P10876 [COTS 2022] Point Set Točkice

Translated from [Izborne Pripreme 2022 (Croatian IOI/CEOI Team Selection)](https://hsin.hr/pripreme2022/) D2T3. $\texttt{1s,0.5G}$。

There are $N$ points $(x_i,y_i)$ on the plane, and no three points are collinear. Two players take turns. In each move, a player chooses two points and connects them with a line segment, with the requirement that it does not intersect any previous segment at a non-endpoint. The player who cannot make a move loses. Determine whether the first player wins or the second player wins.

The first line contains an integer $N$。 The next $N$ lines each contain two integers $x_i,y_i$。

If A (the first player) wins, output `Alenka`; otherwise output `Bara`。

For $100\%$ of the testdata, it is guaranteed that: - $1\le N\le 10^5$； - $1\le x_i,y_i\le 10^6$； - No three points are collinear. | Subtask ID | Score | $N\le$ | |:-----:|:------:|:-------:| | $1$ | $13$ | $7$ | | $2$ | $17$ | $300$ | | $3$ | $21$ | $1\, 000$ | | $4$ | $49$ | $10^5$ | Translated by ChatGPT 5