Inside Circle#3765
There are points on two-dimensional plane. It is guaranteed that any three points are not in a line and any four points are not on a circle. We randomly pick different points to make a circle and compute value , defined as number of points that are inside the circle.
Your task is to calculate the mean value (mathematical expectation) of random variable . Assume that each point has equal probability to be picked.
The first line of input contains a single positive integer , the total number of points (3 \le N \le 1500). Each of following lines contains pair of integers x_i and y_i, - coordinates of the corresponding point.
Output should contain a single real number, average number of points inside a circle, constructed by randomly chosen different points, accurate to two digits after decimal point.
Example 1