Create a finite$-$state machine that accepts strings whose characters are in $\{$a$,$ b$,$ c$\}$ and produces output strings of Ts and Fs$.$ The machine outputs a T once the character pair ab $($the characters must be adjacent$)$ is encountered in the string. Before this occurrence, it should output Fs$.$ Indicate the starting state, and label the states and transitions. Give a diagram, not a state table.