output_description: 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}.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      x_1 y_1
      :
      x_N y_N
attempt: N = int(input())
  XY = [list(map(int, input().split())) for i in range(N)]
  from itertools import combinations
  
  a = 9999
  
  
  def f(X, Y, R2, a):
      if not any([(X - x) ** 2 + (Y - y) ** 2 > R2 for x, y in XY]):
          a = min(a, R2**0.5)
      return a
  
  
  for (x1, y1), (x2, y2), (x3, y3) in combinations(XY, 3):
      e1 = (x2 - x3) ** 2 + (y2 - y3) ** 2
      e2 = (x3 - x1) ** 2 + (y3 - y1) ** 2
      e3 = (x1 - x2) ** 2 + (y1 - y2) ** 2
      p = e1 * (e2 + e3 - e1)
      q = e2 * (e3 + e1 - e2)
      r = e3 * (e1 + e2 - e3)
      if p + q + r == 0:
          continue
      X = (p * x1 + q * x2 * r * x3) / (p + q + r)
      Y = (p * y1 + q * y2 + r * y3) / (p + q + r)
      R2 = (X - x1) ** 2 + (Y - y1) ** 2 + 10e-15
      a = f(X, Y, R2, a)
  for (x1, y1), (x2, y2) in combinations(XY, 2):
      X = (x1 + x2) / 2
      Y = (y1 + y2) / 2
      R2 = (X - x1) ** 2 + (Y - y1) ** 2 + 10e-15
      a = f(X, Y, R2, a)
  print(a)
  
problem_description: 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.
samples: [{"input": "2\n    0 0\n    1 0", "output": "0.500000000000000000\n    \n\nBoth points are contained in the circle centered at (0.5,0) with a radius of\n0.5.\n\n* * *"}, {"input": "3\n    0 0\n    0 1\n    1 0", "output": "0.707106781186497524\n    \n\n* * *"}, {"input": "10\n    10 9\n    5 9\n    2 0\n    0 0\n    2 7\n    3 3\n    2 5\n    10 0\n    3 7\n    1 9", "output": "6.726812023536805158\n    \n\nIf the absolute or relative error from our answer is at most 10^{-6}, the\noutput will be considered correct."}]