In the figure below you can see triangle \textbf{ABC} and its in-circle (Circle that touches all the sides of a triangle internally). The radius of this in circle is \textbf{r}. Three other circles are drawn. Each of them touches two sides of this triangle and the in circle of \textbf{ABC}. The radiuses of these circles are \textbf{r_1}, \textbf{r_2} and \textbf{r_3}. \includegraphics{https://static.e-olymp.com/content/90/90e1e0965db8d4d09307caf29e75c3b922394dfe.jpg} Given the values of \textbf{r}, \textbf{r_1}, \textbf{r_2} and \textbf{r_3} you will have to find the area of triangle \textbf{ABC}. \InputFile The input file can contain up to \textbf{1000} lines of inputs. Each line contains four positive floating-point numbers which denotes the values of \textbf{r}, \textbf{r_1}, \textbf{r_2} and \textbf{r_3} respectively. Input is terminated by a line containing four negative integers. \OutputFile For each line of input produce one line of output. This line contains serial of output followed by a floating-point number which denotes the area of triangle \textbf{ABC}. This floating-point number may have two digits after the decimal point. You can assume that for the given values of \textbf{r}, \textbf{r_1}, \textbf{r_2} and \textbf{r_3} it will always be possible to construct a triangle \textbf{ABC}. If required you can assume that \textbf{pi = 3.141592653589793} and also use double precision floating-point numbers for floating-point calculations. You can assume that there will be no such input for which small precision errors will cause difference in printed output. Look at the output for sample input for details.