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: Wrong Answer)


def santen(x1,y1,x2,y2,x3,y3)
    
    xsi=(y1-y3)*(y1**2 -y2**2 +x1**2 -x2**2) -(y1-y2)*(y1**2 -y3**2 +x1**2 -x3**2)
    xbo=2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3)
    
    ysi= (x1-x3)*(x1**2 -x2**2 +y1**2 -y2**2)-(x1-x2)*(x1**2 -x3**2 +y1**2 -y3**2)
    ybo=2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3)
    
    x=xsi.to_f/xbo.to_f
    y=ysi.to_f/ybo.to_f
    r2=(x-x1)**2+(y-y1)**2
    r=r2**0.5
    
    return [x,y,r]
    
end

def inout(x1,x2,y1,y2,r)
    if y1.finite? && y2.finite? && r.finite?
        return (x1-y1)**2+(x2-y2)**2 <= r**2
    else
    return false
    end
end

n=gets.to_i
array=[]
n.times {
    array<<gets.split.map(&:to_i)
}

if n==2 
    r22=(array[0][0]-array[1][0])**2+(array[0][1]-array[1][1])**2
    puts r22**0.5/2
    exit
end

i=0
n.times {
    j=i+1
    n.times {
        k=j+1
        n.times {
            if i>=n || j>=n || k>=n
                break
            else
              sanarray=santen(array[i][0],array[i][1],array[j][0],array[j][1],array[k][0],array[k][1])
                  l=0
                  n.times {
                      
                      if inout(array[l][0],array[l][1],sanarray[0],sanarray[1],sanarray[2])
                       l+=1
                      else
                       break
                      end
                      if l==n
                       puts sanarray[2]
                       exit
                      end
                    
                  }
            end
            k+=1
        }
        j+=1
    }
    i+=1
}