From a variable point $$P~(t^2,2t),~1\leq t\leq 3$$ on the parabola $$y^{2}=4x$$, perpendicular $$PM$$ is drawn to the tangent at the vertex. Now, from the mid point $$Q$$ of $$PM$$, perpendicular $$QL$$ is drawn to the focal chord through $$P$$. Find the sum of length of focal chord such that $$QL$$ is maximum and maximum length of $$QL$$