0067. Three Spheres

Input file name:	spheres.in
Output file name:	spheres.out
Time limit:	1 s
Memory limit:	64 megabytes

You are given three spheres in the space. Find all their common tangent planes, i.e. such planes that touch each of the given spheres in exactly one point.

Input file

The first line of the input file contains one integer number M – the number of test cases. The following 3M lines contain descriptions of test cases, three lines per test case. Each line in the test case describes one sphere. Each description contains four integer numbers: x, y, z and r – coordinates of the center and the radius of the sphere (-500 ≤ x, y, z ≤ 500, 0 < r ≤ 500). Sphere centers do not coincide and do not lie on the same line.

Output file

For each test case first output K – the number of different tangent planes for given spheres. Next K lines must contain four real numbers A, B, C and D each, such that A²+B²+C²=1 and the equation describing the plane is Ax+By+Cz=D. Plane descriptions may be printed in arbitary order. Output all numbers with at least eight digits after the decimal point.

Examples:

spheres.in	spheres.out
1 0 0 0 1 0 2 0 1 2 0 0 1	4 0.00000000 1.00000000 0.00000000 1.00000000 1.00000000 0.00000000 0.00000000 1.00000000 0.00000000 0.00000000 1.00000000 -1.00000000 0.00000000 0.00000000 1.00000000 1.00000000

Source: Petrozavodsk Winter 2003. St. Petersburg Contest I

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