Description
Background
Line segments are a very common element in computational geometry. A line segment is the set of points forming the shortest path between two points (including those points). Although they are a very basic concept it can be hard to work with them if they appear in huge numbers unless you have an efficient algorithm.
Problem
Given a set of line segments, count how many distinct pairs of line segments are overlapping. Two line segments are said to be overlapping if they intersect in an infinite number of points.
Input
The first line contains the number of scenarios.
Each scenario starts with the number n of line segments (1 <= n <= 100000). Then follow n lines consisting of four integers x1, y1, x2, y2 in the range [0, 1000000] each, representing a line segment that connects the points (x1, y1) and (x2, y2). It is guaranteed that a line segment does not degenerate to a single point.
Output
The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the number of distinct pairs of overlapping line segments followed by an empty line.
Hint: The number of overlapping pairs may not fit into a 32-bit integer.
Sample Input
2
8
1 1 2 2
2 2 3 3
1 3 3 1
10 0 20 0
20 0 30 0
15 0 25 0
50 0 100 0
70 0 80 0
1
0 0 1 1
Sample Output
Scenario #1:
3
Scenario #2:
0
