문제

Authors: Adrian Satja Kurdija, Marin Tomić

You are given N lines, their equations being Ai x + Bi y + Ci = 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.

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: Ai, Bi and Ci, the numbers defining the ith 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. A possible position of lines. Authors: Adrian Satja Kurdija, Marin Tomić

예제 입력 1

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

예제 출력 1

10

예제 입력 2

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

예제 출력 2

10