From http://en.wikipedia.org/wiki/Triangle: enter image description here

Write a program that takes three 2d coordinate tuples (Cartesian), and classifies what shape these three points describe.

In almost all cases these points will describe a triangle of varying types. In some degenerate cases, the points will either describe a singular point or a straight line. The program will determine which of the following tags apply to the described shape:

• Point (3 points are co-incident)
• Line (3 points lie on a straight line - no more than 2 points may be co-incident)
• Equilateral (3 sides equal, 3 angles equal)
• Isosceles (2 sides equal, 2 angles equal)
• Scalene (0 sides equal, 0 angles equal)
• Right (1 angle exactly π/2 (or 90°))
• Oblique (0 angles exactly π/2 (or 90°))
• Obtuse (1 angle > π/2 (or 90°))
• Acute (3 angles < π/2 (or 90°))

Note that for some described shapes, more than one of the above tags will apply. For example, any right-angled will also either be isosceles or scalene.

Input

• The program may read the 3 input coordinates from STDIN, command-line, environment variables or whatever method is convenient for your language of choice.
• The input co-ordinates my be formatted however is convenient for your language of choice. It can be assumed that all input numbers are well-formed with respect to the datatypes you end up using.
• Nothing can be assumed about the ordering of the input coordinates.

Output

• The program will output to STDOUT, dialog box or whatever display method is convenient for your language of choice.
• The output will display all the tags applicable to the shape described by the input coordinates.
• Tags may be output in any order.

Other Rules

• Your language's trigonometric libraries/APIs are allowed, but any APIs that specifically calculate triangle types are banned.
• When determining equality of angles or lengths of sides, you will likely end up comparing floating-point values. Two such values are to be considered "equal" if one is within 1% of the other.
• Standard "loopholes" which are no longer funny
• This is code-golf, so the shortest answer in bytes wins.

Examples

Input Output
(1,2) (1,2) (1,2) Point
(1,2) (3,4) (5,6) Line
(0,0) (1,1) (2,0) Isosceles Right
(0,0) (2,1) (10,1) Scalene Oblique Obtuse