Counting Self-Rotating Subsets
By Pablo Ariel Heiber 
Argentina
By Pablo Ariel Heiber Argentina
A set of points in the plane is self-rotating if there is a point P, the center, and an angle α, expressed in degrees, where 0 < α < 360, such that the rotation of the plane, with center P and angle , maps every point in the set to some point also in the set.
You are given a set of N distinct points, all having integer coordinates. Find the number of distinct subsets of size 1, 2, . . . ,N that are self-rotating. Two subsets are considered distinct if one contains a point that the other does not contain.
The first line of the input contains one integer N representing the number of points in the input set (1 ≤ N ≤ 1000). Each of the following N lines describes a different point of the set, and contains two integers X and Y giving its coordinates in a Cartesian coordinate system (−109 ≤ X, Y ≤ 109). All points in the input set are distinct.
Output a single line containing N integers S1, S2, . . . , SN. For i = 1, 2, . . . ,N the integer Si must be the number of subsets of i points of the input set that are self-rotating. Since these numbers can be very big, output them modulo 109 + 7.
| Input Samples | Output Samples |
|
3 |
3 3 0 |
|
7 |
7 21 5 5 3 1 1 |
|
1 |
1 |