A "terrain" is an -monotone polygon defined by the points where each point has coordinates , and the following three conditions hold:
for
for
Given a terrain defined by the points , find the largest triangle that fits entirely within the terrain, and one of its three vertices is positioned at one of the terrain points through .
:::align{center}
:::
输入格式
The first line of input contains an integer , representing the number of points in the terrain (). The line in the following lines consists of two space-separated integers and , representing the point of the terrain ().
输出格式
Print the area of the largest triangle contained within the terrain. Your output will be considered correct if its absolute or relative error is at most .
:::