Build Your Home#1370
Mr. Tenant plans to buy a new house. In fact, he will buy a piece of land and build his house there. To decide which piece of land to buy, Mr. Tenant needs a program that gives a score to each piece. Each candidate plot is a polygon (not necessarily convex), and Mr. Tenant wonders what the best score is. Among possible scores, he considered the number of vertices, the sum of angles, the minimum number of required guards, and so on. Finally, Mr. Tenant decided that the best score for a piece of land is simply its area. Your task is to write the scoring program.
The input file consists of descriptions of several plots of land. Each plot is a simple polygon (that is, a polygon that does not intersect itself). The description of each polygon starts with a positive integer , followed by vertices, where each vertex consists of two floating-point coordinates: and . The last vertex is connected by an edge to the first vertex. Each polygon may be given either clockwise or counterclockwise. The input ends with the line containing .
For each plot, output exactly one line containing the score of that plot, rounded to the nearest integer. (Halves should be rounded up, but Mr. Tenant never faced such cases.) Hint: The scoring program must correctly handle degenerate cases, such as polygons with only one or two vertices.
Example 1