






'''simple docstring'''



from __future__ import annotations


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



 """simple docstring"""




 lowercase	,		lowercase       : Tuple						=position
 lowercase       : Optional[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       : int						=[]

 for position in positions:
  lowercase	,		lowercase       : List[str]						=position
  if 0 <= y_test < n and 0 <= x_test < n:
   permissible_positions.append(__A      )

 return permissible_positions


def 				lowercase_					(     __A			:							list[list[int]]      )							->   bool:



 """simple docstring"""




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


def 				lowercase_					(     __A			:							list[list[int]]       ,   __A			:							tuple[int, int]       ,   __A			:							int      )							->   bool:



 """simple docstring"""




 if is_complete(__A      ):
  return True

 for position in get_valid_pos(__A       ,   len(__A      )      ):
  lowercase	,		lowercase       : Union[str, Any]						=position

  if board[y][x] == 0:
   lowercase       : Optional[Any]						=curr + 1
   if open_knight_tour_helper(__A       ,   __A       ,   curr + 1      ):
    return True
   lowercase       : Optional[int]						=0

 return False


def 				lowercase_					(     __A			:							int      )							->   list[list[int]]:



 """simple docstring"""




 lowercase       : Dict						=[[0 for i in range(__A      )] for j in range(__A      )]

 for i in range(__A      ):
  for j in range(__A      ):
   lowercase       : Dict						=1
   if open_knight_tour_helper(__A       ,   (i, j)       ,   1      ):
    return board
   lowercase       : int						=0

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()











'''simple docstring'''



from ..utils import DummyObject, requires_backends
class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Dict  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Any  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	Any:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		str		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		List[Any]		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		List[Any]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Any  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Any:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Tuple  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		int		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		int  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Dict		)	->	Optional[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		List[str]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	str:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		Optional[Any]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		Dict		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		int  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Tuple		)	->	Union[str, Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Any  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Optional[Any]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		List[str]  ,   **UpperCAmelCase      :		List[str]		)	->	Optional[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		Any		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[Any]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		Any		)	->	Any:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		List[str]  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		int		)	->	Tuple:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		Dict		)	->	int:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		List[str]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Dict		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		str		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[int]		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Tuple  ,   **UpperCAmelCase      :		Any		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[Any]  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		int		)	->	Tuple:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Optional[int]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	Union[str, Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)



