Triangle 2

Three natural numbers $a$, $b$, and $c$ are provided. You need to output one of the following messages:

1. equilateral, if a triangle with side lengths $a$, $b$, and $c$ is equilateral;

2. isosceles, if a triangle with side lengths $a$, $b$, and $c$ is isosceles;

3. scalene, if a triangle with side lengths $a$, $b$, and $c$ is scalene;

4. invalid, if a triangle with side lengths $a$, $b$, and $c$ cannot exist.