Area of a simple polygon#6349
A polygon is defined on a plane by the integer coordinates of its vertices. Your task is to calculate the area of this polygon.
The polygon is simple, meaning its sides do not intersect or touch each other, except at adjacent vertices. However, it is not necessarily convex.
Read the input data from standard input (keyboard). The first line contains the number of vertices (1 \le N \le 50000). The following lines each contain a pair of integers, representing the coordinates of the vertices. The polygon's sides are formed by connecting the st vertex to the nd, the nd to the rd, and so on, until the (N-1)th vertex is connected to the th, and finally, the th vertex is connected back to the st. The coordinates are integers, with absolute values not exceeding one million.
Output a single number representing the calculated area of the polygon. The result can be presented in either exponential form or standard decimal form. The answer is considered correct if the error does not exceed .
Example 1