






from __future__ import annotations
def       snake_case_		(     lowerCAmelCase_       :						tuple[int, int]       ,       lowerCAmelCase_       :						int      ):
							__lowercase			,			__lowercase      :							int				=     position
							__lowercase      :							Union[str, Any]				=     [
							    (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),
							]
							__lowercase      :							Union[str, Any]				=     []

							for position in positions:
														__lowercase			,			__lowercase      :							int				=     position
														if 0 <= y_test < n and 0 <= x_test < n:
																					permissible_positions.append(lowerCAmelCase_      )

							return permissible_positions
def       snake_case_		(     lowerCAmelCase_       :						list[list[int]]      ):
							return not any(elem == 0 for row in board for elem in row      )
def       snake_case_		(     lowerCAmelCase_       :						list[list[int]]       ,       lowerCAmelCase_       :						tuple[int, int]       ,       lowerCAmelCase_       :						int      ):

							if is_complete(lowerCAmelCase_      ):
														return True

							for position in get_valid_pos(lowerCAmelCase_       ,       len(lowerCAmelCase_      )      ):
														__lowercase			,			__lowercase      :							Union[str, Any]				=     position

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

							return False
def       snake_case_		(     lowerCAmelCase_       :						int      ):
							__lowercase      :							Optional[Any]				=     [[0 for i in range(lowerCAmelCase_      )] for j in range(lowerCAmelCase_      )]

							for i in range(lowerCAmelCase_      ):
														for j in range(lowerCAmelCase_      ):
																					__lowercase      :							Dict				=     1
																					if open_knight_tour_helper(lowerCAmelCase_       ,       (i, j)       ,       1      ):
																												return board
																					__lowercase      :							Optional[int]				=     0

							__lowercase      :							List[Any]				=     F"Open Kight Tour cannot be performed on a board of size {n}"
							raise ValueError(lowerCAmelCase_      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()







from .imports import is_tqdm_available


if is_tqdm_available():
	from tqdm.auto import tqdm as _tqdm

from ..state import PartialState
def       snake_case_		(     lowerCAmelCase_       :						bool = True       ,       *lowerCAmelCase_       :						int       ,       **lowerCAmelCase_       :						List[str]      ):
							if not is_tqdm_available():
														raise ImportError("""Accelerate's `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`."""      )
							__lowercase      :							List[str]				=     False
							if main_process_only:
														__lowercase      :							Optional[int]				=     PartialState().local_process_index == 0
							return _tqdm(*lowerCAmelCase_       ,       **lowerCAmelCase_       ,       disable=lowerCAmelCase_      )