Let $F$ be the set of functional dependencies on relation schema $R=(A,B,C,D,E,F,G).F=\{D$EFG,$GC,DA,GAB,BC,DBFG\}$

a$.(15$ pts$.)$ Find the canonical cover of $F.$

b$.(20$ pts$.)$ Give a dependency preserving lossless$-$loin decomposition of $R$ into BCNF$.$ Assume that $R$ is already in $1NF.$ Show all of your steps clearly to get full score.