问题 D: Chaos Begin

Long long ago, there were $n$ points a1,a2,…,an on the 2D plane. The world keeps stable for a long time. However, it begins to be chaotic recently when another $n$ points b1,b2,…,bn appeared, where bi=ai+(Δx,Δy). And now, these $2n$ points have already lost their identifiers.

You are given these $2n$ points in an arbitrary order, you need to figure out all the possible $(\Delta x,\Delta y)$ to help the world recover from chaos.

The first line contains a single integer $T$ ($1\le T\le 100$), the number of test cases. For each test case:

The first line of the input contains a single integer $n$ ($1\le n\le 50,000$), denoting the number of initial points.

In the next $2n$ lines, the $i$-th line contains two integers xi and yi (∣xi∣,∣yi∣≤1e8), describing the coordinate of a current point.

It is guaranteed that the x-coordinate and y-coordinate of each initial point are chosen uniformly at random from integers in $[-v,v]$, where $v$ is chosen in $[1e7,1e8]$. The randomness condition does not apply to the sample test case, but your solution must pass the sample as well.

It is also guaranteed that the sum of all $n$ is at most $300,000$.