P7676 [COCI 2013/2014 #5] TROKUTI

Given $N$ lines in the Cartesian coordinate plane. Points on these lines satisfy $A_i x + B_i y + C_i = 0$. Please find the number of triangles formed by these lines. Output the answer modulo $10^9+7$. It is guaranteed that no three lines intersect at the same point.

The first line contains an integer $N$, indicating the number of lines. The next $N$ lines each contain three integers $A_i, B_i, C_i$, meaning that line $i$ satisfies the equation.

Output one integer: the number of triangles formed by these lines modulo $10^9+7$.

**[Sample Explanation #1]**  The figure above shows the positions of all lines in the Cartesian coordinate plane, and they form $10$ triangles in total. **[Constraints]** For $100\%$ of the testdata, $1 \le N \le 3 \times 10^5$, and $|A_i|, |B_i|, |C_i| \le 10^9$. **[Notes]** The scoring of this problem follows the original COCI setting, with a full score of $140$. This problem is translated from [COCI2013_2014](https://hsin.hr/coci/archive/2013_2014/) [CONTEST #5](https://hsin.hr/coci/archive/2013_2014/contest5_tasks.pdf) _**T5 TROKUTI*_. Translated by ChatGPT 5