Consider the doubly infinite cylinder whose axis passes through the center of the Cartesian coordinate system, the radius \textbf{R}. In this problem you need to calculate the surface area of a ball centered at \textbf{c} of radius \textbf{r}, which is contained in the cylinder. \InputFile The first line contains four numbers \textbf{r}, \textbf{x_c}, \textbf{y_c}, \textbf{z_c} --- radius of the sphere and the coordinates of its center. The second line contains four numbers \textbf{R}, \textbf{x_v}, \textbf{y_v}, \textbf{z_v} --- cylinder radius and the coordinates of points on its axis (not the same origin). All numbers are integers, do not exceed the absolute value of \textbf{1000}, the radii are positive. \OutputFile Bring out a single number - the surface area of the ball that has fallen into the interior of the cylinder, with an accuracy of less than \textbf{4} decimal places.