

'''simple docstring'''



from __future__ import annotations







def      a__ (						a__   ,					a__		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   0
     __SCREAMING_SNAKE_CASE						     =   len(a__		) - 1
     while left <= right:
          __SCREAMING_SNAKE_CASE						     =   (left + right) // 2
          if left == right:
               if sorted_list[middle] < item:
                    __SCREAMING_SNAKE_CASE						     =   middle + 1
               break
          elif sorted_list[middle] < item:
               __SCREAMING_SNAKE_CASE						     =   middle + 1
          else:
               __SCREAMING_SNAKE_CASE						     =   middle - 1
     sorted_list.insert(a__   ,					a__		)
     return sorted_list







def      a__ (						a__   ,					a__		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   []
     while left and right:
          if left[0][0] < right[0][0]:
               result.append(left.pop(0		)		)
          else:
               result.append(right.pop(0		)		)
     return result + left + right







def      a__ (						a__		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   len(a__		)
     if length <= 1:
          return list_ad
     __SCREAMING_SNAKE_CASE						     =   length // 2
     return merge(sortlist_ad(list_ad[:middle]		)   ,					sortlist_ad(list_ad[middle:]		)		)







def      a__ (						a__		):




     """simple docstring"""


     if len(a__		) <= 1:
          return collection
     __SCREAMING_SNAKE_CASE						     =   []
     __SCREAMING_SNAKE_CASE						     =   False
     for i in range(0   ,					len(a__		)   ,					2		):
          if i == len(a__		) - 1:
               __SCREAMING_SNAKE_CASE						     =   True
          else:
               if collection[i] < collection[i + 1]:
                    two_paired_list.append([collection[i], collection[i + 1]]		)
               else:
                    two_paired_list.append([collection[i + 1], collection[i]]		)
     __SCREAMING_SNAKE_CASE						     =   sortlist_ad(a__		)
     __SCREAMING_SNAKE_CASE						     =   [i[0] for i in sorted_list_ad]
     result.append(sorted_list_ad[-1][1]		)
     if has_last_odd_item:
          __SCREAMING_SNAKE_CASE						     =   collection[-1]
          __SCREAMING_SNAKE_CASE						     =   binary_search_insertion(a__   ,					a__		)
     __SCREAMING_SNAKE_CASE						     =   False
     for i in range(len(a__		) - 1		):
          if result[i] == collection[-1] and has_last_odd_item:
               __SCREAMING_SNAKE_CASE						     =   True
          __SCREAMING_SNAKE_CASE						     =   sorted_list_ad[i][1]
          # If last_odd_item is inserted before the item's index,
          # you should forward index one more.
          if is_last_odd_item_inserted_before_this_index:
               __SCREAMING_SNAKE_CASE						     =   result[: i + 2] + binary_search_insertion(result[i + 2 :]   ,					a__		)
          else:
               __SCREAMING_SNAKE_CASE						     =   result[: i + 1] + binary_search_insertion(result[i + 1 :]   ,					a__		)

     return result


if __name__ == "__main__":
  UpperCAmelCase				: str         =  input('Enter numbers separated by a comma:\n').strip()
  UpperCAmelCase				: Any         =  [int(item) for item in user_input.split(',')]
  print(merge_insertion_sort(unsorted))









'''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__ (						a__   ,					a__		):




     """simple docstring"""


     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 		lowerCAmelCase__     (   torch.optim.Optimizer      ):



 """simple docstring"""



 def __init__(	self      : Tuple      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]      ,							__SCREAMING_SNAKE_CASE      : Dict=True      ,							__SCREAMING_SNAKE_CASE      : List[Any]=None    )						->				str:


      """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(__SCREAMING_SNAKE_CASE      ,							self.accelerator_state.device    )
           else:
                __SCREAMING_SNAKE_CASE						     =   move_to_device(__SCREAMING_SNAKE_CASE      ,							self.accelerator_state.device    )
           self.optimizer.load_state_dict(__SCREAMING_SNAKE_CASE    )
 @property
 def    UpperCAmelCase__	(	self      : str    )						->				Union[str, Any]:


      """simple docstring"""




      return self.optimizer.state
 @state.setter
 def    UpperCAmelCase__	(	self      : List[str]      ,							__SCREAMING_SNAKE_CASE      : Optional[Any]    )						->				List[Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   state
 @property
 def    UpperCAmelCase__	(	self      : Optional[int]    )						->				str:


      """simple docstring"""




      return self.optimizer.param_groups
 @param_groups.setter
 def    UpperCAmelCase__	(	self      : Dict      ,							__SCREAMING_SNAKE_CASE      : str    )						->				List[Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   param_groups
 @property
 def    UpperCAmelCase__	(	self      : List[Any]    )						->				Any:


      """simple docstring"""




      return self.optimizer.defaults
 @defaults.setter
 def    UpperCAmelCase__	(	self      : Any      ,							__SCREAMING_SNAKE_CASE      : Dict    )						->				Optional[Any]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   defaults
 def    UpperCAmelCase__	(	self      : Any      ,							__SCREAMING_SNAKE_CASE      : Any    )						->				List[str]:


      """simple docstring"""




      self.optimizer.add_param_group(__SCREAMING_SNAKE_CASE    )
 def    UpperCAmelCase__	(	self      : List[str]      ,							__SCREAMING_SNAKE_CASE      : List[str]    )						->				Dict:


      """simple docstring"""




      if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
           xm.send_cpu_data_to_device(__SCREAMING_SNAKE_CASE      ,							self.accelerator_state.device    )
      self.optimizer.load_state_dict(__SCREAMING_SNAKE_CASE    )
 def    UpperCAmelCase__	(	self      : Union[str, Any]    )						->				Union[str, Any]:


      """simple docstring"""




      return self.optimizer.state_dict()
 def    UpperCAmelCase__	(	self      : List[str]      ,							__SCREAMING_SNAKE_CASE      : List[str]=None    )						->				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=__SCREAMING_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    UpperCAmelCase__	(	self      : List[str]      ,							__SCREAMING_SNAKE_CASE      : List[Any]=None    )						->				Dict:


      """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=__SCREAMING_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      ,							__SCREAMING_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(__SCREAMING_SNAKE_CASE    )
 def    UpperCAmelCase__	(	self      : Union[str, Any]      ,							__SCREAMING_SNAKE_CASE      : Any    )						->				Any:


      """simple docstring"""




      for param_group in self.optimizer.param_groups:
           __SCREAMING_SNAKE_CASE						     =   [parameters_map.get(__SCREAMING_SNAKE_CASE      ,							__SCREAMING_SNAKE_CASE    ) for p in param_group["""params"""]]
 @property
 def    UpperCAmelCase__	(	self      : int    )						->				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."""      ,							__SCREAMING_SNAKE_CASE      ,							)
      return self._is_overflow
 @property
 def    UpperCAmelCase__	(	self      : Union[str, Any]    )						->				Optional[int]:


      """simple docstring"""




      return self._is_overflow
 def __getstate__(	self      : Tuple    )						->				str:


      """simple docstring"""




      return self.__dict__.copy()


 def __setstate__(	self      : str      ,							__SCREAMING_SNAKE_CASE      : Optional[int]    )						->				Any:


      """simple docstring"""




      self.__dict__.update(__SCREAMING_SNAKE_CASE    )






