Random Points#1630
Unlike a straight line, a segment between two points P_1 and P_2 is a line that connects these two points and does not extend beyond them. A third point P_3 is said to be incident to the segment if P_3 lies on the straight line and between P_1 and P_2. In this case, the segment is said to include P_3. By definition, P_1 and P_2 are included in the segment. Write a program to find the segment that contains the largest number of the given points.
Your program will be tested on one or more test cases. Each test case includes a set of two or more unique points, where the Cartesian coordinates of each point are specified on a separate line using two integers and , where 0 \leq |X|, |Y| < 1000000. No test case has more than points. An input line made of two or more '-' (minus signs) signals the end of a test case. After the last test case, there is one more input line consisting of two or more '-' (minus signs).
For each test case, output the result on a single line in the following format:
k. n
Where is the test case number (starting from ), and is the number of points on the segment.
Example 1