Consider the relational schemas given below and the respective sets of functional dependencies valid in the schemas.

$R=(P,Q,R,S,T,U,V,W)$

$Fd$: $\{\begin{array}{c}\text{:}[RWV]\\ PQR\\ TP\\ UTV\end{array}$

i$.$ Determine the highest normal form, which is valid for a schema. Justify your answer. Justification must include the derivations of minimal keys from the functional dependencies and testing the validity of all normal forms $(2NF,3NF,BCNF)$ against the relational schemas, minimal keys, and functional dependencies.

ii$.$ If a schema is not in BCNF$,$ then decompose it into a minimum number of schemas so that each one of them is in BCNF$.$ Justify your answer.