Design a deterministic finite-state automaton that consists of four states (including the start and final states), and accepts strings over alphabets {A,B}. The automaton generates strings that either begin with A and end with B, or strings that begin with B and end with A. In either case, there are equal number of A8 and B8 in between the first and last symbols. An example of an accepted string is ABABAB. (8 marks)