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Problems

Incidental Points

Incidental Points

Time limit 1 second
Memory limit 64 MiB

Unlike a straight line, a straight segment between two points P_1, P_2 (normally written as ) is a line that links the two points but doesn’t extend beyond them. A third point P_3 is said to be incident to iff P_3 lies on the straight line and between the points P1 and P2. is said to include P_3. By definition, P_1 and P_2 are included in . Write a program to find the segment that includes the most number of given points.

Input data

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 is specified on a separate line using two integers X and Y where 0 ≤ |X|, |Y| < 1000000. 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.

Output data

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), and n is the number of points on the segment.

Examples

Input example #1
1 1
1 5
5 9
9 5
5 5
3 2
5 3
----
1 5
5 1
1 1
5 5
----
--
Output example #1
1. 4
2. 2