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.
上完现代美术课后，农夫约翰开始对在农场周围的所有地方寻找几何图案感兴趣。
他仔细绘制了他的 N 头奶牛的位置，每头奶牛在二维平面上占据一个不同的点。
他想知道这组点共有多少条不同的对称线。
对称线是指满足线两边的点互为镜像的一条直线。
* 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).
第一行包含整数 N。
接下来 N 行，每行包含两个整数，表示一头牛的位置坐标 (x,y)。
输出不同对称线的数量。
4
0 0
0 1
1 0
1 1 4
数据范围
2≤N≤1000,
−10000≤x,y≤10000
四头牛的位置位于一个正方形的四个顶点上。
共有 4 条对称线，一条水平、一条垂直、两条对角线。