Twinkle☆Magic

Hello, Sensei. It is Mari.

The Trinity Carnival is in full swing, and the school is bustling with people. Since the event is not confined to a single stage, with booths, smaller venues, and cafés scattered all around... I imagine many people will have to watch from a distance, unable to reach the main stage.

So, I have a favor to ask.

I would like as many people as possible to see and hear the performance by our idol group, Antique Seraphim, wherever they may be. We plan to install three large relay screens, but I am told that the area from which people can enjoy the performance depends on where we place them.

I have written down the details below. Could you please help us, Sensei?

Mari has decided that three large relay screens will be enough for many students to watch the performance. Regard the Trinity Carnival as a two-dimensional coordinate plane. The screens may be installed at any positions in the carnival. Students standing inside or on the boundary of the triangle formed by the three screens can see the video and hear the music without difficulty. Each student's position is represented by a point with integer coordinates on this plane. To ensure that nobody misses the performance, all $N$ student positions must lie inside or on the boundary of this triangle.

However, if the triangle is too large, students will have to travel excessive distances, and managing sound and safety over such a wide area will be difficult. Therefore, the positions of the three screens should satisfy the following conditions.

1. The screens may have real-valued coordinates.
2. Every student lies inside or on the boundary of the triangle formed by the three screens.
3. The area of the triangle is as small as possible.

Find the area of this triangle for Mari.

The first line contains a positive integer $N$. $(3 \le N \le 200\,000)$

The next $N$ lines contain the students' coordinates. The $i$-th of these lines contains , , separated by a space, representing a student's position when the Trinity Carnival is viewed as a two-dimensional plane.

On the first line, print the minimum possible area of the triangle formed by the three screens. An absolute or relative error of at most $10^{-6}$ is allowed.