Kids Like Cakes

Kids like cakes. In this problem we only consider cakes shaped like a convex polygon, as seen from above.

Every cake must be cut into pieces. Each piece must be a non-degenerate triangle whose three corners are vertices of the original cake. The pieces may not overlap, and together they must exactly cover the whole cake. In other words, cutting the cake means triangulating the convex polygon using only its own vertices.

Some kids also care about fairness. For one fixed way of cutting a cake, take its largest piece and its smallest piece and look at the difference of their areas. The unfairness number of the cake is the largest such difference that can be achieved over all valid ways of cutting it.

Given a cake, compute its unfairness number.

The first line contains a single integer $n$, the number of vertices of the cake ($4 \le n \le 5000$).

Each of the next $n$ lines contains two integers $x_i$ and $y_i$, the coordinates of one vertex ($-10^8 \le x_i, y_i \le 10^8$). The vertices are listed in order along the boundary of the polygon (either clockwise or counter-clockwise).

Output a single number with exactly one digit after the decimal point: the unfairness number of the cake.