Competitions

# 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 contains a binary string s (1 ≤ |s| ≤ 106) - the string with which Alice and Bob play.

#### Output

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

#### 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.

Time limit 1 second
Memory limit 128 MiB
Input example #1
010

Output example #1
Alice

Input example #2
1111

Output example #2
Bob

Input example #3
1010

Output example #3
Bob

Input example #4
1010001011001

Output example #4
Alice

Source 2020 SEERC South Eastern European Regional Programming Contest, Vinnica & Bucharest, May 23, Problem B