Problem:
Score : 600 points

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

2 \leq N \leq 50

0 \leq x_i \leq 1000

0 \leq y_i \leq 1000

The given N points are all different.

The values in input are all integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N=gets.to_i
$x,$y=N.times.map{gets.split.map(&:to_i)}.transpose
def dist(x,y)
    res=0.0
    N.times do |i|
        d=((x-$x[i])**2+(y-$y[i])**2)**(1/2.0)
        res=res<d ? d : res
    end
    return res
end

ylrec=0.0
lx=0.0
rx=1000.0
80.times do |i|
    cl=(lx*2+rx)/3
    cr=(lx+rx*2)/3
    ly1=0.0
    ry1=1000.0
    80.times do |j|
        ccl=(ly1*2+ry1)/3
        ccr=(ly1+ry1*2)/3
        if dist(cl,ccl)>dist(cl,ccr)
            ly1=ccl
        else
            ry1=ccr
        end
    end
    ylrec=ly1
    ly1=0.0
    ry1=1000.0
    80.times do |j|
        ccl=(ly1*2+ry1)/3
        ccr=(ly1+ry1*2)/3
        if dist(cr,ccl)>dist(cr,ccr)
            ly1=ccl
        else
            ry1=ccr
        end
    end
    yrrec=ly1
    if dist(cl,ylrec)<dist(cr,yrrec)
        rx=cr
    else
        lx=cl
    end
end
puts dist(lx,ylrec)