




'''simple docstring'''






from __future__ import annotations






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		)    ->   list[tuple[int, int]]:
      snake_case__      ,							snake_case__       :   Any	      =    position
      snake_case__       :   Tuple	      =    [
          (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__       :   Union[str, Any]	      =    []

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

      return permissible_positions






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE		)    ->   bool:
      return not any(elem == 0 for row in board for elem in row		)






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		)    ->   bool:

      if is_complete(__SCREAMING_SNAKE_CASE		):
            return True

      for position in get_valid_pos(__SCREAMING_SNAKE_CASE				,      len(__SCREAMING_SNAKE_CASE		)		):
            snake_case__      ,							snake_case__       :   Optional[int]	      =    position

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

      return False






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE		)    ->   list[list[int]]:
      snake_case__       :   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		):
                  snake_case__       :   str	      =    1
                  if open_knight_tour_helper(__SCREAMING_SNAKE_CASE				,      (i, j)				,      1		):
                        return board
                  snake_case__       :   Tuple	      =    0

      snake_case__       :   Optional[int]	      =    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 DummyObject, requires_backends






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Optional[Any]     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Tuple     ,							*__lowerCamelCase     :					str     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Any     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					List[str]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					int     ,							*__lowerCamelCase     :					str     ,							**__lowerCamelCase     :					Union[str, Any]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Optional[Any]     ,							*__lowerCamelCase     :					List[str]     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Optional[Any]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					List[str]     ,							*__lowerCamelCase     :					str     ,							**__lowerCamelCase     :					str			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Union[str, Any]     ,							*__lowerCamelCase     :					str     ,							**__lowerCamelCase     :					str			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Any     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Optional[Any]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					str			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					str     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					int			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Optional[Any]     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					Union[str, Any]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Optional[int]     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					Optional[Any]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[Any]     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					int			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Tuple     ,							*__lowerCamelCase     :					List[str]     ,							**__lowerCamelCase     :					str			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					List[Any]     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					Union[str, Any]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Any     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[Any]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Dict     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					Any			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[Any]     ,							*__lowerCamelCase     :					Optional[int]     ,							**__lowerCamelCase     :					List[str]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Union[str, Any]     ,							*__lowerCamelCase     :					str     ,							**__lowerCamelCase     :					Any			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Tuple     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					Dict			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[Any]     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					List[Any]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					int     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					str			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Union[str, Any]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					int			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Any     ,							*__lowerCamelCase     :					List[str]     ,							**__lowerCamelCase     :					int			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[str]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					List[str]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Union[str, Any]     ,							*__lowerCamelCase     :					Optional[Any]     ,							**__lowerCamelCase     :					List[Any]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Any     ,							*__lowerCamelCase     :					Optional[int]     ,							**__lowerCamelCase     :					int			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					str     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					List[Any]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Optional[Any]     ,							*__lowerCamelCase     :					Union[str, Any]     ,							**__lowerCamelCase     :					Union[str, Any]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Union[str, Any]     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					Optional[Any]			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					str     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					Union[str, Any]     ,							*__lowerCamelCase     :					List[Any]     ,							**__lowerCamelCase     :					Optional[int]			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Optional[int]     ,							*__lowerCamelCase     :					Tuple     ,							**__lowerCamelCase     :					Tuple			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Dict     ,							*__lowerCamelCase     :					Dict     ,							**__lowerCamelCase     :					Optional[Any]			):
           requires_backends(cls     ,							['flax']			)






class        lowercase_      (						metaclass=lowerCAmelCase_							):
     A_											=			["flax"]





     def __init__(     self     :					str     ,							*__lowerCamelCase     :					int     ,							**__lowerCamelCase     :					Dict			):
           requires_backends(self     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					List[str]     ,							*__lowerCamelCase     :					Optional[int]     ,							**__lowerCamelCase     :					Tuple			):
           requires_backends(cls     ,							['flax']			)





     @classmethod
     def 			_lowerCAmelCase      (     cls     :					Dict     ,							*__lowerCamelCase     :					Optional[int]     ,							**__lowerCamelCase     :					Optional[Any]			):
           requires_backends(cls     ,							['flax']			)
