\problemname{Dragon Balls}

\illustration{0.3}{dragonballs2.png}{\href{https://www.skyringecrafts.com/dragon-ball/anime-dragon-ball-z-resin-acrylic-dragon-ball.html}{Dragon Balls} by Skyringe Crafts}%
During the showdown with Frieza on Namek, Krillin died yet again and needs to
be brought back to life using the \emph{Dragon Balls}. As everybody else is
still busy fighting Frieza, the task of retrieving all seven Dragon Balls has
fallen to you.

The balls are hidden at unknown locations in a 2D plane and you have been
handed a Dragon Radar, designed by Bulma, that you must use to locate them.
You can repeatedly fly to arbitrary locations, and the radar
will then inform you about the distance to the closest Dragon Ball. If this
distance is $0$ this means that you found one of the balls and you can then
recalibrate the radar so that it ignores the ball you just found.

With the battle still going on, and the radar having limited energy, you
are obviously in a great hurry. You need to make sure to collect all the
balls by using the radar no more than $1\,000$ times.

\begin{Interaction}
This is an interactive problem. Your submission will be run against an
\emph{interactor}, which reads the standard output of your submission and
writes to the standard input of your submission. This interaction needs to
follow a specific protocol:

The interactor first sends an integer $n$ ($1 \le n \le 7$), the number of
Dragon Balls you still need to find. The $n$ balls are hidden at integer
locations $(x,y)$ with $0 \le x,y \le 10^6$. Your submission may not guess
outside this area.

Your submission then repeatedly sends such an integer location $(x,y)$ and the
interactor replies with an integer $d$ ($0 \le d \le 2\cdot 10^{12}$), the
square of the distance from $(x,y)$ to the closest remaining ball.

If $d = 0$, the ball at $(x,y)$ is considered found and ignored in further guesses.
When all balls are found,
your submission should exit. Each location holds at most one ball.

Make sure you flush the buffer after each write.

A testing tool is provided to help you develop your solution.
\end{Interaction}
