Truss Beam Triangle Classification

A structural engineer has three straight steel beams and wants to bolt their ends together to form a single rigid triangular truss. Given the lengths of the three beams, first decide whether they can actually be joined into a valid triangle at all (three lengths can form a triangle only if the sum of any two of them strictly exceeds the third). If they cannot, report that. Otherwise, classify the resulting truss by its beam lengths: 'equilateral' if all three beams are the same length, 'isosceles' if exactly two of the three beams share a length (but not all three), and 'scalene' if all three beam lengths are different.

Input format

A single line containing three space-separated integers a, b, c: the lengths of the three beams.

Output format

Print exactly one of the following words: 'equilateral', 'isosceles', 'scalene', or 'none' (if the three beams cannot form a valid triangle).

Constraints

• 1 <= a, b, c <= 10^9

4 4 4

equilateral

1 2 5

none