Problem:
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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).

Input

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.

Output

Print "4", "3", "2", "1" or "0" in a line.

Constraints

$-1,000 \leq c1x, c1y, c2x, c2y \leq 1,000$

$1 \leq c1r, c2r \leq 1,000$

$c1$ and $c2$ are different

Sample Input 1

1 1 1
6 2 2

Sample Output 1

4

Sample Input 2

1 2 1
4 2 2

Sample Output 2

3

Sample Input 3

1 2 1
3 2 2

Sample Output 3

2

Sample Input 4

0 0 1
1 0 2

Sample Output 4

1

Sample Input 5

0 0 1
0 0 2

Sample Output 5

0

Solution in Python3 (judge verdict: Accepted)

import math

while True:
    try:
        C1=list(map(int,input().split()))
        C2=list(map(int,input().split()))
        
        d = math.sqrt(math.pow(C2[0]-C1[0],2)+math.pow(C2[1]-C1[1],2))
        if(d > C1[2]+C2[2]):
            print("4")
        elif(d == C1[2]+C2[2]):
            print("3")
        elif(math.fabs(C1[2]-C2[2]) < d and d < C1[2]+C2[2]):
            print("2")
        elif(d == math.fabs(C1[2]-C2[2])):
            print("1")
        elif(d < math.fabs(C1[2]-C2[2])):
            print("0")
    except:
        break;