P2665 [USACO08FEB] Game of Lines S

Farmer John has challenged Bessie to the following game: FJ has a board with dots marked at N (2 ≤ N ≤ 200) distinct lattice points. Dot i has the integer coordinates Xi and Yi (-1,000 ≤ Xi ≤ 1,000; -1,000 ≤ Yi ≤ 1,000). Bessie can score a point in the game by picking two of the dots and drawing a straight line between them; however, she is not allowed to draw a line if she has already drawn another line that is parallel to that line. Bessie would like to know her chances of winning, so she has asked you to help find the maximum score she can obtain.

第 $1$ 行：输入一个正整数：$N$。 第 $2 \sim N+1$ 行：第 $i+1$ 行用 $2$ 个用空格隔开的整数 $X_i,Y_i$，描述了点 $i$ 的坐标。

第 $1$ 行：输出一个整数，表示贝茜的最大得分，即她能画出的互不平行的线段数。

样例解释： 贝茜能画出以下 $4$ 种斜率的直线：$-1$，$0$，$\dfrac{1}{3}$ 以及 $1$。