Start by sorting the three side lengths ascending. Then check whether the two smaller sides sum to more than the largest side — if not, the sides cannot form any triangle.

Once the triangle inequality passes, compare the three sides: all equal means equilateral, exactly two equal means isosceles, and none equal means scalene.

Remember that a degenerate triangle (where `a + b == c`) does NOT count as a valid triangle — return "not a triangle" for that case.