Bipartite Graphs and Matchings · Superchallenge problem

Men $A,B,C,D$ rank women $W,X,Y,Z$ as $A\!:\!W,Y,X,Z$; $B\!:\!Z,Y,X,W$; $C\!:\!X,W,Y,Z$; $D\!:\!Y,Z,X,W$. Women rank men as $W\!:\!B,A,C,D$; $X\!:\!A,D,C,B$; $Y\!:\!A,B,C,D$; $Z\!:\!C,D,A,B$. How many different stable matchings does this preference profile admit?