



from __future__ import annotations
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	tuple[int, int]     ,				_SCREAMING_SNAKE_CASE   :	int				)->list[tuple[int, int]]:
      _lowerCAmelCase			,   _lowerCAmelCase 			=  position
      _lowerCAmelCase 			=  [
          (y + 1, x + 2),
          (y - 1, x + 2),
          (y + 1, x - 2),
          (y - 1, x - 2),
          (y + 2, x + 1),
          (y + 2, x - 1),
          (y - 2, x + 1),
          (y - 2, x - 1),
      ]
      _lowerCAmelCase 			=  []

      for position in positions:
            _lowerCAmelCase			,   _lowerCAmelCase 			=  position
            if 0 <= y_test < n and 0 <= x_test < n:
                  permissible_positions.append(_SCREAMING_SNAKE_CASE				)

      return permissible_positions
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list[list[int]]				)->bool:
      return not any(elem == 0 for row in board for elem in row				)
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list[list[int]]     ,				_SCREAMING_SNAKE_CASE   :	tuple[int, int]     ,				_SCREAMING_SNAKE_CASE   :	int				)->bool:

      if is_complete(_SCREAMING_SNAKE_CASE				):
            return True

      for position in get_valid_pos(_SCREAMING_SNAKE_CASE     ,				len(_SCREAMING_SNAKE_CASE				)				):
            _lowerCAmelCase			,   _lowerCAmelCase 			=  position

            if board[y][x] == 0:
                  _lowerCAmelCase 			=  curr + 1
                  if open_knight_tour_helper(_SCREAMING_SNAKE_CASE     ,				_SCREAMING_SNAKE_CASE     ,				curr + 1				):
                        return True
                  _lowerCAmelCase 			=  0

      return False
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	int				)->list[list[int]]:
      _lowerCAmelCase 			=  [[0 for i in range(_SCREAMING_SNAKE_CASE				)] for j in range(_SCREAMING_SNAKE_CASE				)]

      for i in range(_SCREAMING_SNAKE_CASE				):
            for j in range(_SCREAMING_SNAKE_CASE				):
                  _lowerCAmelCase 			=  1
                  if open_knight_tour_helper(_SCREAMING_SNAKE_CASE     ,				(i, j)     ,				1				):
                        return board
                  _lowerCAmelCase 			=  0

      _lowerCAmelCase 			=  f'''Open Kight Tour cannot be performed on a board of size {n}'''
      raise ValueError(_SCREAMING_SNAKE_CASE				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()











import functools
import gc
import inspect

import torch

from .imports import is_npu_available, is_xpu_available
def 							UpperCAmelCase__		(				*_SCREAMING_SNAKE_CASE   :	Tuple				)->List[Any]:
      if not isinstance(_SCREAMING_SNAKE_CASE     ,				_SCREAMING_SNAKE_CASE				):
            _lowerCAmelCase 			=  list(_SCREAMING_SNAKE_CASE				)
      for i in range(len(_SCREAMING_SNAKE_CASE				)				):
            _lowerCAmelCase 			=  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 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	Exception				)->bool:
      _lowerCAmelCase 			=  [
          '''CUDA out of memory.''',  # CUDA OOM
          '''cuDNN error: CUDNN_STATUS_NOT_SUPPORTED.''',  # CUDNN SNAFU
          '''DefaultCPUAllocator: can\'t allocate memory''',  # CPU OOM
      ]
      if isinstance(_SCREAMING_SNAKE_CASE     ,				_SCREAMING_SNAKE_CASE				) and len(exception.args				) == 1:
            return any(err in exception.args[0] for err in _statements				)
      return False


def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	callable = None     ,				_SCREAMING_SNAKE_CASE   :	int = 1_2_8				)->Optional[int]:
      if function is None:
            return functools.partial(_SCREAMING_SNAKE_CASE     ,				starting_batch_size=_SCREAMING_SNAKE_CASE				)

      _lowerCAmelCase 			=  starting_batch_size

      def decorator(*_SCREAMING_SNAKE_CASE   :	Optional[int]     ,				**_SCREAMING_SNAKE_CASE   :	Optional[Any]				):
            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()
            _lowerCAmelCase 			=  list(inspect.signature(_SCREAMING_SNAKE_CASE				).parameters.keys()				)
            # Guard against user error
            if len(_SCREAMING_SNAKE_CASE				) < (len(_SCREAMING_SNAKE_CASE				) + 1):
                  _lowerCAmelCase 			=  ''', '''.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(_SCREAMING_SNAKE_CASE     ,				*_SCREAMING_SNAKE_CASE     ,				**_SCREAMING_SNAKE_CASE				)
                  except Exception as e:
                        if should_reduce_batch_size(_SCREAMING_SNAKE_CASE				):
                              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