Goal
You are given a set of infinite lines in a 2D (x-y) plane.
Your task is to find all the intersection points of these lines.
Input
First line: an integer N — the number of infinite lines
Next N lines: four space-separated integers x1 y1 x2 y2 describing one infinite line passing through points (x1, y1) and (x2, y2)
Output
First line: an integer K — the number of intersection points.
Next K lines: two space-separated real numbers x y representing the coordinates of each intersection point.
Output the points in ascending order, sorted by x-coordinate and then by y-coordinate.
Each coordinate must be rounded and printed to 3 decimal places.
When multiple lines intersect in the same point, output it only once.
NOTES:
In geometry, two coincident lines have infinite number of intersection points.
However, for the purpose of this puzzle, coincident lines are treated as parallel and no intersection point should be output.
Constraints
0 ≤ N ≤ 10
0 ≤ K ≤ 45
−100 ≤ x1, y1, x2, y2 ≤ 100
For each given line, (x1, y1) ≠(x2, y2).
Example
Input
3
-6 -5 12 12
4 -44 9 19
4 -44 50 19
Output
3
4.000 -44.000
8.156 8.370
117.955 112.068
