| Lining Up |
``How am I ever going to solve this problem?" said the pilot.
Indeed, the pilot was not facing an easy task. She had to drop packages at specific points scattered in a dangerous area. Furthermore, the pilot could only fly over the area once in a straight line, and she had to fly over as many points as possible. All points were given by means of integer coordinates in a two-dimensional space. The pilot wanted to know the largest number of points from the given set that all lie on one line. Can you write a program that calculates this number?
Your program has to be efficient!
The input begins with a single positive integer on a line by itself
indicating the number of the cases following, each of them as described below.
This line is followed by a blank line, and there is also a blank line between
two consecutive inputs.
The input consists of N pairs of integers,
where 1 < N < 700. Each pair of integers is separated by one blank
and ended by a new-line character. The list of pairs is ended with an
end-of-file character. No pair will occur twice.
For each test case, the output must follow the description below. The outputs
of two consecutive cases will be separated by a blank line.
The output
consists of one integer representing the largest number of points that all lie
on one line.
1 1 1 2 2 3 3 9 10 10 11
3