Let $$E_1$$ and $$E_2$$ be two ellipses whose centers are at the origin. The major axes of $$E_1$$ and $$E_2$$ lie along the x-axis and the y-axis, respectively. Let S be the circle $$x^2 + (y - 1)^2 = 2.$$ The straight line x + y = 3 touches the curves S, $$E_1$$ and $$E_2$$ at P, Q and R, respectively. Suppose that $$PQ = PR = \frac{2 \sqrt 2}{3}.$$ If $$e_1$$ and $$e_2$$ are the eccentricities of $$E_1$$ and $$E_2$$, respectively, then the correct expression(s) is(are)