Binary String Game

We define a function $f$ on a binary string $S$ of length $N$ as follows: $f(S) = \sum_{i = 1}^{N - 1} |S_{i+1} - S_{i}|$. JJ and Uttu have a binary string $S$ of length $N$ and they decide to play a game using it. The rules of the game are as follows: - JJ starts the game with players making moves in alternate turns thereafter. - In one move, a player can pick $L, R$ such that $1 \leq L \leq R