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 ~1\,000\,000\,007~.

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 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^\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\%~ of total points, ~N~ will be at most ~1\,000~.

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