Party Location#2643
After the programming contest, all of the contestants want to throw a party. However, after the party it will be late, and the contestants will be too tired to walk a long distance home. In particular, each contestant will not attend the party if it is more than km from their house.
To solve this, the party should be held as close as possible to as many contestants' houses as possible. Your task is to determine the optimal location for the party, so that the maximum number of contestants are willing to attend.
We consider the city to be a flat square, km on each side. A contestant can walk directly from the party to their house in a straight line (there are no obstacles).
Standard input consists of several lines, each containing two floating point numbers indicating the coordinates of a contestant's house. Each coordinate is between and (km). Each house is at a distinct location. There are at most contestants.
Standard output consists of a single integer: the maximum number of contestants that can attend the party.
Exemplul 1