Jeffrey is studying for his bio exam! One of the most crucial skills in biology is the ability to find the area of a shape, given only its points. Mr. White, Jeffrey's biology teacher, taught him a way to find that area: the Shoelace Theorem. The Shoelace Theorem only works if the shape is a simple polygon, i.e., it has a two dimensional shape consisting of straight, non-intersecting line segments that, when joined pair-wise, form a path. This means that exactly two edges meet at each vertex, no sides intersect, the number of edges are equal to the number of vertices, and the area enclosed by the shape will always be measurable.
The Shoelace Theorem works for simple polygons. However, since Jeffrey is horrible at biology, you have to help him implement the Shoelace Theorem. Since Jeffrey is similarly bad with decimal numbers, print the smallest integer not less than the area (the ceiling function).
On the first line will be an integer , the number of points that define the shape. The next lines will each contain two integers and , denoting a Cartesian point in the shape. The points will be given in counterclockwise order.
On a single line, print out the ceiling of the area of the shape defined by these points.
5 3 4 5 6 9 5 12 8 5 11
Explanation for Sample Output
Here is an image of the given polygon:
Using the Shoelace Theorem, the area of this polygon is: