Problems

# Triangle

# Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments.

Triangles can be classified according to the relative lengths of their sides:

- In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring
**60°**. - In an isosceles triangle, two sides are equal in length. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem.
- In a scalene triangle, all sides are unequal. The three angles are also all different in measure. Some (but not all) scalene triangles are also right triangles.

**Input**

The first line of input contains an integer (**1** ≤ **T** ≤ **100**), the number of test cases. T test data sets follow, each data set consists of **3** integers **A**, **B** and **C**, where (**1** ≤ **A**, **B**, **C** ≤ **1000000**) the triangle side lengths.

**Output**

For each test case, print "**equilateral**", "**isosceles**" or "**scalene**" describing the triangle type. If the input doesn’t create a valid triangle output "**invalid!**". Follow the output format below.

Input example #1

2 3 3 4 6 4 2

Output example #1

Case #1: isosceles Case #2: invalid!