###### Category

###### Similar Problems

## 0709. Maximal Area Quadrilateral

###### Time limit : 1000 ms

Memory limit : 64 mb

Iahub has drawn a set of *n* points in the cartesian plane which he calls "special
points". A quadrilateral is a simple polygon without self-intersections
with four sides (also called edges) and four vertices (also called corners).
Please note that a quadrilateral doesn't have to be convex. A special
quadrilateral is one which has all four vertices in the set of special points.
Given the set of special points, please calculate the maximal area of a special
quadrilateral.

Input

The first line contains
integer *n* (4 ≤ *n* ≤ 300).
Each of the next *n* lines
contains two integers: *x _{i}*,

*y*( - 1000 ≤

_{i}*x*,

_{i}*y*≤ 1000) — the cartesian coordinates of

_{i}*i*th special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide.

Output

Output a single real
number — the maximal area of a special quadrilateral with precision 10^{-6}.

Sample

№ |
Input |
Output |

1 |
5 0 0 0 4 4 0 4 4 2 3 |
16.000000 |

Note

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Text from: codeforces.ru