The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, a circle is produced. For a plane that is not perpendicular to the axis and that intersects only a single nappe, the curve produced is either an ellipse or a parabola. The curve produced by a plane intersecting both nappes is a hyperbola.
conic section equation
circle x2+y2=a2
ellipse x2/a2+y2/b2=1
parabola y2=4ax
hyperbola x2/a2-y2/b2=1
Input
There are multiple test cases. The first line of input is an integer T ≈ 10000 indicating the number of test cases.
Each test case consists of a line containing 6 real numbers a, b, c, d, e, f. The absolute value of any number never exceeds 10000. It's guaranteed that a2+c2>0, b=0, the conic section exists and it is non-degenerate.
Output
For each test case, output the type of conic section ax2+bxy+cy2+dx+ey+f=0. See sample for more details.
Sample Input
5
1 0 1 0 0 -1
1 0 2 0 0 -1
0 0 1 1 0 0
1 0 -1 0 0 1
2 0 2 4 4 0
Sample Output
circle
ellipse
parabola
hyperbola
circle
