Triangle 2

The program receives input consisting of three natural numbers a, b, and c, provided in a single line and separated by spaces. The output should be one of the following messages:

• equilateral: if a triangle with side lengths a, b, and c can be equilateral;

• isosceles: if a triangle with side lengths a, b, and c can be isosceles;

• versatile: if a triangle with side lengths a, b, and c can be scalene;

• invalid: if a triangle with side lengths a, b, and c cannot exist.

Input

Three natural numbers a, b, and c are provided in a single line, separated by spaces.

Output

The appropriate message based on the input.

Examples