Background

Translated from Izborne Pripreme 2022 (Croatian IOI/CEOI Team Selection) D2T3. $\texttt{1s,0.5G}$。

Problem Description

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.

Input Format

The first line contains an integer $N$。

The next $N$ lines each contain two integers $x_i,y_i$。

Output Format

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

4
0 0
0 10
10 0
10 10

Alenka

5
2 1
1 3
6 4
3 5
5 2

Alenka

4
4 2
2 4
2 2
1 1

Bara

Hint

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.

Translated by ChatGPT 5