Minimal Key help

I am revising for a test here but I am struggling with this question
Here is a relation R(A,B,C,D,E,F,G,H)
These are its functional dependencies
Fd1: A → BCD
Fd2: AD → E
Fd3: EFG → H
Fd4: F → GH

Whats the minimal key and what dependency can be removed without changing the key

I think that Fd4 being removed won't change the key and that the minimal key is AEFG

Am I on the right track or totally going wrong guys