Swamp Things

A photograph is a set of bright spots on a black background, given as points in the plane. Some of the spots are lights from train windows, and the train runs along a perfectly straight track, so those spots are collinear.

To remove them, find the line that passes through the most spots. If four or more spots lie on that line, eliminate all of the spots on it (they are assumed to be train windows). If two or more lines are tied for the most spots, any one of them may be chosen, but the number of eliminated spots is the same either way. If no line passes through four or more spots, assume there is no train and eliminate nothing.

For each photograph, report how many spots are eliminated.

The input is a series of test cases. Each test case describes one photograph: a line with a positive integer $n$ ($n \le 1000$), the number of distinct spots, followed by $n$ lines, each containing the integer coordinates $x$ $y$ of one spot. All coordinates are between $0$ and $10000$.

A line containing a single $0$ follows the last photograph and must not be processed.

For each photograph, output one line of the form Photo k: c points eliminated, where $k$ is the photograph number (starting at $1$) and $c$ is the number of spots eliminated.