




'''simple docstring'''




from __future__ import annotations

def    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      int       ):
 '''simple docstring'''





 UpperCAmelCase__										=    [0] * max_one

 for i in range(0       ,						SCREAMING_SNAKE_CASE__       ):
  UpperCAmelCase__										=    i

 for i in range(2       ,						SCREAMING_SNAKE_CASE__       ):
  if totients[i] == i:
   for j in range(SCREAMING_SNAKE_CASE__       ,						SCREAMING_SNAKE_CASE__       ,						SCREAMING_SNAKE_CASE__       ):
    totients[j] -= totients[j] // i

 return totients

def    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      int       ,						SCREAMING_SNAKE_CASE__			:      int       ):
 '''simple docstring'''





 return sorted(str(SCREAMING_SNAKE_CASE__       )       ) == sorted(str(SCREAMING_SNAKE_CASE__       )       )

def    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      int = 10000000       ):
 '''simple docstring'''





 UpperCAmelCase__										=    1  # i
 UpperCAmelCase__										=    0  # φ(i)
 UpperCAmelCase__										=    get_totients(max_n + 1       )

 for i in range(2       ,						max_n + 1       ):
  UpperCAmelCase__										=    totients[i]

  if i * min_denominator < min_numerator * t and has_same_digits(SCREAMING_SNAKE_CASE__       ,						SCREAMING_SNAKE_CASE__       ):
   UpperCAmelCase__										=    i
   UpperCAmelCase__										=    t

 return min_numerator


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






'''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    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      Tuple       ,						SCREAMING_SNAKE_CASE__			:      Dict       ):
 '''simple docstring'''





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







class 						lowerCAmelCase_   ( torch.optim.Optimizer   ):







  '''simple docstring'''







  def __init__(						self    :	List[str]						,		_UpperCAmelCase    :	Any						,		_UpperCAmelCase    :	Union[str, Any]=True						,		_UpperCAmelCase    :	List[str]=None ):






   """simple docstring"""






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

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


  @property
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Dict ):






   """simple docstring"""






   return self.optimizer.state


  @state.setter
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[int]						,		_UpperCAmelCase    :	List[str] ):






   """simple docstring"""






   UpperCAmelCase__										=    state


  @property
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Any ):






   """simple docstring"""






   return self.optimizer.param_groups


  @param_groups.setter
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[int]						,		_UpperCAmelCase    :	List[Any] ):






   """simple docstring"""






   UpperCAmelCase__										=    param_groups


  @property
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[Any] ):






   """simple docstring"""






   return self.optimizer.defaults


  @defaults.setter
  def 							SCREAMING_SNAKE_CASE__			(						self    :	int						,		_UpperCAmelCase    :	str ):






   """simple docstring"""






   UpperCAmelCase__										=    defaults


  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[int]						,		_UpperCAmelCase    :	Union[str, Any] ):






   """simple docstring"""






   self.optimizer.add_param_group(_UpperCAmelCase )


  def 							SCREAMING_SNAKE_CASE__			(						self    :	List[str]						,		_UpperCAmelCase    :	Tuple ):






   """simple docstring"""






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


  def 							SCREAMING_SNAKE_CASE__			(						self    :	str ):






   """simple docstring"""






   return self.optimizer.state_dict()


  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[int]						,		_UpperCAmelCase    :	List[Any]=None ):






   """simple docstring"""






   if self.gradient_state.sync_gradients:
    UpperCAmelCase__										=    """set_to_none""" in inspect.signature(self.optimizer.zero_grad ).parameters
    if accept_arg:
     if set_to_none is None:
      UpperCAmelCase__										=    False
     self.optimizer.zero_grad(set_to_none=_UpperCAmelCase )
    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 							SCREAMING_SNAKE_CASE__			(						self    :	Any						,		_UpperCAmelCase    :	List[str]=None ):






   """simple docstring"""






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

    else:
     self.optimizer.step(_UpperCAmelCase )


  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[Any]						,		_UpperCAmelCase    :	str ):






   """simple docstring"""






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


  @property
  def 							SCREAMING_SNAKE_CASE__			(						self    :	str ):






   """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."""						,		_UpperCAmelCase						,		)
   return self._is_overflow


  @property
  def 							SCREAMING_SNAKE_CASE__			(						self    :	Optional[int] ):






   """simple docstring"""






   return self._is_overflow


  def __getstate__(						self    :	Dict ):






   """simple docstring"""






   return self.__dict__.copy()



  def __setstate__(						self    :	Dict						,		_UpperCAmelCase    :	Tuple ):






   """simple docstring"""






   self.__dict__.update(_UpperCAmelCase )
