An Interactive Problem

Troubles in the jury! The contest day of NWERC is tomorrow already, and they still need a nice interactive problem for the problem set. During this test session, the jury have gathered in an emergency meeting and started discussing problem ideas. All of the $n^2$ jury members have an idea for an interactive problem, and even after hours of arguing, they cannot decide which idea is the nicest. To resolve the discussion as quickly as possible, they decide to draw lots.

Each member of the jury draws a lot from a collection of unique numbers. Because the number of jury members is square and they like regular shapes, they place all the lots face-down on a table, laid out in the shape of a square. They task you to be the independent lot-drawer, to see which jury member has drawn the highest number. To make sure you are truly independent, you are not allowed to see the table, hence you to pick the lots on the table by shouting coordinates. They are in a hurry, though, so you need to find the lot with the highest number in at most $n^2 + 100$ commands. You do not know the size of the square beforehand, but you do know that $n$ is at least $1$ and at most $100$.