Tangent to the sphere

Input

The first line contains the number of tests $M$ . The following $3 M$ lines describe the spheres. Each sphere is given by four integers: the coordinates of its center and its radius. All numbers are integers; all coordinates are within $- 500$ to $500$ , the radius is greater than zero and does not exceed $500$ . The centers of the spheres do not coincide and do not lie on a straight line.

Output

For each test, output the number of distinct common tangent planes $K$ . The next $K$ lines describe these planes. Each line should contain four real numbers $A$ , $B$ , $C$ , $D$ , describing the plane $A x + B y + C z = D$ Ax + By + Cz = D such that $A^{2} + B^{2} + C^{2} = 1$ A^2 + B^2 + C^2 = 1. The planes can be printed in any order. The numbers must be printed with at least $5$ digits after the decimal point.

Examples

Example 1

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