Goal
You have to output the nature of the triangles whose vertices’ coordinates are given. The output should follow this format:
Name of triangle is a/an side nature and a/an angle nature triangle.
Name of triangle follows the same order as the vertices given.
Side nature is:
• “scalene” if all sides have different lengths, or
• “isosceles in vertex” if exactly two sides have the same length and they have a common vertex of vertex.
Angle nature is:
• “acute” if all angles are acute, or
• “right in vertex” if the angle at vertex is 90°, or
• “obtuse in vertex (degrees°)” if the angle at vertex is obtuse. In this case, output the measure of the obtuse angle in degrees, rounded to the nearest integer.
Output examples
BAC is a scalene and a right in A triangle.
DEF is an isosceles in D and an obtuse in D (120°) triangle.
Input
Line 1: An integer N for the number of triangles.
Next N lines: Each vertex followed by its x and y coordinates, one triangle per line.
Output
N lines: The nature of the triangles, one triangle per line, in the same order as the input.
Constraints
1 ⩽ N ⩽ 8
-20 ⩽ x, y ⩽ 20
x and y are integers.
Degenerate triangles do not appear in this puzzle.
Equilateral triangles do not appear in this puzzle because they involve non-integer coordinates (calculation involves √3).
Example
Input
2
A 5 -2 B 8 2 C -1 -9
O 0 0 A 3 0 B 1 2
Output
ABC is a scalene and an obtuse in A (176°) triangle.
OAB is a scalene and an acute triangle.
