\begin{problem}{Largest Area}{\textsl{standard input}}{\textsl{standard output}}{1 second}{1024 mebibytes}

You are given a rectangle on the plane with vertices at integer points. Calculate the area of the largest ellipse that can fit entirely within this rectangle. Recall that a \textit{rectangle} is a convex quadrilateral with all right angles, and an \textit{ellipse} is a figure on the plane defined by two focal points $F_1$ and $F_2$ (not necessarily with integer coordinates; possibly $F_1 = F_2$) and a real number $d > |F_1 F_2|$, consisting of points $P$ on the plane such that $|F_1 P| + |F_2 P| \le d$.

\InputFile
The input consists of a single line containing eight integers $x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4$: the coordinates of four points ($-1000 \le x_i, y_i \le 1000$). The points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$, $(x_4, y_4)$ are the vertices of a rectangle with a positive area, listed in counterclockwise order.

\OutputFile
Output a single real number: the largest area of an ellipse that can be drawn inside the rectangle given in the input. The answer is considered correct if its relative or absolute error does not exceed $10^{-6}$.

\Examples

\exmpthreewidinf=0.25\thelinewidth
\exmpthreewidouf=0.25\thelinewidth
\exmpthreewidnote=0.4\thelinewidth
\def\kwExampleNotes{\textsl{explanation}}

\begin{examplethree}
\exmpfile{example.01}{example.01.a}{
\vspace{-1mm}
\center
\includegraphics{ellipsis-in-rectangle_sample-1}
}%
\exmpfile{example.02}{example.02.a}{
\vspace{-1mm}
\center
\includegraphics{ellipsis-in-rectangle_sample-2}
}%
\end{examplethree}

\end{problem}

