


from __future__ import annotations





def 						_lowerCAmelCase							(     _lowerCAmelCase   ,						_lowerCAmelCase			)    ->						list[tuple[int, int]]:


						'''simple docstring'''






						__snake_case		,       __snake_case				=		position
						__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),
						]
						__snake_case				=		[]

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

						return permissible_positions





def 						_lowerCAmelCase							(     _lowerCAmelCase			)    ->						bool:


						'''simple docstring'''






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





def 						_lowerCAmelCase							(     _lowerCAmelCase   ,						_lowerCAmelCase   ,						_lowerCAmelCase			)    ->						bool:


						'''simple docstring'''






						if is_complete(_lowerCAmelCase			):
												return True

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

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

						return False





def 						_lowerCAmelCase							(     _lowerCAmelCase			)    ->						list[list[int]]:


						'''simple docstring'''






						__snake_case				=		[[0 for i in range(_lowerCAmelCase			)] for j in range(_lowerCAmelCase			)]

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

						__snake_case				=		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			)    ->						int:


						'''simple docstring'''






						assert column_title.isupper()
						__snake_case				=		0
						__snake_case				=		len(_lowerCAmelCase			) - 1
						__snake_case				=		0

						while index >= 0:
												__snake_case				=		(ord(column_title[index]			) - 64) * pow(26   ,						_lowerCAmelCase			)
												answer += value
												power += 1
												index -= 1

						return answer


if __name__ == "__main__":
	from doctest import testmod

	testmod()





