| UTPC Spring 2024 Open Contest |
|---|
| Finished |
Vinny is having guests over for dinner, and wants to play some music to accompany her famed vindaloo. Vinny is, of course, an avid fan of old-school vinyls and cassettes, and owns a collection of songs in her attic.
Unfortunately, the attic doesn't have any lights, so Vinny can't find what she needs! Vinny is holding an object, but she can't tell what it is. She has identified $$$10$$$ points $$$(x_i, y_i)$$$ on the boundary of the object. If it's a vinyl, the object boundary is a circle. If it's a cassette, the object boundary is a rectangle. What is Vinny holding?
The input consists of $$$10$$$ lines, each with two floats $$$x_i, y_i$$$ ($$$-100 \le x_i, y_i \le 100$$$) denoting a point on the boundary of the object.
The $$$10$$$ points are guaranteed to lie on a circle in the case of a vinyl, and a rectangle in the case of a cassette. Coordinates are given with up to $$$10$$$ decimal places. Points may deviate from the true circle or rectangle outline by at most $$$10^{-6}$$$.
If the points lie on a rectangle, the rectangle is guaranteed to be aligned with the $$$x$$$ and $$$y$$$ axes.
It is guaranteed that all points will be distinct (specifically, any two points will differ in at least one coordinate by at least $$$0.05$$$).
Output "VINYL" if the object is a vinyl, and "CASSETTE" if the object is a cassette tape.
0 23 3-1 1-2 -2-1 -53 -76 -68 -26 27 1
VINYL
2.2 -2.22.2 32.2 1.53.8 34.5 14.5 1.24.5 1.94.5 -14.5 -24.5 -1.8
CASSETTE
The first sample test case looks like this, which is a vinyl: 
The second sample test case looks like this, which is a cassette: 
| Name |
|---|


