During the showdown with Frieza on Namek, Krillin died
yet again and needs to be brought back to life using the

*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.

## Interaction

This is an interactive problem. Your submission will be run
against an *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.

Read |
Sample
Interaction 1 |
Write |

Read |
Sample
Interaction 2 |
Write |