21553_Symmetry

After taking a modern art class, Farmer John has become interested in finding geometric patterns in everything around his farm.  He carefully plots the locations of his N cows (2 ≤ N ≤ 1000), each one occupying a distinct point in the 2D plane, and he wonders how many different lines of symmetry exist for this set of points.  A line of symmetry, of course, is a line across which the points on both sides are mirror images of each-other.

Please help FJ answer this most pressing geometric question.

* Line 1: The single integer N.

* Lines 2..1+N: Line i+1 contains two space-separated integers representing the x and y coordinates of the i-th cow (-10,000 ≤ x, y ≤ 10,000).

4
0 0
0 1
1 0
1 1

4

INPUT DETAILS:

The 4 cows form the corners of a square.

OUTPUT DETAILS:

There are 4 lines of symmetry -- one vertical, one horizontal, and two diagonal.