SP4142 ELLIPSE - Ellipse

Given 5 points on a ellipse, calculate the area of the ellipse. We accept solutions with **absolute error less than 10 $ ^{-6} $ or relative error less than 10 $ ^{-9} $** .

Many test cases. Each contains a line with 10 integers with absolute value less than 1000 - the X and Y coordinates of the 5 points, respectively. Input terminates by EOF. Note that there can be extra spaces in a single line.

Each line contains a single float-point number - the area of the corresponding ellipse, or "IMPOSSIBLE" if the ellipse doesn't exist or can't be unique determined.