
from __future__ import annotations






def      lowerCamelCase__       (       __lowerCAmelCase						:						tuple[int, int]					,							__lowerCAmelCase						:						int       ):




			"""simple docstring"""


			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(__lowerCAmelCase       )

			return permissible_positions






def      lowerCamelCase__       (       __lowerCAmelCase						:						list[list[int]]       ):




			"""simple docstring"""


			return not any(elem == 0 for row in board for elem in row       )






def      lowerCamelCase__       (       __lowerCAmelCase						:						list[list[int]]					,							__lowerCAmelCase						:						tuple[int, int]					,							__lowerCAmelCase						:						int       ):




			"""simple docstring"""


			if is_complete(__lowerCAmelCase       ):
						return True

			for position in get_valid_pos(__lowerCAmelCase					,							len(__lowerCAmelCase       )       ):
						lowerCAmelCase_			,						lowerCAmelCase_      			=			position

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

			return False






def      lowerCamelCase__       (       __lowerCAmelCase						:						int       ):




			"""simple docstring"""


			lowerCAmelCase_      			=			[[0 for i in range(__lowerCAmelCase       )] for j in range(__lowerCAmelCase       )]

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

			lowerCAmelCase_      			=			F"""Open Kight Tour cannot be performed on a board of size {n}"""
			raise ValueError(__lowerCAmelCase       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





def      lowerCamelCase__       (       __lowerCAmelCase						:						list[list[int]]					,							__lowerCAmelCase						:						int					,							__lowerCAmelCase						:						int					,							__lowerCAmelCase						:						set       ):




			"""simple docstring"""


			lowerCAmelCase_			,						lowerCAmelCase_      			=			len(__lowerCAmelCase       ), len(grid[0]       )
			if (
			    min(__lowerCAmelCase					,							__lowerCAmelCase       ) < 0
			    or row == row_length
			    or col == col_length
			    or (row, col) in visit
			    or grid[row][col] == 1
			):
						return 0
			if row == row_length - 1 and col == col_length - 1:
						return 1

			visit.add((row, col)       )

			lowerCAmelCase_      			=			0
			count += depth_first_search(__lowerCAmelCase					,							row + 1					,							__lowerCAmelCase					,							__lowerCAmelCase       )
			count += depth_first_search(__lowerCAmelCase					,							row - 1					,							__lowerCAmelCase					,							__lowerCAmelCase       )
			count += depth_first_search(__lowerCAmelCase					,							__lowerCAmelCase					,							col + 1					,							__lowerCAmelCase       )
			count += depth_first_search(__lowerCAmelCase					,							__lowerCAmelCase					,							col - 1					,							__lowerCAmelCase       )

			visit.remove((row, col)       )
			return count


if __name__ == "__main__":
			import doctest

			doctest.testmod()



