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K. Fence 'Em In
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You want to create a zombie farm. Luckily you've recently stumbled upon a zombie spawner. However, you can't break the spawner to move it elsewhere, so the farm needs to be built around it. Additionally, to trap the zombies in, you need to build a fence around the spawner.

However, due to the new update, the farm requires a very specific type of fence. The fence needs to be a non-degenerate triangle with vertices at 3 of $$$N$$$ pre-determined fence posts, located on a 2d grid. If needed, the spawner can lie directly on the fence.

To give the mobs more space to spawn (maximizing profits), you want to make the area enclosed by the fence as large as possible. What is the largest possible area that such a fence can enclose, if one exists?

Input

The first line of input is the integer $$$N$$$ ($$$3 \le N \le 50000$$$): the number of fence posts in the grid. The second line has two space-separated integers, $$$g_x$$$ and $$$g_y$$$ ($$$-5000 \le g_x,g_y \le 5000$$$): the coordinates of the spawner. The next $$$N$$$ lines each contain two space-separated integers, $$$x_i$$$ and $$$y_i$$$ ($$$-5000 \le x,y \le 5000$$$): the coordinates of the $$$i^\text{th}$$$ fence posts.

Output

Output a single floating point value: The maximum area enclosed by a triangular fence containing the spawner, and with vertices at $$$3$$$ of the given fence posts. If no such triangular fence exists, output -1.

Example
Input
4
1 1
0 0
0 3
10 3
5 0
Output
15.000000000000