Practice Conditions and Trigonometry with the exercise "Nature of triangles"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

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.

Solve it

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