Dirby just draw a triangle with red ink, and then he draw its circumscircle and its incircle with blue ink. However, he spilled some water into his drawing and unfortunately the red ink disappeared. Dirby is too lazy to make another drawing, so he wants to reconstruct the triangle given the two circles. Since he is not too good in geometry, he wants you to do this task for him. Can you?

**Input**

Input consists of several cases,
each one with six real numbers *x*_{1}, *y*_{1}, *r*_{1}, *x*_{2}, *y*_{2} and *r*_{2},
which indicate the center and the radius
of the circumcircle and of the incircle, respectively.
You can assume that he incircle is inside the circumcircle,
that the coordinates do not exceed 1000 in absolute value,
and that they have at most 8 decimal digits.
No given case is ill-conditioned.

**Output**

For every case,
print with 8 digits after the decimal point
the coordinates *x*, *y* of the vertices of a triangle
that has the desired circumcircle and incircle, all separated by spaces.
If there is more than one solution, print any of them.
If there is no solution, print “`impossible`”.

**Observations**

Calculate using the `long double` type.
Solutions that fulfill the mathematical conditions
with a “reasonable small” error will be accepted.
Similarly, assume that a solution is possible
when the distances the the circles are “small enough”.
For this problem, the judge will use a huge ε = 10^{−4}.

Public test cases

**Input**

4 3 5 2 2 2 4 3 5 2 2 2.5

**Output**

0.00000000 0.00000000 8.00000000 0.00000000 0.00000000 6.00000000 impossible

Information

- Author
- Ivan Geffner
- Language
- English
- Official solutions
- C++
- User solutions
- C++