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B. Maximal Area Quadrilateral

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub 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*_{i} ( - 1000 ≤ *x*_{i}, *y*_{i} ≤ 1000) — the cartesian coordinates of *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. The answer will be considered correct if its absolute or relative error does't exceed 10^{ - 9}.

Examples

Input

5

0 0

0 4

4 0

4 4

2 3

Output

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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