Incidental Points

Unlike a line, the segment $P_1P_2$ joining two points $P_1$ and $P_2$ connects them without extending beyond either endpoint. A third point $P_3$ is said to be incident to $P_1P_2$ if it lies on the straight line through $P_1$ and $P_2$ and falls between them; in that case the segment $P_1P_2$ is said to include $P_3$. By definition, the endpoints $P_1$ and $P_2$ are themselves included in $P_1P_2$.

Given a set of points in the plane, choose two of them to form a segment. Write a program that finds the largest number of the given points that a single such segment can include.

Your program is tested on one or more test cases. Each test case is a set of two or more distinct points; the Cartesian coordinates of each point are given on their own line as two integers $X$ and $Y$ with $0 \le |X|,\ |Y| < 10^6$. No test case contains more than 1000 points. A line consisting of two or more - (minus signs) marks the end of a test case. One additional line of two or more - follows the last test case.

For each test case, print the result on a single line in the format k. n, where $k$ is the test case number (starting from 1), the period is followed by a single space, and $n$ is the number of points lying on the segment that includes the most points.