




__a							     =					[0, 2, 4, 6, 8]
__a							     =					[1, 3, 5, 7, 9]







def lowerCamelCase__  (     _lowercase					,		_lowercase					,		_lowercase					,		_lowercase ):

     '''simple docstring'''


     if remaining_length == 0:
          if digits[0] == 0 or digits[-1] == 0:
               return 0

          for i in range(length // 2 - 1					,		-1					,		-1 ):
               remainder += digits[i] + digits[length - i - 1]

               if remainder % 2 == 0:
                    return 0

               remainder //= 10

          return 1

     if remaining_length == 1:
          if remainder % 2 == 0:
               return 0

          UpperCAmelCase_     :				Any  =     0
          for digit in range(10 ):
               UpperCAmelCase_     :				int  =     digit
               result += reversible_numbers(
                   0					,		(remainder + 2 * digit) // 10					,		_lowercase					,		_lowercase )
          return result

     UpperCAmelCase_     :				Optional[int]  =     0
     for digita in range(10 ):
          UpperCAmelCase_     :				Tuple  =     digita

          if (remainder + digita) % 2 == 0:
               UpperCAmelCase_     :				Union[str, Any]  =     ODD_DIGITS
          else:
               UpperCAmelCase_     :				int  =     EVEN_DIGITS

          for digita in other_parity_digits:
               UpperCAmelCase_     :				Any  =     digita
               result += reversible_numbers(
                   remaining_length - 2					,		(remainder + digita + digita) // 10					,		_lowercase					,		_lowercase					,		)
     return result







def lowerCamelCase__  (     _lowercase = 9 ):

     '''simple docstring'''


     UpperCAmelCase_     :				List[Any]  =     0
     for length in range(1					,		max_power + 1 ):
          result += reversible_numbers(_lowercase					,		0					,		[0] * length					,		_lowercase )
     return result


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

"""simple docstring"""
import os
import socket
from contextlib import contextmanager

import torch

from ..commands.config.default import write_basic_config  # noqa: F401
from ..state import PartialState
from .dataclasses import DistributedType
from .imports import is_deepspeed_available, is_tpu_available
from .transformer_engine import convert_model
from .versions import is_torch_version


if is_deepspeed_available():
			from deepspeed import DeepSpeedEngine

if is_tpu_available(check_device=False):
			import torch_xla.core.xla_model as xm

def  lowercase     (_lowerCAmelCase						):
						if is_torch_version("""<""" ,    """2.0.0"""						) or not hasattr(_lowerCAmelCase ,    """_dynamo"""						):
												return False
						return isinstance(_lowerCAmelCase ,    torch._dynamo.eval_frame.OptimizedModule						)

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase = True						):
						__lowerCAmelCase     =  (torch.nn.parallel.DistributedDataParallel, torch.nn.DataParallel)

						__lowerCAmelCase     =  is_compiled_module(_lowerCAmelCase						)
						if is_compiled:
												__lowerCAmelCase     =  model
												__lowerCAmelCase     =  model._orig_mod

						if is_deepspeed_available():
												options += (DeepSpeedEngine,)

						while isinstance(_lowerCAmelCase ,    _lowerCAmelCase						):
												__lowerCAmelCase     =  model.module

						if not keep_fpaa_wrapper:
												__lowerCAmelCase     =  getattr(_lowerCAmelCase ,    """forward"""						)
												__lowerCAmelCase     =  model.__dict__.pop("""_original_forward""" ,    _lowerCAmelCase						)
												if original_forward is not None:
																		while hasattr(_lowerCAmelCase ,    """__wrapped__"""						):
																								__lowerCAmelCase     =  forward.__wrapped__
																								if forward == original_forward:
																														break
																		__lowerCAmelCase     =  forward
												if getattr(_lowerCAmelCase ,    """_converted_to_transformer_engine""" ,    _lowerCAmelCase						):
																		convert_model(_lowerCAmelCase ,    to_transformer_engine=_lowerCAmelCase						)

						if is_compiled:
												__lowerCAmelCase     =  model
												__lowerCAmelCase     =  compiled_model

						return model

def  lowercase     ():
						PartialState().wait_for_everyone()

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase						):
						if PartialState().distributed_type == DistributedType.TPU:
												xm.save(_lowerCAmelCase ,    _lowerCAmelCase						)
						elif PartialState().local_process_index == 0:
												torch.save(_lowerCAmelCase ,    _lowerCAmelCase						)

@contextmanager
def  lowercase     (**_lowerCAmelCase						):
						for key, value in kwargs.items():
												__lowerCAmelCase     =  str(_lowerCAmelCase						)

						yield

						for key in kwargs:
												if key.upper() in os.environ:
																		del os.environ[key.upper()]

def  lowercase     (_lowerCAmelCase						):
						if not hasattr(_lowerCAmelCase ,    """__qualname__"""						) and not hasattr(_lowerCAmelCase ,    """__name__"""						):
												__lowerCAmelCase     =  getattr(_lowerCAmelCase ,    """__class__""" ,    _lowerCAmelCase						)
						if hasattr(_lowerCAmelCase ,    """__qualname__"""						):
												return obj.__qualname__
						if hasattr(_lowerCAmelCase ,    """__name__"""						):
												return obj.__name__
						return str(_lowerCAmelCase						)

def  lowercase     (_lowerCAmelCase ,    _lowerCAmelCase						):
						for key, value in source.items():
												if isinstance(_lowerCAmelCase ,    _lowerCAmelCase						):
																		__lowerCAmelCase     =  destination.setdefault(_lowerCAmelCase ,    {}						)
																		merge_dicts(_lowerCAmelCase ,    _lowerCAmelCase						)
												else:
																		__lowerCAmelCase     =  value

						return destination



def  lowercase     (_lowerCAmelCase = None						):
						if port is None:
												__lowerCAmelCase     =  2_9500
						with socket.socket(socket.AF_INET ,    socket.SOCK_STREAM						) as s:
												return s.connect_ex(("""localhost""", port)						) == 0
