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 Ruby (judge verdict: Accepted)

x0,y0,r0,x1,y1,r1=$<.read.split.map(&:to_i)
d=Math.hypot(x0-x1,y0-y1)
r0,r1=[r0,r1].minmax
if d>r0+r1
	p 4
elsif d==r0+r1
	p 3
elsif d>r1-r0
	p 2
elsif d==r1-r0
	p 1
else
	p 0
end