Quadrilateral $ABCD$ is congruent to quadrilateral $PQRS$, where $A,B,C,$ and $D$ correspond to $P,Q,R,$ and $S,$ respectively. The side lengths of quadrilateral $ABCD$ are $AB=5$, $BC=8$, $CD=6$, and $DA=7$. What is the perimeter of quadrilateral $PQRS$?