Binary String Randomizer

Chef JJ is a fan of random events and calculating probabilities. He designed a machine called the binary string randomizer (BSRand). BSRand takes a binary string $A$ (say, of length $N$) as input and then generates a binary string $B$ (of the same length $N$) as output using the following algorithm: For each $i$ from $1$ to $N$, - Uniformly randomly choose an integer $j$ between $1$ and $N$. - U