Triangle Classification

You are given three integers representing the side lengths of a triangle. Your task is to classify the triangle into one of the following categories:

• Equilateral: All three sides are equal.
• Isosceles: Exactly two sides are equal.
• Scalene: All three sides are different.

However, if the three sides do not satisfy the triangle inequality, i.e. if any of the following conditions fails:

$$a + b > c,\quad b + c > a,\quad c + a > b,$$

then the three sides cannot form a valid triangle and you should output "not a triangle".

The input will be provided through standard input (stdin) and the output should be printed to standard output (stdout).

inputFormat

The input consists of a single line containing three space-separated integers a, b, and c which represent the side lengths of a triangle.

outputFormat

Output a single string that is one of the following: "equilateral", "isosceles", "scalene", or "not a triangle".

2 2 2

equilateral