A square $ABCD$ has side length $ 1$. A circle passes through the vertices of the square. Let $P, Q, R, S$ be the midpoints of the arcs which are symmetrical to the arcs $AB$, $BC$, $CD$, $DA$ when reflected on sides $AB$, $B$C, $CD$, $DA$, respectively. The area of square $PQRS$ is  $a+b\sqrt2$, where $a$ and $ b$ are integers. Find the value of $a+b$.
[img]https://cdn.artofproblemsolving.com/attachments/4/3/fc9e1bd71b26cfd9ff076db7aa0a396ae64e72.png[/img]