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 $s(1\le |s|\le 10^6)$ — the string with which Alice and Bob play.

Output

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

Examples

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.