Problem Statement

You are given a non-negative integer sequence of length N: $A=(A_1,A_2,\cdots,A_N)$.
Here, all elements of A are pairwise distinct.
Alice and Bob will play a game.
They will alternately play a turn, with Alice going first.
In each turn, the player does the operation below.

• Choose the largest element in A at the moment, and replace it with a smaller non-negative integer.
  Here, all elements in A must still be pairwise distinct after this operation.

The first player to be unable to do the operation loses.
Determine the winner when both players play optimally.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$

Output

If Alice wins, print Alice; if Bob wins, print Bob.

Constraints

• $2 \leq N \leq 3 \times 10^5$
• $0 \leq A_1 < A_2 < \cdots < A_N \leq 10^9$
• All values in input are integers.

Sample Input 1

2
2 4

Sample Output 1

Alice

In Alice's first turn, she may replace 4 with 0, 1, or 3.
If she replaces 4 with 0 or 1, Bob's move in the next turn will make Alice unable to do the operation and lose.
On the other hand, if she replaces 4 with 3, she can win regardless of Bob's subsequent moves.
Thus, Alice wins in this input.

Sample Input 2

3
0 1 2

Sample Output 2

Bob

见题面 Input 部分

见题面 Output 部分