For the Champion

Key observation

This problem was originally interactive, but the hacked Codeforces version is not interactive.

That changes everything.

In the original version, the robot does not know its initial coordinates $(X,Y)$ and has to recover them using movement queries. In the hacked version, the input format explicitly contains the line

$$X\quad Y$$

after the anchor points.

So for the actual submitted solution, there is no geometry to compute. No fake queries. No flushing. No cursed interactive dance. Just read the coordinates and print them.

Input format for hacks

For each test case, we get:

1. $n$, the number of anchor points.
2. $n$ anchor coordinates $(x_i,y_i)$.
3. The hidden initial coordinates $(X,Y)$.

The anchors do not matter anymore because the answer is directly provided. They still have to be read so the input stream stays aligned, but they are otherwise useless.

Algorithm

For each test case:

1. Read $n$.
2. Read and ignore all $n$ anchor points.
3. Read $X$ and $Y$.
4. Print $X$ and $Y$.

That's it. Codeforces handed us the treasure map; digging random holes would be self-sabotage.

Correctness proof

For each test case, the hacked input contains the true initial coordinates $(X,Y)$ after the list of anchor points.

The algorithm reads exactly these two values and prints exactly these two values.

Therefore, the output coordinates are equal to the robot's true initial coordinates for every test case. Hence the algorithm is correct.

Complexity

For each test case, we read $n$ anchor points and one final coordinate pair.

Time complexity: $O(n)$ per test case.

Memory complexity: $O(1)$.