Point of View in Flatland

Everything is flat in Flatland. The planets are round but flat; that is, each is a disc lying in a plane.

You are given the centers and radii of three planets in Flatland. Find the point from which all three planets are seen at the same angle — that is, they have the same apparent size measured as angular diameter. Call such a point an isoobservation point. There can be at most two such points, and you must report the one that gives the largest angular diameter of the planets.

To simplify the problem you may assume that:

• The centers of the three discs are not all collinear.
• The discs are totally disjoint.
• The discs are transparent and non-refractive: a disc is visible with the same apparent shape and size whether or not another disc lies in front of it.
• The input is such that the existence or non-existence of such a point is computable even with slight rounding error — but use double precision.

The input consists of several cases, each on a single line. Each line has nine numbers, three for each disc. Each triple gives the x and y coordinates of a disc center and the radius r of that disc.

The input is terminated by a line of nine zeros, which must not be processed.

For each case, print the x and y coordinates of the isoobservation point described above, each rounded to two decimal places and separated by a single space. If no such point exists, print No solution.