Triangle Classification

Ggung learned about triangles at school today. Triangles are grouped by their side lengths.

• An equilateral triangle has three sides of the same length. All three angles are 60 degrees.
• An isosceles triangle has two sides of the same length. Two of its angles are also equal.
• A scalene triangle has three sides of different lengths, and all three angles differ. Some scalene triangles are right triangles.

The math teacher assigned homework: classify a triangle from its three side lengths. Ggung would much rather go play, so do the homework for him.

The first line contains the number of test cases $T$ ($1 \le T \le 100$).

Each of the next $T$ lines contains three space-separated integers $A$, $B$, $C$ ($1 \le A, B, C \le 1{,}000{,}000$), the three sides of a triangle.

For each test case print one line in the form Case #x: type, where $x$ is the test case number starting at 1 and type is the kind of triangle.

If the three lengths form a triangle, print equilateral, isosceles, or scalene. Otherwise print invalid!. The lengths form a triangle only when the longest side is shorter than the sum of the other two. If the two values are equal, it is not a triangle.