Same Parity Swaps in Binary Strings

You are given a binary string $S$ of length $N$ (i.e. every character of $S$ is either $0$ or $1$). You can perform the following operation on $S$: - select any two indices $i, j$ of the same parity, i.e. either both $i, j$ are odd or both $i, j$ are even - swap $S_i$ and $S_j$ For example, in the string $1110$, we can swap the second and the fourth characters to get $1011$. However, we can neve