Consecutive XOR

Chef has two binary strings $A$ and $B$, both having length $N$. He can perform the following operation on $A$ any number of times (possibly zero): - Select any index $i$ $(1 \le i \le N - 1)$ and simultaneously set $A_i := A_i \oplus A_{i + 1}$ and $A_{i + 1} := A_i \oplus A_{i + 1}$. Formally, if initially $A_i = x$ and $A_{i + 1} = y$ then set $A_i := x \oplus y$ and $A_{i + 1} := x \oplus y$