



'''simple docstring'''

from __future__ import annotations






def       __lowercase  (_SCREAMING_SNAKE_CASE      :tuple[int, int]    ,	_SCREAMING_SNAKE_CASE      :int       ):
				SCREAMING_SNAKE_CASE					,					SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= position
				SCREAMING_SNAKE_CASE  :						List[str]      					= [
				    (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),
				]
				SCREAMING_SNAKE_CASE  :						Tuple      					= []

				for position in positions:
								SCREAMING_SNAKE_CASE					,					SCREAMING_SNAKE_CASE  :						List[str]      					= position
								if 0 <= y_test < n and 0 <= x_test < n:
												permissible_positions.append(_SCREAMING_SNAKE_CASE       )

				return permissible_positions






def       __lowercase  (_SCREAMING_SNAKE_CASE      :list[list[int]]       ):
				return not any(elem == 0 for row in board for elem in row       )






def       __lowercase  (_SCREAMING_SNAKE_CASE      :list[list[int]]    ,	_SCREAMING_SNAKE_CASE      :tuple[int, int]    ,	_SCREAMING_SNAKE_CASE      :int       ):

				if is_complete(_SCREAMING_SNAKE_CASE       ):
								return True

				for position in get_valid_pos(_SCREAMING_SNAKE_CASE    ,	len(_SCREAMING_SNAKE_CASE       )       ):
								SCREAMING_SNAKE_CASE					,					SCREAMING_SNAKE_CASE  :						Optional[Any]      					= position

								if board[y][x] == 0:
												SCREAMING_SNAKE_CASE  :						List[str]      					= curr + 1
												if open_knight_tour_helper(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	curr + 1       ):
																return True
												SCREAMING_SNAKE_CASE  :						Any      					= 0

				return False






def       __lowercase  (_SCREAMING_SNAKE_CASE      :int       ):
				SCREAMING_SNAKE_CASE  :						Optional[int]      					= [[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       ):
												SCREAMING_SNAKE_CASE  :						Tuple      					= 1
												if open_knight_tour_helper(_SCREAMING_SNAKE_CASE    ,	(i, j)    ,	1       ):
																return board
												SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= 0

				SCREAMING_SNAKE_CASE  :						Tuple      					= 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()









'''simple docstring'''

from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
	from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline




