Tori
A torus is created by rotating a circle around an axis that lies in the plane of the circle but does not intersect it. Alternatively, a torus can also be formed by rotating a sphere around an axis that does not intersect it; in this scenario, a sphere with diameter d moves its center along a guiding circle l.
Vasya and Petro have positioned two donuts (tori) in space such that their guiding circles lie in the same plane. Your task is to assist Vasya and Petro in determining the area of the intersection of the projections of these tori onto the plane where the guiding circles are located.
Input
The input consists of two lines, each describing a torus. Each line contains 5 real numbers separated by spaces: X, Y, Z — the coordinates of the center of the guiding circle, with absolute values not exceeding 100, followed by R (0 < R ≤ 100) — the radius of the guiding circle, and d (0 < d < 2∙R) — the diameter of the sphere.
Output
Output a single number — the area of the intersection of the projections of the tori, rounded to three decimal places.