The summer camp for young computer scientists has been held on the island of Krk for years. The young computer scientists usually spend their little free time swimming at Dražica, a popular sandy beach, accompanied by adult, responsible persons.

Alenka and Bara are two (ir)responsible persons. Instead of watching the children, they decided to pass the time by playing in the sand. At one point, Alenka draws $N$ points, making sure that no three points are collinear, and says:

“Let’s play the dots game. We will take turns making moves, and I will go first. In each turn, we will draw a line segment connecting two points, such that the segment does not intersect any of the previously drawn segments. The newly drawn segment may touch one of the previously drawn segments at an endpoint. The person who makes the last move is the winner!”

Given the arrangement of points, determine who will win the dots game, assuming both players play optimally.

Input

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

In the $i$-th of the following $N$ lines, there are two natural numbers $x_i, y_i$ ($1 \le x_i, y_i \le 10^6$) representing the coordinates of the $i$-th point.

No three points will be collinear, and every two points will be distinct.

Output

In the only line, print Alenka if Alenka will win the game, or Bara if Bara will win the game.

Subtasks

Examples

Input 1

4
0 0
0 10
10 0
10 10

Output 1

Alenka

Input 2

5
2 1
1 3
6 4
3 5
5 2

Output 2

Alenka

Input 3

4
4 2
2 4
2 2
1 1

Output 3

Bara