Suspense String

Alice and Bob are playing a game with a binary string $S$ of length $N$ and an empty string $T$. They both take turns and Alice plays first. - In Alice's turn, she picks the **first** character of string $S$, appends the character to either the **front** or **back** of string $T$ and deletes the chosen character from string $S$. - In Bob's turn, he picks the **last** character of string $S$, ap