





from __future__ import annotations
def 							a_	(    __magic_name__		,     __magic_name__		,     __magic_name__		,     __magic_name__		,     __magic_name__		,     )				->			List[Any]:




				"""simple docstring"""






				snake_case   :					str    						=				len(lowerCamelCase_   )

				# If row is equal to the size of the board it means there are a queen in each row in
				# the current board (possible_board)
				if row == n:
								# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
								# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
								boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]   )
								return

				# We iterate each column in the row to find all possible results in each row
				for col in range(lowerCamelCase_   ):
								# We apply that we learned previously. First we check that in the current board
								# (possible_board) there are not other same value because if there is it means
								# that there are a collision in vertical. Then we apply the two formulas we
								# learned before:
								#
								# 45º: y - x = b or 45: row - col = b
								# 135º: y + x = b or row + col = b.
								#
								# And we verify if the results of this two formulas not exist in their variables
								# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
								#
								# If any or these are True it means there is a collision so we continue to the
								# next value in the for loop.
								if (
								    col in possible_board
								    or row - col in diagonal_right_collisions
								    or row + col in diagonal_left_collisions
								):
												continue

								# If it is False we call dfs function again and we update the inputs
								depth_first_search(
								    [*possible_board, col]		,     [*diagonal_right_collisions, row - col]		,     [*diagonal_left_collisions, row + col]		,     lowerCamelCase_		,     lowerCamelCase_		,     )
def 							a_	(    __magic_name__   )				->			List[str]:




				"""simple docstring"""






				snake_case   :					list[list[str]]    						=				[]
				depth_first_search([]		,     []		,     []		,     lowerCamelCase_		,     lowerCamelCase_   )

				# Print all the boards
				for board in boards:
								for column in board:
												print(lowerCamelCase_   )
								print(''''''   )

				print(len(lowerCamelCase_   )		,     '''solutions were found.'''   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			n_queens_solution(4)







'''simple docstring'''




from ..utils import DummyObject, requires_backends




class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[int]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[int]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			str      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			Union[str, Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Tuple      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[str]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



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







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Tuple      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



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


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



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



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



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



