Counting Self-Rotating Subsets

A set of points in the plane is self-rotating if there is a point $P$ and an angle $\alpha$ in degrees with $0 < \alpha < 360$ such that rotating the plane around $P$ by $\alpha$ sends every point of the set to a point that also belongs to the set. The point $P$ is the center of the rotation.

You are given a set of $N$ distinct points whose coordinates are integers. For each size $1, 2, \dots, N$, count the subsets of that size that are self-rotating. Two subsets are different when one of them contains a point that the other does not contain.

The first line contains one integer $N$, the number of points ($1 \le N \le 1000$).

Each of the next $N$ lines contains two integers $X$ and $Y$, the coordinates of one point ($-10^9 \le X, Y \le 10^9$). The $N$ given points are all distinct.

Print one line with $N$ integers $S_1, S_2, \dots, S_N$ separated by single spaces. $S_i$ is the number of self-rotating subsets that contain exactly $i$ points. These counts can be very large, so print each one modulo $10^9 + 7$.