2592 - [Usaco2012 Feb]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. 上过现代艺术课后，FJ开始感兴趣于在他农场中的几何图样。他计划将奶牛放置在二维平面上的N个互不相同的点(1<=N<=1000),他希望找出这个点集有多少条对称轴。他急切地需要你帮忙解决这个几何问题。

• 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 ith cow (-10,000 <= x,y <= 10,000).

• Line 1: The number of different lines of symmetry of the point set.