output_description: Print "4", "3", "2", "1" or "0" in a line.
input_description: Coordinates and radii of $c1$ and $c2$ are given in the following format.
  
  $c1x \; c1y \; c1r$  
  $c2x \; c2y \; c2r$
  
  $c1x$, $c1y$ and $c1r$ represent the center coordinate and radius of the first
  circle. $c2x$, $c2y$ and $c2r$ represent the center coordinate and radius of
  the second circle. All input values are given in integers.
attempt: import math
  from enum import Enum, auto
  
  
  class TwoCircle(Enum):
      DISTANT = auto()
      CIRCUMCSCRIBING = auto()
      INTERSECTING = auto()
      INSCRIBING = auto()
      CONTAINING = auto()
  
  
  class Point:
      def __init__(self, x, y):
          self.x = x
          self.y = y
  
      def distance(self, pnt):
          return math.sqrt((self.x - pnt.x) ** 2 + (self.y - pnt.y) ** 2)
  
  
  class Circle:
      def __init__(self, x, y, r):
          self.c = Point(x, y)
          self.r = r
  
      def is_intersected(self, cir):
          d = self.c.distance(cir.c)
          if d > self.r + cir.r:
              return TwoCircle.DISTANT
          elif d == self.r + cir.r:
              return TwoCircle.CIRCUMCSCRIBING
          elif d == abs(self.r - cir.r):
              return TwoCircle.INSCRIBING
          elif d < abs(self.r - cir.r):
              return TwoCircle.CONTAINING
          else:
              return TwoCircle.INTERSECTING
  
  
  x1, y1, r1 = list(map(int, input().split(" ")))
  x2, y2, r2 = list(map(int, input().split(" ")))
  cir1 = Circle(x1, y1, r1)
  cir2 = Circle(x2, y2, r2)
  
  judged = cir1.is_intersected(cir2)
  if judged == TwoCircle.DISTANT:
      print(4)
  elif judged == TwoCircle.CIRCUMCSCRIBING:
      print(3)
  elif judged == TwoCircle.INTERSECTING:
      print(2)
  elif judged == TwoCircle.INSCRIBING:
      print(1)
  elif judged == TwoCircle.CONTAINING:
      print(0)
  
problem_description: Intersection of Circles
  
  For given two circles $c1$ and $c2$, print
  
      
      
      4
      
  
  if they do not cross (there are 4 common tangent lines),
  
      
      
      3
      
  
  if they are circumscribed (there are 3 common tangent lines),
  
      
      
      2
      
  
  if they intersect (there are 2 common tangent lines),
  
      
      
      1
      
  
  if a circle is inscribed in another (there are 1 common tangent line),
  
      
      
      0
      
  
  if a circle includes another (there is no common tangent line).
samples: [{"input": "1 1 1\n    6 2 2", "output": "4"}, {"input": "1 2 1\n    4 2 2", "output": "3"}, {"input": "1 2 1\n    3 2 2", "output": "2"}, {"input": "0 0 1\n    1 0 2", "output": "1"}, {"input": "0 0 1\n    0 0 2", "output": "0"}]