Dezider's Coverup

Time Limit: Java: 1000 ms / Others: 1000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB


Zlatica to his house for dinner. The trouble is, he tripped with the sauce in his hands (thankfully this was in the morning and Zlatica did not see it) and many bright red droplets fell on his white carpet. Now Dezider is starting to panic because he wants to have a perfectly clean house to impress Zlatica. Fortunately, there is a store nearby which sells all sizes of (expensive) circular rugs. Dezider does not have much money so he wants to buy the smallest rug with an integer radius which will cover all the droplets. You need to write a program to help him determine the right size to buy.


Each test cases starts with one positive integer n, the number of droplets on the carpet. Each of the following n lines contains two floating-point numbers, separated by white space, which represent the x- and y-coordinate of the corresponding droplet.


One line for each test case which consists of a single integer, the radius of the smallest circular rug needed to cover all the droplets.

Sample Input

1 -0.5
1.5 0
0.5 0.5
1 0.5

Sample Output


because a circular rug of radius 1 and center for example at 1,0 will cover the four droplets
described by the input.




Northeast North Ameriaca Regional Contest 200