2014 AIME I Problem 5

Let the set S=\left\{P_{1}, P_{2}, \ldots, P_{12}\right\} consist of the twelve vertices of a regular 12-gon. A subset Q of S is called communal if there is a circle such that all points of Q are inside the circle, and all points of S not in Q are outside of the circle. How many communal subsets are there? (Note that the empty set is a communal subset.)