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: Accepted)

n = int(input())
l = [tuple(map(int, input().split())) for _ in range(n)]
ans = 10**5
dist = lambda p,q: ((p[0]-q[0])**2 + (p[1]-q[1])**2)**.5
check = lambda c,d: all(dist(c,p)<=d for p in l)

def S(p1,p2,p3):
  a,b = p1; c,d = p2; e,f = p3
  return abs((d-b)*(e-a) - (f-b)*(c-a))

def disk(p1,p2,p3):
  x1,y1 = p1; x2,y2 = p2; x3,y3 = p3
  a2 = (x2 - x3) **2 + (y2 -y3) ** 2 
  b2 = (x1 - x3) **2 + (y1 -y3) ** 2
  c2 = (x2 - x1) **2 + (y2 -y1) ** 2
  area = ((x2 - x1) * (y3 -y1) - (x3 -x1) * (y2- y1)) / 2
  if area == 0:
    return (0,0),10**5
  x = (a2*(b2+c2-a2)*x1 + b2*(c2+a2-b2)*x2 +c2*(a2+b2-c2)*x3) / (16*area*area)
  y = (a2*(b2+c2-a2)*y1 + b2*(c2+a2-b2)*y2 +c2*(a2+b2-c2)*y3) / (16*area*area) 
  r = ((x1 - x ) ** 2 + (y1 - y) ** 2)**.5
  return (x,y), r

for i in range(n-1):
  for j in range(i+1,n):
    c = ((l[i][0]+l[j][0])/2, (l[i][1]+l[j][1])/2)
    d = dist(l[i],l[j])/2
    if check(c,d) and d < ans:
      ans = d
    
for i in range(n-2):
  for j in range(i+1,n-1):
    for k in range(j+1,n):
      c,d = disk(l[i],l[j],l[k])
      if check(c,d) and d < ans:
        ans = d
        
print(ans)