01 Game

Alica and Bob are playing a game.

Initially they have a binary string $$$s$$$ consisting of only characters 0 and 1.

Alice and Bob make alternating moves: Alice makes the first move, Bob makes the second move, Alice makes the third one, and so on. During each move, the current player must choose two different adjacent characters of string $$$s$$$ and delete them. For example, if $$$s = 1011001$$$ then the following moves are possible:

1. delete $$$s_1$$$ and $$$s_2$$$: $$$\textbf{10}11001 \rightarrow 11001$$$;
2. delete $$$s_2$$$ and $$$s_3$$$: $$$1\textbf{01}1001 \rightarrow 11001$$$;
3. delete $$$s_4$$$ and $$$s_5$$$: $$$101\textbf{10}01 \rightarrow 10101$$$;
4. delete $$$s_6$$$ and $$$s_7$$$: $$$10110\textbf{01} \rightarrow 10110$$$.

If a player can't make any move, they lose. Both players play optimally. You have to determine if Alice can win.