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: import math
  
  cx = 0
  cy = 0
  r = 0
  x1 = 0
  y1 = 0
  x2 = 0
  y2 = 0
  x3 = 0
  y3 = 0
  c = 0
  
  for i in range(int(input())):
      x, y = map(int, input().split())
      l = math.sqrt((x - cx) ** 2 + (y - cy) ** 2)
      print(x, y, l)
      if c == 0:
          x1 = x
          y1 = x
          cx = x
          cy = y
          c += 1
      if l > r:
          if c == 1:
              x2 = x
              y2 = y
              cx = (x1 + x2) / 2
              cy = (y1 + y2) / 2
              r = math.sqrt((cx - x1) ** 2 + (cy - y1) ** 2)
              c += 1
          elif c == 2:
              x3 = x
              y3 = y
              d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
              cx = (
                  (y1 - y3) * (y1**2 - y2**2 + x1**2 - x2**2)
                  - (y1 - y2) * (y1**2 - y3**2 + x1**2 - x3**2)
              ) / d
              cy = (
                  (x1 - x3) * (x1**2 - x2**2 + y1**2 - y2**2)
                  - (x1 - x2) * (x1**2 - x3**2 + y1**2 - y3**2)
              ) / -d
              r = math.sqrt((cx - x1) ** 2 + (cy - y1) ** 2)
              print(r)
              c += 1
          elif c == 3:
              l1 = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
              l2 = math.sqrt((x - x2) ** 2 + (y - y2) ** 2)
              l3 = math.sqrt((x - x3) ** 2 + (y - y3) ** 2)
              if min([l1, l2, l3]) == l1:
                  x1 = x
                  y1 = y
              if min([l1, l2, l3]) == l2:
                  x2 = x
                  y2 = y
              if min([l1, l2, l3]) == l3:
                  x3 = x
                  y3 = y
              d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
              cx = (
                  (y1 - y3) * (y1**2 - y2**2 + x1**2 - x2**2)
                  - (y1 - y2) * (y1**2 - y3**2 + x1**2 - x3**2)
              ) / d
              cy = (
                  (x1 - x3) * (x1**2 - x2**2 + y1**2 - y2**2)
                  - (x1 - x2) * (x1**2 - x3**2 + y1**2 - y3**2)
              ) / -d
              r = math.sqrt((cx - x1) ** 2 + (cy - y1) ** 2)
  
  print(r)
  
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."}]