This should work:
WITH contacts AS(
SELECT a.gid AS gid1,b.gid AS gid2, ST_Intersection(a.the_geom, b.the_geom) AS intersection
FROM final_layer as a, final_layer as b
WHERE ST_Touches(a.the_geom, b.the_geom)
AND a.gid<b.gid
)
SELECT *
FROM contacts c1
LEFT JOIN contacts c2
ON ((c1.gid1=c2.gid1 AND c1.gid2<>c2.gid2) OR (c1.gid1=c2.gid2 AND c1.gid1<>c1.gid2))
AND c1.intersection=c2.intersection
WHERE c2.gid1 IS NULL;
It will perform better if ST_Intersection is moved to the final query but I wanted to make it simple.