3. A "goods train" is defined to be a string of cars, which must begin with one or two engines. These are followed by one or more trucks, which are followed by one Guard Van. Example: E E T T T T G Non-goods trains: E G; E T T T; E E E T T T G a. Write a DFA to recognize a goods train. Use E = engine, T = truck, G = guard van. b. Write a regular expression that generates all legal goods trains. c. Write a program that recognizes goods trains (says OK or not OK). (Input can be in any convenient form) use JAVA. Run your program! Submit code (short please) and outputs. Use your DFA translate DFA to code.