,      _snake_case)				->					List[str]:
								UpperCAmelCase_		:   Union[str, Any]													=       state


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


							@param_groups.setter
							def     _snake_case				(      self     ,      _snake_case)				->					Optional[int]:
								UpperCAmelCase_		:   Dict													=       param_groups


							@property
							def     _snake_case				(      self)				->					str:
								return self.optimizer.defaults


							@defaults.setter
							def     _snake_case				(      self     ,      _snake_case)				->					Any:
								UpperCAmelCase_		:   int													=       defaults


							def     _snake_case				(      self     ,      _snake_case)				->					Optional[int]:
								self.optimizer.add_param_group(a_)


							def     _snake_case				(      self     ,      _snake_case)				->					Optional[int]:
								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     _snake_case				(      self)				->					Optional[Any]:
								return self.optimizer.state_dict()


							def     _snake_case				(      self     ,      _snake_case=None)				->					List[Any]:
								if self.gradient_state.sync_gradients:
									UpperCAmelCase_		:   int													=       'set_to_none' in inspect.signature(self.optimizer.zero_grad).parameters
									if accept_arg:
										if set_to_none is None:
											UpperCAmelCase_		:   Optional[int]													=       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     _snake_case				(      self     ,      _snake_case=None)				->					Union[str, Any]:
								if self.gradient_state.sync_gradients:
									if self.accelerator_state.distributed_type == DistributedType.TPU:
										UpperCAmelCase_		:   Any													=       {'closure': closure} if closure is not None else {}
										xm.optimizer_step(self.optimizer     ,      optimizer_args=a_)
									elif self.scaler is not None:
										UpperCAmelCase_		:   List[str]													=       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
											UpperCAmelCase_		:   Optional[Any]													=       self.scaler.get_scale()
											UpperCAmelCase_		:   Tuple													=       True
										self.scaler.step(self.optimizer     ,      a_)
										self.scaler.update()
										UpperCAmelCase_		:   List[Any]													=       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.
											UpperCAmelCase_		:   str													=       scale_after < self._last_scale
										UpperCAmelCase_		:   Optional[int]													=       scale_after

									else:
										self.optimizer.step(a_)


							def     _snake_case				(      self     ,      _snake_case)				->					Optional[Any]:
								for param_group in self.optimizer.param_groups:
									UpperCAmelCase_		:   Any													=       [parameters_map.get(a_     ,      a_) for p in param_group['params']]


							@property
							def     _snake_case				(      self)				->					int:
								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     _snake_case				(      self)				->					List[Any]:
								return self._is_overflow


							def __getstate__(      self)				->					int:
								return self.__dict__.copy()





							def __setstate__(      self     ,      _snake_case)				->					Any:
								self.__dict__.update(a_)











import math
from decimal import Decimal, getcontext

def       A_   (						__a  :					int = 4_000_000		):

				"""simple docstring"""

				try:
								a__					   =		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."""		)
				a__					   =		100
				a__					   =		(Decimal(5		) ** Decimal(0.5		) + 1) / Decimal(2		)

				a__					   =		(math.floor(math.log(n * (phi + 2)			,		__a		) - 1		) // 3) * 3 + 2
				a__					   =		Decimal(round(phi ** Decimal(index + 1		)		)		) / (phi + 2)
				a__					   =		num // 2
				return int(__a		)


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

