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: Wrong Answer)

INF=float('inf')
N=int(input())
xy=[list(map(int, input().split())) for i in range(N)]

out=INF
def f2(x1, y1, x2, y2):
  cx, cy=centor(x1, y1, x2, y2)
  r2=length2(cx, cy, x1, y1)
  return r2, cx, cy

def f3(x1, y1, x2, y2, x3, y3):
  a1=grad(x1, y1, x2, y2)
  a2=grad(x2, y2, x3, y3)
  if a1==a2:
    return False, False, False
  
  c1x, c1y=centor(x1, y1, x2, y2)
  c2x, c2y=centor(x2, y2, x3, y3)
  b1=c1y-a1*c1x
  b2=c2y-a2*c2x
  if a1<a2:
    a1, a2=a2, a1
    b1, b2=b2, b1
    c1x, c2x=c2x, c1x
    c1y, c2y=c2y, c1y
    
  if a1==float('inf'):
    cx, cy=c1x, a2*c1x+b2
  else:
    cx, cy=lines_cross_point(a1, b1, a2, b2)
  
  r2=length2(x1, y1, cx, cy)
  return r2, cx, cy
  
def lines_cross_point(a1, b1, a2, b2):
  cross_x=-(b1-b2)/(a1-a2)
  cross_y=a1*cross_x+b1
  return cross_x, cross_y

def length2(x1, y1, x2, y2):
  return (x1-x2)**2+(y1-y2)**2

def centor(x1, y1, x2, y2):
  return (x1+x2)/2, (y1+y2)/2

def grad(x1, y1, x2, y2):
  if x1==x2:
    return float('inf')
  else:
    return (y1-y2)/(x1-x2)
  
def enc2(r2, cx, cy):
  for i in range(N):
    if length2(xy[i][0], xy[i][1], cx, cy)>r2+10**(-3):
      return False
  return True

for i in range(N-1):
  for j in range(i+1, N):
    r2, cx, cy=f2(xy[i][0], xy[i][1], xy[j][0], xy[j][1])
    if enc2(r2, cx, cy) and r2<out:
      out=r2
      
for i in range(N-2):
  for j in range(i+1, N-1):
    for k in range(j+1, N):
      r2, cx, cy=f3(xy[i][0], xy[i][1], xy[j][0], xy[j][1], xy[k][0], xy[k][1])
      if enc2(r2, cx, cy) and r2<out:
        out=r2
        
print(pow(out, 1/2))