See Problem N for PDF statements.

Twilight Sparkle finds that each of the black holes is a convex regular polyhedron with faces (a convex polyhedron whose faces are identical regular polygons), and the length of its edges is .

Every day the black hole will shrink exactly once. If a black hole shrinks, it will become the convex hull of geometry centers of the original black hole's faces. And whenever the black hole isn't a regular polyhedron, it will disappear forever.

Twilight Sparkle has made records for the black holes she has observed. Each of the records can be described as a tuple , indicating that a convex regular polyhedron black hole with edges of length and faces initially has shrunk times. However, naughty Rainbow Dash replaced some of the records with impossible ones. Can you find out the impossible records and calculate the final and after times of shrinking for those possible records?

The first line contains an integer  , denoting the number of the records.

In the following  lines, each line describes a record and contains three integers  (, , ).

For each of the records, if the record is impossible, output  in a single line. Otherwise, output  followed by an integer  and a real number  in a single line, separated by spaces.  is considered correct if the relative or absolute error between yours and the standard solution is not greater than .

3
2 10 1
4 10 1
6 10 1

impossible
possible 4 3.333333333333
possible 8 7.071067811865

For the first record, it's impossible to find a convex regular polyhedron with  faces.

For the second record, a -face convex regular polyhedron is a tetrahedron. After taking all its faces' geometry centers to make a convex hull, we get a smaller tetrahedron.

For the third record, a -face convex regular polyhedron is a cube. After taking all its faces' geometry centers to make a convex hull, we get an octahedron, a.k.a. an -face convex regular polyhedron.