Bipartite Graphs and Matchings · Superchallenge problem

Men $A,B,C,D$ rank women $W,X,Y,Z$ as $A\!:\!Y,Z,W,X$; $B\!:\!X,W,Z,Y$; $C\!:\!Z,X,W,Y$; $D\!:\!X,Z,Y,W$. Women rank men as $W\!:\!A,B,D,C$; $X\!:\!A,C,D,B$; $Y\!:\!D,C,B,A$; $Z\!:\!D,A,C,B$. Among ALL stable matchings this profile admits, what is the SMALLEST possible value of the combined total (sum of every man's rank of his partner, plus every woman's rank of her partner)?