22398_IncidentalPoints

Unlike a straight line, a straight segment between two points P₁, P₂ (normally written as ) is a line that links the two points but doesn't extend beyond them. A third point P₃ is said to be incident to iff P₃ lies on the straight line and between the points P₁ and P₂. is said to include P₃. By definition, P₁ and P₂ are included in . Write a program to find the segment that includes the most number of given points.

Your program will be tested on one or more test cases. Each est case includes a set of two or more unique points, where the Cartesian coordinates of each point is specified on a separate line using two integers X and Y where 0 ≤ |X| , |Y| < 1,000,000. No test case has more than 1000 points. An input line made of two or more '-' (minus signs) signals the end of a test case. An extra input line of two or more '-' (minus signs) follow the last test case.

For each test case, output the result on a single line using the following format:

k. n

Where k is the test case number (starting at 1,)  ' ' is a single space, and n is the number of points on the segment.

1 1
1 5
5 9
9 5
5 5
3 2
5 3
----
1 5
5 1
1 1
5 5
--
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1. 4
2. 2