There are \textbf{N} 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 \textbf{3} different points to make a circle and compute value \textbf{I}, defined as number of points that are inside the circle. Your task is to calculate the mean value (mathematical expectation) of random variable \textbf{I}. Assume that each point has equal probability to be picked. \InputFile The first line of input contains a single positive integer \textbf{N}, the total number of points (\textbf{3} ≤ \textbf{N} ≤ \textbf{1500}). Each of following \textbf{N} lines contains pair of integers \textbf{x_i} and \textbf{y_i}, - coordinates of the corresponding point. \OutputFile Output should contains a single real number, average number of points inside a circle, constructed by randomly chosen \textbf{3} different points, accurate to two digits after decimal point.