G :: Party Location

Time Limit: 10 Seconds    Memory Limit: 131072 KB

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).

 

Input

The input will consist of multiple tests. For each test there will be a single integer N ≤ 200, the number of contestants. Next there will be N lines, each containing two floating point numbers indicating the (x, y) coordinates of the house of one of the
contestants. Each coordinate is between 0.0 and 50.0 (km). Each house is at a distinct location.

Output

For each test output a single integer, the maximum number of contestants that can attend the party.

Sample Input

8
4.0 4.0
4.0 5.0
5.0 6.0
1.0 20.0
1.0 21.0
1.0 22.0
1.0 25.0
1.0 26.0

Sample Output

4

Submit

Source: University of Waterloo Local Contest 2011.10.02