Largest Triangle

Given $N$ points on a $2$-dimensional space, determine the area of the largest triangle that can be formed using $3$ of those $N$ points. If there is no triangle that can be formed, the answer is $0$.

The first line contains an integer $N$ ($3
\le N \le 5\, 000$) denoting the number of points. Each
of the next $N$ lines
contains two integers $x$
and $y$ ($0 \leq x, y \leq 4 \cdot 10^7$).
There are **no** specific constraints on
these $N$ points, i.e. the
points are not necessarily distinct, the points are not given
in specific order, there may be $3$ or more collinear points, etc.

Print the answer in one line. Your answer should have an absolute error of at most $10^{-5}$.

Sample Input 1 | Sample Output 1 |
---|---|

7 0 0 0 5 7 7 0 10 0 0 20 0 10 10 |
100.00000 |