Let $$L_1, L_2$$ be the lines passing through the point $$P(0, 1)$$ and touching the parabola $$9x^2 + 12x + 18y - 14 = 0$$. Let $$Q$$ and $$R$$ be the points on the lines $$L_1$$ and $$L_2$$ such that the $$\triangle PQR$$ is an isosceles triangle with base $$QR$$. If the slopes of the lines $$QR$$ are $$m_1$$ and $$m_2$$, then $$16(m_1^2 + m_2^2)$$ is equal to _______