After the programming contest, all of the contestants would like to throw a party. After the party, however, it will be late, and the contestants will be too tired to walk a long way home. In particular, each contestant refuses to come to the party if it is more than 2.5 km from his or her house.
The solution is to hold the party as close to as many of the contestants' houses as possible. This is where you come in: your job is to determine the optimal location for the party, so that as many contestants as possible will be willing to attend it.
We consider the city to be a flat square, 50 km on each side. A contestant can walk directly from the party in a straight line to his or her house (there are no obstacles).
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