


a : str		=				[0, 2, 4, 6, 8]
a : List[str]		=				[1, 3, 5, 7, 9]


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase  ):


			'''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

						__lowercase 					=   0
						for digit in range(10  ):
									__lowercase 					=   digit
									result += reversible_numbers(
									    0       ,			(remainder + 2 * digit) // 10       ,			_UpperCamelCase       ,			_UpperCamelCase  )
						return result

			__lowercase 					=   0
			for digita in range(10  ):
						__lowercase 					=   digita

						if (remainder + digita) % 2 == 0:
									__lowercase 					=   ODD_DIGITS
						else:
									__lowercase 					=   EVEN_DIGITS

						for digita in other_parity_digits:
									__lowercase 					=   digita
									result += reversible_numbers(
									    remaining_length - 2       ,			(remainder + digita + digita) // 10       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			)
			return result


def 		lowercase_  (     _UpperCamelCase = 9  ):


			'''simple docstring'''







			__lowercase 					=   0
			for length in range(1       ,			max_power + 1  ):
						result += reversible_numbers(_UpperCamelCase       ,			0       ,			[0] * length       ,			_UpperCamelCase  )
			return result


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






import functools
import gc
import inspect

import torch

from .imports import is_npu_available, is_xpu_available


def 		lowercase_  (     *_UpperCamelCase  ):


			'''simple docstring'''







			if not isinstance(_UpperCamelCase       ,			_UpperCamelCase  ):
						__lowercase 					=   list(_UpperCamelCase  )
			for i in range(len(_UpperCamelCase  )  ):
						__lowercase 					=   None
			gc.collect()
			if is_xpu_available():
						torch.xpu.empty_cache()
			elif is_npu_available():
						torch.npu.empty_cache()
			else:
						torch.cuda.empty_cache()
			return objects


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   [
			    '''CUDA out of memory.''',  # CUDA OOM
			    '''cuDNN error: CUDNN_STATUS_NOT_SUPPORTED.''',  # CUDNN SNAFU
			    '''DefaultCPUAllocator: can\'t allocate memory''',  # CPU OOM
			]
			if isinstance(_UpperCamelCase       ,			_UpperCamelCase  ) and len(exception.args  ) == 1:
						return any(err in exception.args[0] for err in _statements  )
			return False





def 		lowercase_  (     _UpperCamelCase = None       ,			_UpperCamelCase = 1_28  ):


			'''simple docstring'''







			if function is None:
						return functools.partial(_UpperCamelCase       ,			starting_batch_size=_UpperCamelCase  )

			__lowercase 					=   starting_batch_size

			def decorator(*_UpperCamelCase       ,			**_UpperCamelCase  ):
						nonlocal batch_size
						gc.collect()
						if is_xpu_available():
									torch.xpu.empty_cache()
						elif is_npu_available():
									torch.npu.empty_cache()
						else:
									torch.cuda.empty_cache()
						__lowercase 					=   list(inspect.signature(_UpperCamelCase  ).parameters.keys()  )
						# Guard against user error
						if len(_UpperCamelCase  ) < (len(_UpperCamelCase  ) + 1):
									__lowercase 					=   ''', '''.join([F'{arg}={value}' for arg, value in zip(params[1:]       ,			args[1:]  )]  )
									raise TypeError(
									    F'Batch size was passed into `{function.__name__}` as the first argument when called.'
									    F'Remove this as the decorator already does so: `{function.__name__}({arg_str})`'  )
						while True:
									if batch_size == 0:
												raise RuntimeError('''No executable batch size found, reached zero.'''  )
									try:
												return function(_UpperCamelCase       ,			*_UpperCamelCase       ,			**_UpperCamelCase  )
									except Exception as e:
												if should_reduce_batch_size(_UpperCamelCase  ):
															gc.collect()
															if is_xpu_available():
																		torch.xpu.empty_cache()
															elif is_npu_available():
																		torch.npu.empty_cache()
															else:
																		torch.cuda.empty_cache()
															batch_size //= 2
												else:
															raise

			return decorator


