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Problems

Points

Points

Time limit 1 second
Memory limit 64 MiB

On a plane are set N points. Separately on a plane two base points are set.

Write a task program POINTS, which can find the maximal quantity of points which will get in a bar created the pair of parallel lines arbitrarily of conducted through base points. It is not needs to include base points to the sum of points. If a point lies on a line you must account it in a sum.

Input data

The first line contains one integer N (0N10000) - the qauntity of points. The second line contains the coordinates of two base points in the format x_1, y_1x_2y_2. Each of next N lines contains the co-ordinates of the point of plane in the format x, y. Coordinates of points are integers, which does not exceed 10000 by the module. Base points differ at least one coordinate.

Output data

Print one integer - the maximal quantity of points, which will be in a bar, which will be formed the optimum conducted parallel lines through base points.

Examples

Input example #1
4
0 0 50 0
0 -50
-1 0
50 0
100 50
Output example #1
3
Author Bogdan Rublev, Taras Galkovskiy
Source 2008 XXI All-Ukrainian Informatics Olympiad, Lvov, April 5 - 11, Round 2