




from __future__ import annotations







def        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_,snake_case_,snake_case_,):
						_A							:  List[str]    =		len(snake_case_  )

						# 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(snake_case_  ):
												# 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],snake_case_,snake_case_,)







def        lowerCAmelCase_			(  snake_case_  ):
						_A							:  Optional[int]    =		[]
						depth_first_search([],[],[],snake_case_,snake_case_  )

						# Print all the boards
						for board in boards:
												for column in board:
																		print(snake_case_  )
												print(""""""  )

						print(len(snake_case_  ),"""solutions were found."""  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		n_queens_solution(4)







import operator







def        lowerCAmelCase_			(  snake_case_,snake_case_ = False,snake_case_ = None  ):
      _A							:  str    =		operator.lt if reverse else operator.gt
      _A							:  Optional[Any]    =		solution or []

      if not arr:
            return solution

      _A							:  Dict    =		[arr.pop(0  )]
      for i, item in enumerate(snake_case_  ):
            if _operator(snake_case_,sublist[-1]  ):
                  sublist.append(snake_case_  )
                  arr.pop(snake_case_  )

    #  merging sublist into solution list
      if not solution:
            solution.extend(snake_case_  )
      else:
            while sublist:
                  _A							:  Union[str, Any]    =		sublist.pop(0  )
                  for i, xx in enumerate(snake_case_  ):
                        if not _operator(snake_case_,snake_case_  ):
                              solution.insert(snake_case_,snake_case_  )
                              break
                  else:
                        solution.append(snake_case_  )

      strand_sort(snake_case_,snake_case_,snake_case_  )
      return solution


if __name__ == "__main__":
  assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
  assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]

