Time Limit: 2 Seconds
Memory Limit: 65536 KB
There are three circles in the plane. And some of them may coincide. Your task is to find a circle orthogonal to all the three circles.
Two circle are orthogonal to each other if one of them cuts the other at right angles.
There are multiple test cases. The first line of input contains an integer T(T≤ 10000) indicating the number of test cases. For each test case:
There are 9 integers one line: x1, y1, r1, x2, y2, r2 and x3, y3, r3. (xi, yi) and ri are the center and the radius of the i-th circle. (1≤ xi, yi, ri≤ 105)
Each test case in one line: output the coordinate the center of the circle you found if possible, otherwise, output "Impossible!". The coordinates should be integers or irreducible fractions. If there are multiple solutions, you can choose arbitrary one. And each line you output should be no more than 100 characters.