An estate is a simple polygon with n integer-coordinate vertices listed in order around its boundary. Count the integer grid points that lie strictly inside the estate (points exactly on an edge or at a vertex do not count).
Input format
Line 1: an integer n, the number of vertices.
Next n lines: two integers x y, the vertices in boundary order.
Output format
A single integer: the number of strictly interior integer grid points.
Constraints
- 3 <= n <= 100000
- -1000000 <= x, y <= 1000000
- The vertices describe a simple (non-self-intersecting) polygon.