Random OR

Chef is playing a game, which he starts with a score of $S = 0$. He also has an integer $N$. In one move, Chef does the following: - Uniformly randomly pick an integer $X$ between $0$ and $2^N - 1$ (inclusive of both ends) - Update his score as $S \rightarrow S \mid X$, where $\mid$ denotes the [bitwise OR](https://en.wikipedia.org/wiki/Bitwise_operation#OR) operation For example, if Chef's curr