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# Counting Self-Rotating Subsets

**Timelimit: 1**

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 (−10^{9} ≤ **X, Y** ≤ 10^{9}). All points in the input set are distinct.

Output a single line containing **N** integers **S _{1}, S_{2}, . . . , S_{N}**. For

Input Samples | Output Samples |

3 |
3 3 0 |

7 |
7 21 5 5 3 1 1 |

1 |
1 |