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ZOJ Problem Set - 1769
Three Sides Make a Triangle

Time Limit: 2 Seconds      Memory Limit: 65536 KB

You work for an art store that has decided to carry every style and size of drafting triangle in existence. Unfortunately, sorting these has become a problem. The manager has given you the task of organizing them. You have decided to classify them by edge length and angles. To measure each triangle, you set it on a large sheet of very accurate graph paper and record the coordinate of each point. You then run these three points through a computer program to classify the triangles according to:

Scalene: no equal sides
Isosceles: two equal sides
Equilateral: three equal sides

and

Acute: all angles under 90
Right: one angle equal 90
Obtuse: one angle over 90

Of course, sometimes you make mistakes entering the data, so if you input points that do notform a valid triangle, your program should tell you.


Input

One triangle is described per line. Each line has six measurements taken to the nearest 0.001 in the order:

x1 y1 x2 y2 x3 y3

The final line of input will contain only a -1.

None of the test sets contain non-right angles in the range 88-92 degrees, nor do any of the test sets include any non-equal side lengths for one triangle within 0.01 of one another.


Output

You will output one line for each triangle, which will contain two words:

<length classification> <angle classification>

or

Not a Triangle

The final line of your output file will be:

End of Output


Sample Input

10.000 10.000 10.000 20.000 20.000 10.000
0.000 0.000 4.000 0.000 2.000 3.464
-1


Sample Output

Isosceles Right
Equilateral Acute
End of Output


Source: Mid-Atlantic USA 2003
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