Power Transmission (Hard Edition)

题意翻译

**题目翻译：** 在二维平面上，给你 $n$ 个坐标，任意 $2$ 个点都有一条直线连接。请问一共有多少对直线是相交的。 **注意：** 1. 如果多点共线，不算直线相交。 2. 如果多线共点，记线数为 $sum$，相交数等于 $\frac12 sum (sum−1)$。

题目描述

This problem is same as the previous one, but has larger constraints. It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic. At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates $ (x_i, y_i) $ . Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire. Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 2 \le n \le 1000 $ ) — the number of electric poles. Each of the following $ n $ lines contains two integers $ x_i $ , $ y_i $ ( $ -10^4 \le x_i, y_i \le 10^4 $ ) — the coordinates of the poles. It is guaranteed that all of these $ n $ points are distinct.

输出格式

Print a single integer — the number of pairs of wires that are intersecting.

输入输出样例

输入样例 #1

4
0 0
1 1
0 3
1 2

输出样例 #1

14

输入样例 #2

4
0 0
0 2
0 4
2 0

输出样例 #2

6

输入样例 #3

3
-1 -1
1 0
3 1

输出样例 #3

0

说明

In the first example: In the second example: Note that the three poles $ (0, 0) $ , $ (0, 2) $ and $ (0, 4) $ are connected by a single wire. In the third example: