Let A and B be the two points of intersection of the line $y + 5 = 0$ and the mirror image of the parabola $y ^ { 2 } = 4 x$ with respect to the line $x + y + 4 = 0$. If d denotes the distance between A and B, and a denotes the area of $\triangle S A B$, where $S$ is the focus of the parabola $y ^ { 2 } = 4 x$, then the value of $( a + d )$ is