# Problem F

Human Observation

It is known by all that the *creepy* *Lord Pooty*
loves observing people for *“research”* purposes. Today,
he is in a mall and would like to stare at people like usual.
The mall is modelled as a grid and there are $N$ people, standing at locations
$(x_ i, y_ i)$ that
*Lord Pooty* wants to observe. There are also
$K$ seats at locations
$(x_ i,y_ i)$ that
*Lord Pooty* can sit at to do his observation. **Due to the inherent randomness of the universe that
none can control, all the locations of people and seats are
random.**

He want to choose a seat where the **maximum** distance^{1} from the seat
to any one person is **minimised**, to
allow him better observation. As his fellow *research*
buddy, help him find such a seat! If more than one seat is
optimal, give him the **minimum**
$(x,y)$ pair (i.e.
$x$ is minimised, followed
by $y$)!

## Input

The first line contains integers $N$. ($1 \leq N \leq 200\, 000$). This is followed by $N$ lines of the following form: $x~ y$ ($-10^9 \leq x,y \leq 10^9$). These are the locations of the people. Then, you have an integer $K$. ($1 \leq K \leq 200\, 000$). This is followed by $K$ lines of the following form: $x~ y$ ($-10^9 \leq x,y \leq 10^9$). These are the locations of the seats.

**All location inputs (people and seats)
$(x, y)$ are UNIFORMLY,
INDEPENDENTLY, RANDOMLY GENERATED integers from the range
$[-10^9, 10^9]$. Note that
it is possible for multiple inputs (seats and people) to be in
the same location.**

## Output

Print $x$ and $y$, the location of the optimal seat. If more than one seat is optimal, print the minimum one.

Sample Input 1 | Sample Output 1 |
---|---|

2 10 0 0 0 3 1 0 5 1 5 -1 |
5 -1 |

**Footnotes**

- Similar to the non-relativistic
classical model of our Universe, this problem is set in a
Euclidean space but of dimension $2$. Recall that Euclidean metric
$d$ is defined as:
d

R

^{n}×R^{n}↦R(

**x**,**y**) ↦∑_{i = 1}^{n}(x_{i}- y_{i})^{2}