Background

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

Problem Description

Fish and Light are playing a game.

Flame has drawn $N$ points $(x_i, y_i)$ on a two-dimensional plane, where no three points are collinear.

Starting with Fish, the two players take turns playing the game:

• Select two points $(x_i, y_i), (x_j, y_j)$ ($i \neq j$). If the line segment connecting these two points does not intersect with any previous segments, a segment is drawn between the two points.
• The player who cannot make a move loses.

It is important to note that line segments can intersect at vertices.

Both Fish and Light are extremely intelligent, and Flame wants to know who will win.

Input Format

The first line contains an integer $N$.

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

Output Format

If the first player (Fish) wins, output Alenka; otherwise, output Bara.

Sample Input and Output

Sample Input #1

4
0 0
0 10
10 0
10 10

Sample Output #1

Alenka

Sample Input #2

5
2 1
1 3
6 4
3 5
5 2

Sample Output #2

Alenka

Sample Input #3

4
4 2
2 4
2 2
1 1

Sample Output #3

Bara

Notes

For $100\%$ of the data, the following conditions are guaranteed:

• $1 \le N \le 10^5$;
• $1 \le x_i, y_i \le 10^6$;
• No three points are collinear.

见题面 Input 部分

见题面 Output 部分