Let the $L_2$ language be defined by the following regular expression:

$L_2=a^{**}(b{b}^{**}+c{c}^{**})d^{**}$

a$)$ Construct the transition diagram of the finite automata $($NFA$)$ that recognizes the $L_2$ language. $($in the diagram, name the initial state as $S$ and the other states as $A,B,C,$dots. $)$

b$)$ If the diagram you created contains $-$ transitions, find the equivalent transition diagram without $-$ transition by eliminating the $-$ transitions in the transition diagram.