class NQueens
  def initialize size
    @size = size
  end

  def solutions
    @solutions = 0
    n_queens([])
    puts @solutions
  end

  def n_queens(queens)
    if queens.count == @size
      print_queens(queens)
      @solutions += 1
      return
    end
    @size.times do |col|
      princess = new_queen(queens.count, col)
      n_queens(queens + [princess]) if valid_position?(queens, princess)
    end
  end

  # column, diagonal 1, diagonal 2
  def new_queen(x, y)
    [y, x + y, x - y]
  end

  def valid_position?(queens, new_queen)
    !queens.any? { |queen| queen[0] == new_queen[0] ||
                           queen[1] == new_queen[1] ||
                           queen[2] == new_queen[2] }
  end

  def print_queens(queens)
    queens.each do |queen|
      puts "." * queen[0] + 'Q' + "." * (@size - 1 - queen[0])
    end
    puts
  end
end

if ARGV.length == 1
  NQueens.new(ARGV[0].to_i).solutions
else
  NQueens.new(8).solutions
end