Bipartite Graphs and Matchings · Hard problem

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