Table: Triangles

+-------------+------+ 
| Column Name | Type | 
+-------------+------+ 
| A           | int  | 
| B           | int  |
| C           | int  |
+-------------+------+
(A, B, C) is the primary key for this table.
Each row include the lengths of each of a triangle's three sides.

Write a query to find the type of triangle. Output one of the following for each row:

• Equilateral: It's a triangle with 3 sides of equal length.
• Isosceles: It's a triangle with 2 sides of equal length.
• Scalene: It's a triangle with 3 sides of differing lengths.
• Not A Triangle: The given values of A, B, and C don't form a triangle.

Return the result table in any order.

The result format is in the following example.

 

Example 1:

Input: 
Triangles table:
+----+----+----+
| A  | B  | C  |
+----+----+----+
| 20 | 20 | 23 |
| 20 | 20 | 20 |
| 20 | 21 | 22 |
| 13 | 14 | 30 |
+----+----+----+
Output: 
+----------------+
| triangle_type  | 
+----------------+
| Isosceles      | 
| Equilateral    |
| Scalene        |
| Not A Triangle |
+----------------+
Explanation: 
- Values in the first row from an Isosceles triangle, because A = B.
- Values in the second row from an Equilateral triangle, because A = B = C.
- Values in the third row from an Scalene triangle, because A != B != C.
- Values in the fourth row cannot form a triangle, because the combined value of sides A and B is not larger than that of side C.