TROKUTI

문제

You are given N lines, their equations being A_ix + B_iy + C_i = 0 in the coordinate plane. Calculate the number of triangles whose sides lie on the given lines. Since the result can be very large, output the number modulo 1 000 000 007. 

A possible position of lines.

Important note: No three lines will intersect at the same point. 

입력

The first line of input contains the integer N (1 ≤ N ≤ 300 000), the number of lines. 

Each of the following N lines contains three integers: A_i, B_i and C_i, the numbers defining the i^th line. All numbers will be lesser than 10⁹. 

출력

The first and only line of output must consist of the required number from the task. 

힌트

Clarification of the first example: The example corresponds to the image in the task.

6
0 1 0
-5 3 0
-5 -2 25
0 1 -3
0 1 -2
-4 -5 29

10

5
-5 3 0
-5 -3 -30
0 1 0
3 7 35
1 -2 -1

10