You are an incredible Mordekaiser player and a lover of geometry (xD), and you have been fascinated by Morde's passive, it's amazing, a circle.
You know that this passive needs three hits, the same number of points with which you can define a circle, incredible coincidence.
After playing for ten hours straight, you've started to see flashes on the screen, probably due to a drop in FPS, and for a moment, everything was just white dots in your head, and something occurred to you.
How many circles can I define with those points?
More formally, given a set of points, find the number of circles that pass through at least three points of the set. And as you know, League of Legends is a 3D game, so the points will also be 3D, for extra fun ^^.
The first line of the input will contain one integer, $$$n$$$ $$$(3 \leq n \leq 100)$$$, where $$$n$$$ represents the number of points.
The following $$$n$$$ lines will each contain three integers $$$x_i$$$, $$$y_i$$$ and $$$z_i$$$ $$$( x_i, y_i, z_i \leq |10^2|)$$$, representing the coordinates of a point.
No two points will have identical coordinates.
Print one integer — the number of distinct circles that pass through at least three points.
30 0 00 2 01 1 0
1
40 0 00 2 01 1 0-1 1 0
1
