Let be a sphere with radius and center . Let be points on the surface of . The positions of are fixed while the position of is a uniform random point on the surface of . Let be if there exists a hemisphere of that contains and otherwise. Calculate the expected value of .
输入格式
The first line contains an integer denoting the number of points ().
The -th line of the next lines contains three integers denoting the point ().
It is guaranteed that are distinct.
输出格式
Output the answer.
The answer will be considered correct if its absolute or relative error doesn't exceed .
