## 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.