Cut the watermelon#1840
Vasya and Petya decided to cut a watermelon into two parts (let us consider the watermelon as a perfect sphere with unit radius). To do this, they make cuts. A single cut consists of a sector of a circle, in the plane of which the cut is made. The arc of the sector is defined by two points that do not lie on a single diameter of the sphere. The cuts form a continuous closed polyline on the surface of the sphere and divide the surface of the watermelon into two parts, such that for any segment it is true that the entire polyline lies on one side of the plane passing through the given segment. We assume that the center of the sphere is at the origin. No two consecutive segments of the polyline belong to the same straight line on the sphere.
The first line contains the integer (3 \leq n \leq 10) — the number of nodes of the polyline. The next lines describe the points, each given by a triple of integers x_i, y_i, z_i, i = 1..n (-50 \leq x_i, y_i, z_i \leq 50). The points are given in arbitrary order. A point on the sphere is defined as the intersection of the sphere with the ray from to the point (x_i, y_i, z_i).
Output the volume of the smaller of the two pieces with at least digits after the decimal point.
Example 1