Two Circles

Two circles are given on a 2D plane. Write a program that computes the area of the region where the two circles overlap (their intersection), accurate to three decimal places.

The first line contains six real numbers $x_1$, $y_1$, $r_1$, $x_2$, $y_2$, $r_2$, separated by spaces. $(x_1, y_1)$ and $(x_2, y_2)$ are the centers of the first and second circle, and $r_1$ and $r_2$ are their radii. Each real number is given with at most two digits after the decimal point.

On the first line, print the area of the overlapping region, rounded to three decimal places. If the two circles do not overlap, print $0.000$.