Count It

Roger loves drawing polygons. For an arbitrary sequence of points in a 2D plane $P_0, P_1, \ldots, P_{M-1}$, he can draw a polygon with $M$ sides by connecting the points $P_i$ and $P_{(i+1)\%M}$ with a straight line segment for each valid $i$. As a result, any point forms a polygon with $M = 1$, any two distinct points also form a polygon with $M = 2$ and a polygon may have sides with length $0$.