Problem Description
You have N points on a plot of land. You are allowed to select up to 4 points and fence up the area contained within the selected points. However, you are greedy and want to maximize the largest area you can have. Find out what is this maximum area!
Input
First line of input contains an integer, N.
Following N lines will have 2 floating point values each, the X and Y co-ordinates of each point respectively.
Please use double type floating point (or higher precision) to input the co-ordinates.
Output
The maximum possible area contained within up to 4 of the N points. Print your answer to 3 decimal places.
Limits
For all testcases, -105 ≤ X, Y ≤ 105.
Subtask 1 (30%): 4 ≤ N ≤ 50.
Subtask 2 (20%): 4 ≤ N ≤ 1000. In addition, the points are randomly distributed in an uniform manner.
Subtask 3 (50%): 4 ≤ N ≤ 2000.
Subtask 4 (0%): Sample Testcases.
Sample Testcase
Input
5
0 0
1 0
1 1
0 1
0.5 0.5
Output
1.000