Easy Geometry

Eva studies geometry. The current topic is convex polygons, but Eva prefers rectangles. Her workbook has several convex polygons drawn in it, and she wants to know the area of the largest rectangle that fits inside each of them.

Help Eva. Given a convex polygon, find the largest possible area of a rectangle that fits inside it. The sides of the rectangle must be parallel to the coordinate axes.

The first line contains a single integer $n$, the number of sides of the polygon ($3 \le n \le 100\,000$). Each of the following $n$ lines contains the Cartesian coordinates of one vertex of the polygon, two integers $x_i$ and $y_i$ ($-10^9 \le x_i, y_i \le 10^9$). The vertices are given in clockwise order.

The polygon is convex.

Print one line with the largest area of a rectangle that fits inside the polygon and has its sides parallel to the coordinate axes, rounded to six digits after the decimal point. Always print all six digits.

No answer in the input data lies on a rounding boundary.