Area Sums in Convex Polygons

You are given a **convex** polygon $P$ with $N$ vertices. The vertices (in clockwise order) are $v_1, v_2, \dots v_N$. The coordinates of $v_i$ are $(x_i, y_i)$. All vertices have integer coordinates. A *diagonal* of $P$ is a line segment $l$ joining two distinct vertices $v_i$ and $v_j$ of $P$, such that $l$ is not already an edge of $P$. Every diagonal of $P$ splits it into two smaller convex p