Palindromic Substrings

Alice has a **binary** string $S$ of length $N$. Alice and Bob decided to play a game on this string, taking turns. On their turn, a player does the following: - If there is no palindromic *cyclic* substring of length $\gt 1$, this player loses the game. - Otherwise, the player will perform the following two-step process: - Choose any palindromic *cyclic* substring of $S$ with length $\gt 1$.