Problem Statement  
In Euclidean Geometry, triangles can be categorized into one of three types
based on their angle measures. A triangle is acute if all three angles are
less than 90 degrees. A triangle is obtuse if one angle is greater than 90
degrees. Lastly, a triangle with one angle at exactly 90 degrees is a right
triangle.
It could also be the case that three positive integers can not possibly form the sidelengths of a triangle. This happens when the length of one side is equal to or larger than the sum of the lengths of the other two sides, because it would not be possible to connect the end points of the three sides in such a way that a triangle was formed. Write a method that takes as input three positive integer sidelengths of a triangle. Return "IMPOSSIBLE" if a triangle cannot be formed. Return "ACUTE" if the triangle is acute, "OBTUSE" if the triangle is obtuse, and "RIGHT" if the triangle is right.  
Definition  
 
Notes  
  For a triangle with sidelengths x, y, and z and x <= y <= z. * The triangle is right if x*x + y*y = z*z. * The triangle is obtuse if x*x + y*y < z*z. * The triangle is acute if x*x + y*y > z*z. * It is impossible to have x + y <= z.  
Constraints  
  a, b, and c are between 1 and 10,000, inclusive.  
Examples  
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