Maple trees

Time Limit: 1000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

There are a lot of trees in HDU. Kiki want to surround all the trees with the minimal required length of the rope . As follow,

To make this problem more simple, consider all the trees are circles in a plate. The diameter of all the trees are the same (the diameter of a tree is 1 unit). Kiki can calculate the minimal length of the rope , because it's so easy for this smart girl.
But we don't have a rope to surround the trees. Instead, we only have some circle rings of different radius. Now I want to know the minimal required radius of the circle ring. And I don't want to ask her this problem, because she is busy preparing for the examination.
As a smart ACMer, can you help me ?

Input

The input contains one or more data sets. At first line of each input data set is number of trees in this data set n (1 <= n <= 100), it is followed by n coordinates of the trees. Each coordinate is a pair of integers, and each integer is in [-1000, 1000], it means the position of a tree’s center. Each pair is separated by blank.
Zero at line for number of trees terminates the input for your program.

Output

Minimal required radius of the circle ring I have to choose. The precision should be 10^-2.

Sample Input

2 1 0 -1 0 0

Sample Output

1.50

Hint

lcy

Source


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