You are given a relation R with $4$ attributes ABCD, R$($A$,$B$,$C$,$D$).$ The following are functional dependencies that held on R:

B $$ C$,$ D $$ A

Assuming these FDs are the only dependencies that hold on R$,$ do the following:

Identify the key$($s$)$ for R$.$

Identify the highest normal form that R satisfies $(1$NF$,2$NF$,3$NF$,$ or BCNF$).$

If R is not in BCNF$,$ decompose it into a set of BCNF relations.