In $△PQR$, $PQ=PR=32$ and $QR=24$. Points $S,T,$ and $U$ are on sides $\overline{PQ},\overline{QR},$ and $\overline{PR}$, respectively, such that $\overline{ST}$ and $\overline{TU}$ are parallel to $\overline{PR}$ and $\overline{PQ}$, respectively. What is the perimeter of parallelogram $PSTU$?