In $△PQR$ shown, $PQ=QR=8\sqrt{2}$ and $m\angle P=45^{\circ }$. If $\overline{QS}$ is an altitude to $\overline{PR}$, what is the length of $\overline{PS}$?

(A diagram similar to the original would be provided, showing an isosceles triangle PQR with altitude QS, where PQ=QR=8sqrt(2) and angle P = 45 degrees.)