Consider the circle $$C : x^2 + y^2 = 4$$ and the parabola $$P : y^2 = 8x$$. If the set of all values of $$\alpha$$, for which three chords of the circle $$C$$ on three distinct lines passing through the point $$(\alpha, 0)$$ are bisected by the parabola $$P$$ is the interval $$(p, q)$$, then $$(2q - p)^2$$ is equal to ________