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 Python (3.4.3) (judge verdict: Runtime Error)

import math

n=int(input())
xy=[list(map(int,input().split())) for i in range(n)]
#xy+=[(xy[0][0]+xy[1][0])//2, (xy[0][1]+xy[1][1])//2]

def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
    y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
    r = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
    return x,y,r

r=10**9
for i in range(n-1):
 x1=xy[i][0]
 y1=xy[i][1]
 for j in range(i+1,n):
  x2=xy[j][0]
  y2=xy[j][1]
  for k in range(j+1,n+1):
   x3=xy[k][0]
   y3=xy[k][1]
   d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
   if d!=0:
    rx,ry,rr=get_circle_center_and_radius(x1, y1, x2, y2, x3, y3)
   for z in range(n):
    xz=xy[z][0]
    yz=xy[z][1]
    check=1
    if xz!=x1 and xz!=x2 and xz!=x3 and yz!=y1 and yz!=y2 and yz!=y3:
     if ((xz-rx)**2+(yz-ry)**2)**0.5>rr:
      check=-1
   if check==1:
    try:
     r=min(r,rr)
    except:
     pass

print(r)