2020 Fermat Problem 18

Four teams play in a tournament in which each team plays exactly one game against each of the other three teams. At the end of each game, either the two teams tie or one team wins and the other team loses. A team is awarded 3 points for a win, 0 points for a loss, and 1 point for a tie. If S is the sum of the points of the four teams after the tournament is complete, which of the following values can S *not* equal?

\textbf{(A)}\ 13\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 16\quad \textbf{(E)}\ 15

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.