Signal

A telecommunications company is building a GSM (mobile phone) network in Beijing. The network should serve $n$ houses in the city, but because of a limited budget the company can build only a single antenna.

The antenna is placed by choosing $3$ of the $n$ houses and building it at the center of the circle that passes through those three houses. Then every house that lies inside or on the boundary of that circle receives a signal. The company plans to pick the three houses at random, and to estimate how many houses would receive a signal it wants the average, over all possible choices of three houses, of the number of houses that receive a signal.

Your task is: given the positions of the houses, compute the average number of houses that receive a signal. The positions are given as integer coordinates in the plane. No three houses are collinear, and no four houses lie on the boundary of a common circle.

The first line contains a positive integer $n$ ($3 \le n \le 1500$), the number of houses. Each of the next $n$ lines describes one house: for $1 \le i \le n$, line $i+1$ contains two integers $x_i$ and $y_i$, the coordinates of house $i$, separated by a space.

All coordinates are integers with $-1000000 \le x_i, y_i \le 1000000$. No three houses are collinear, and no four houses lie on the boundary of a common circle.

Output the average number of houses that receive a signal, as an exact fraction in lowest terms: if the average equals $\frac{p}{q}$ in lowest terms with $q > 1$, print it as p/q; if the average is an integer, print just that integer.