CF340B.Maximal Area Quadrilateral

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.

伊阿胡布在笛卡尔平面上画出了一组包含 $n$ 个点的集合，他称这些点为“特殊点”。四边形是指一个无自交的简单多边形，具有四条边（也称为边）和四个顶点（也称为角）。请注意，四边形不一定是凸的。特殊四边形是指其四个顶点均属于特殊点集合的四边形。给定特殊点集合，请计算特殊四边形的最大面积。

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.

第一行包含一个整数 $n$（$4 \leq n \leq 300$）。接下来的 $n$ 行每行包含两个整数：$x_i$、$y_i$（$-1000 \leq x_i, y_i \leq 1000$），表示第 $i$ 个特殊点的笛卡尔坐标。保证任意三点不共线，且任意两点不重合。

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.

输出一个实数——特殊四边形的最大面积。若答案的绝对误差或相对误差不超过 $10^{-9}$，则视为正确。

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.

在测试样例中，我们可以选择前 4 个点作为四边形的顶点。它们构成一个边长为 4 的正方形，因此面积为 $4 \cdot 4 = 16$。