





from __future__ import annotations






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				tuple[int, int]       , UpperCamelCase__:				int     ):
		SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   position
		SCREAMING_SNAKE_CASE__								=   [
		    (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__								=   []

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

		return permissible_positions






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






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				list[list[int]]       , UpperCamelCase__:				tuple[int, int]       , UpperCamelCase__:				int     ):

		if is_complete(UpperCamelCase__     ):
				return True

		for position in get_valid_pos(UpperCamelCase__       , len(UpperCamelCase__     )     ):
				SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   position

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

		return False






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				int     ):
		SCREAMING_SNAKE_CASE__								=   [[0 for i in range(UpperCamelCase__     )] for j in range(UpperCamelCase__     )]

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()





import unittest

from accelerate import debug_launcher
from accelerate.test_utils import require_cpu, test_ops, test_script




@require_cpu
class 		__A   (      unittest.TestCase      ):

						def      A__    (		self :Tuple			):
										'''simple docstring'''

										debug_launcher(test_script.main			)


						def      A__    (		self :Dict			):
										'''simple docstring'''

										debug_launcher(test_ops.main			)




