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ZOJ Problem Set - 3488
Conic Section

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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 sectionequation
circlex2+y2=a2
ellipsex2/a2+y2/b2=1
parabolay2=4ax
hyperbolax2/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.

```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
```

#### References

Author: WU, Zejun
Contest: The 8th Zhejiang Provincial Collegiate Programming Contest
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