






'''simple docstring'''






from __future__ import annotations




def        _SCREAMING_SNAKE_CASE  (				A  :       list[int]  ,		A  :       list[int]  ,		A  :       list[int]  ,		A  :       list[list[str]]  ,		A  :       int  ,		)    -> None:







   """simple docstring"""
   __snake_case				:      str     							= len(A  )

   # 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(A  ):
      # 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]  ,		A  ,		A  ,		)




def        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> None:







   """simple docstring"""
   __snake_case				:      list[list[str]]     							= []
   depth_first_search([]  ,		[]  ,		[]  ,		A  ,		A  )

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

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      n_queens_solution(4)







'''simple docstring'''






def        _SCREAMING_SNAKE_CASE  (				A  :       float  ,		A  :       list[float]  )    -> float:







   """simple docstring"""
   if discount_rate < 0:
      raise ValueError('Discount rate cannot be negative'  )
   if not cash_flows:
      raise ValueError('Cash flows list cannot be empty'  )
   __snake_case				:      List[str]     							= sum(
       cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(A  )  )
   return round(A  ,		ndigits=2  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()