JNU SSS 2013 Question 20: Logic and proof techniques

A number of species faced extinction during the Mesozoic era. Species $R$, $S$, $T$, $U$, $V$, $W$ and $X$ were species that all became extinct during this era and scientists have determined that their extinction occurred based on the following constraints : $W$ became extinct before $X$. $U$ became extinct after $T$. $S$ became extinct before $T$. $X$ became extinct before $U$. $V$ became extinct after $U$. $S$ became extinct before $W$. $R$ became extinct before $S$.

How many possible orders are there for the species’ extinction pattern?