Lines and Points

Question

Let $S_1$ and $S_2$ be the set of points in x-y plane (where $x>0$ and $y$ is real) defined as: $$S_1 = \{(x,y) : | x + |x|| + |y + |y|| < 2\}$$ $$S_2 = \{(x,y) : | x - |x|| + |y - |y|| < 2\}$$ If the area of intersection of $S_1$ and $S_2$ is $A$, then find the value of $A$.