Triangle and Its Three Sides

Given the lengths of the three sides of a triangle, classify it according to the following definitions.

• Equilateral: all three sides have the same length
• Isosceles: exactly two sides have the same length
• Scalene: all three sides have different lengths

However, if the three given lengths cannot form a triangle, output "Invalid". The lengths cannot form a triangle when the sum of the two shorter sides is not greater than the longest side (that is, less than or equal to it). For example, 6, 3, 2 is such a case, since the longest side 6 is greater than 3 + 2 = 5.

Given the three side lengths, print the result according to the definitions above.

Each line contains three positive integers, each not exceeding 1,000, separated by spaces. The last line is 0 0 0; this line marks the end of the input and is not processed.

For each input line, print the corresponding result (Equilateral, Isosceles, Scalene, or Invalid), one per line.