A land surveyor records the corner posts of a plot as a simple polygon, listing the vertices in order around the boundary (either clockwise or counter-clockwise). All vertices have integer coordinates. To avoid fractions, report twice the area enclosed by the boundary; for a polygon with integer vertices this doubled value is always a whole number.
Input format
Line 1: an integer n, the number of vertices.
Next n lines: two integers x y, the coordinates of each vertex in boundary order.
Output format
A single integer: twice the area enclosed by the polygon.
Constraints
- 3 <= n <= 100000
- -1000000 <= x, y <= 1000000
- The vertices describe a simple (non-self-intersecting) polygon.