## Eliot Andersol

Points: 15 (partial)
Time limit: 1.5s
Python 3 5.0s
Memory limit: 256M

Author:
Problem type

Eliot Andersol is a vigilante hacker who's objective is to save the world from conspiracy.

Recently he started investigating in a very scary subject : He thinks that the earth is flat and that governments are trying to hide it for an unknown reason. In the top secret classified documents he gained access to, there are $$N$$ $$3D$$ points measured from different points on the surface of earth. We want you to check if those points can represent a flat surface.

#### Input Specification

The first line of the input file contains an integer $$T$$ the number of test cases $$1 \leq T \leq 100$$

Each test case starts with a line with one integer $$N$$ the number of points.

Then follow $$N$$ lines containing $$3$$ integers $$a_{ij}$$: the $$j^{th}$$ integer of the $$i^{th}$$ line contains the jth coordinate of the ith point $$-10^9 \leq a_{ij} \leq 10^9$$.

You are guaranteed the following :

• No two points coincide.
• No $$4$$ points are co-circular (that is, no circle can contain 4 points).
• The set of the $$N$$ points can be a part of either a 2D disk or 3D Sphere of any radius.

#### Output Specification

For each test case output 'Yes' if those points represent a flat surface, otherwise output 'No' (Case sensitive).

#### Scoring

• $$4 \leq N \leq 100$$ (2 points).
• $$4 \leq N \leq 1000$$ (2 points).
• $$4 \leq N \leq 10^5$$ (3 points).

#### Sample Input

2
4
0 0 1
0 0 2
0 0 3
0 0 4
4
1 0 0
0 1 0
0 0 1
0 0 -1

#### Sample Output

Yes
No