Cutting to a Triangle

You are given a convex polygon. In the current polygon, choose three consecutive vertices and cut away the triangle formed by those vertices. After the cut, this is equivalent to removing the middle vertex of the three chosen vertices, so the remaining convex polygon has one fewer vertex.

Repeat this process until only a triangle remains. Depending on the order of cuts, different final triangles may remain.

Find the maximum possible area of the final triangle.

The first line contains the number of vertices N of the convex polygon. (3 <= N <= 35)

Each of the next N lines contains the coordinates x and y of one vertex, given in clockwise order. Every coordinate is a natural number not greater than 10,000.

Print the maximum possible area of the final triangle on the first line. An absolute or relative error of at most 10^-9 is accepted.