Professor vs Alicia

We are in a parallel universe and Inspector Alicia and Professor loves each other, as somethings never change both try to outsmart each other every time. This time Professor gave Alicia a very difficult problem to solve. The question is that you will be given two binary strings $a$ and $b$ of the same length $N$. You can perform the following two operations on string $a$: $1)$ Swap any two bits a