 2020 NA Regionals Practice Contest 11

Start

2021-02-06 09:00 AKST

2020 NA Regionals Practice Contest 11

End

2021-02-06 14:00 AKST
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Problem ELargest 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 $0$.

Input

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.

Output

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