


from __future__ import annotations


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			):


			'''simple docstring'''







			__lowercase 					=   len(_UpperCamelCase  )

			# 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(_UpperCamelCase  ):
						# 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]       ,			_UpperCamelCase       ,			_UpperCamelCase       ,			)


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   []
			depth_first_search([]       ,			[]       ,			[]       ,			_UpperCamelCase       ,			_UpperCamelCase  )

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	n_queens_solution(4)






from ..utils import DummyObject, requires_backends
class 	lowerCamelCase_       (				metaclass=lowerCAmelCase__				):



					'''simple docstring'''







					__UpperCAmelCase            =				["speech"]






					def __init__(				self ,       *snake_case_ ,       **snake_case_						)   ->			List[str]:







								'''simple docstring'''

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




class 	lowerCamelCase_       (				metaclass=lowerCAmelCase__				):



					'''simple docstring'''







					__UpperCAmelCase            =				["speech"]






					def __init__(				self ,       *snake_case_ ,       **snake_case_						)   ->			Tuple:







								'''simple docstring'''

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


