Broken
A closed polygonal chain is given on the plane.
Your task is to find the area of the region enclosed by this polygonal chain. The closed polygonal chain consists of a sequence of N points {p_i}i=1^N and N segments that connect each consecutive pair of points in the sequence, including a segment that connects the first and last points. The enclosed region is defined as the set of points on the plane that cannot be connected to the point (∞, 0) by a continuous curve that does not intersect the polygonal chain.
Input
The first line contains the integer N (1 ≤ N ≤ 1000), which represents the number of vertices in the polygonal chain. The following N lines each contain two integers: x_i, y_i (0 ≤ x_i, y_{i }≤ 1000), which are the coordinates of the i-th vertex of the polygonal chain.
Output
Output one real number, which is the area of the enclosed region, with an absolute or relative error of at most 10^{-8}.