Reverse Game

Alice and Bob are playing a turn-based game. The rules of the game are as follows:

1. At the beginning of the game some binary string s is chosen.

2. On his turn player has to choose some substring t of s, equal to one of 10, 110, 100, 1010. Then the

player has to reverse t. For example, if s = 010101, the player can select substring t = 1010 and reverse it, obtaining s = 001011

3. The player who can’t make a move (who can’t choose an appropriate substring t) loses.

4. The players cannot skip a turn.

Which player has the winning strategy, if Alice moves first? A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

Input

The only line of the input contains a binary string s (1 ≤ |s| ≤ 10^6) — the string with which Alice and Bob play.

Output

If Alice wins, output Alice. Otherwise, output Bob.

Examples

Input

010

Output

Alice

Input

1111

Output

Bob

Input

1010

Output

Bob

Input

1010001011001

Output

Alice

Note

In the first sample, Alice can choose substring 10 of 010 and reverse it, obtaining string 001. Bob can’t make any move with this string, and loses. In the second sample, Alice can’t make a single move and loses.