Zhang3 and Aunt are playing with tomatoes. They throw tomatoes onto a sphere. The center of the sphere is at $(0, 0, 0)$, and the radius is $R$. Each time a tomato is thrown, it will burst on the surface of the sphere, then the tomato juice will cover a certain circle on the surface of the sphere, which is called a spherical circle for short. A spherical circle can be represented as $(x, y, z, r)$, where $(x, y, z)$ is the center, a point on the surface, and $r$ is the radius, which is the spherical distance between center and border of the circle. Those points on the surface whose spherical distance to center $(x, y, z)$ is not greater than $r$ are in the circle. (As you know, the spherical distance between two points on the surface is the shortest distance to travel from one to another, passing through only points on the surface of the sphere.)
Zhang3 has already thrown $n$ tomatoes, the $i^\mathrm{th}$ of which covered a spherical circle $(x_i, y_i, z_i, r_i)$ with tomato juice.
Aunt decides to throw an extra tomato. She will randomly choose a point on the surface of the sphere, called $(x, y, z)$, and then let tomato juice cover a spherical circle $(x, y, z, r_0)$, where $r_0$ is given.
Zhang3 wants to know the expected area which is covered by tomato juice at least once. Please calculate and print the value.