Consider a relation schema R = (A, B, C, D, E) and a set F consisting of the following functional dependencies that hold on R:

A -> C, AC -> E, AD -> B, B -> ADE, D-> E.

A candidate key of a relation schema is a minimal superkey, i.e. it is a set of attributes that functionally determines all attributes of the schema (under a set of functional dependencies that hold on the schema) and no subset of it is also a superkey. Find all candidate keys for R under F. Justify your answer by computing the closure of each attribute set that you claim to be a candidate key.