You are given $N$ lines, their equations being $A_{i}x+B_{i}y+C_i=0$ 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 $1000000007$.

A possible position of lines.

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

Input Specification

The first line of input contains the integer $N$ $(1\le N\le 300000)$, the number of lines.

Each of the following $N$ lines contains three integers: $A_i$, $B_i$ and $C_i$, the numbers defining the $i^{\text{th}}$ line.

All numbers will have absolute value at most ${10}^9$.

Output Specification

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

Scoring

In test cases worth $40\mathrm{\%}$ of total points, $N$ will be at most $1000$.

Sample Input 1

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

Sample Output 1

10

Explanation for Sample Output 1

The example corresponds to the image in the task.

Sample Input 2

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

Sample Output 2

10