All Aside

You are given a **binary** string $S$ of length $N$. You can perform the following operation on it: - Choose an index $i$ ($1 \le i \le N$) - Let $[L, R]$ be the maximal segment of equal values containing index $i$. - More formally, $L$ is the smallest index such that $S_L = S_{L+1} = \ldots = S_i$, and $R$ is the largest index such that $S_i = S_{i+1} = \ldots = S_R$. - Flip the values at i