Točkice (Dot Game)

Time limit1sMemory limit1024 MB

Summary

Given N points with no three collinear, decide which player wins the game where both alternately draw non-crossing segments between the points.

Level: Medium6 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

A summer camp for young computer science students has been held on the island of Krk for many years. In their free time, the students mostly swim at Dražica, a popular sandy beach, and adult supervisors walk them there.

Alenka and Bara are two supervisors who are not very responsible. Instead of watching the children, they pass the time playing in the sand. At one point, Alenka draws $N$ points, making sure that no three of them are collinear, and says:

"Let's play the game Točkice. We take turns drawing lines, and I will go first. On each turn, a player draws a segment that connects two of the points, but the segment may not cross any segment drawn before. A new segment may touch an earlier segment at an endpoint. The player who makes the last move wins!"

For a given arrangement of points, determine who wins the game if both players play optimally.

Input

The first line contains the natural number $N$ from the problem statement.

Each of the next $N$ lines contains two natural numbers $x_i$ , $y_i$ ( $1 \le x_i, y_i \le 10^6$ ), the coordinates of the $i$ -th point.

No three points are collinear, and no two points are the same.

Output

Print one line containing Alenka if Alenka wins the game, or Bara if Bara wins. Assume both players play optimally.

Examples3

Example 1
Input
```
4
0 0
0 10
10 0
10 10
```
Expected output
```
Alenka
```
Example 2
Input
```
5
2 1
1 3
6 4
3 5
5 2
```
Expected output
```
Alenka
```
Example 3
Input
```
4
4 2
2 4
2 2
1 1
```
Expected output
```
Bara
```