AMC 12 2019a Problem 8

For a set of four distinct lines in a plane, there are exactly $N$ distinct points that lie on two or more of the lines. What is the sum of all possible values of $N$?

$\textbf{(A) } 14 \textbf{(B) } 16 \textbf{(C) } 18 \textbf{(D) } 19 \textbf{(E) } 21$