Yet Another Bitwise Problem

Chef gives you an array $A = [A_1, A_2, \ldots, A_N]$ of length $N$. Let $f(S)$ denote the [bitwise OR](https://en.wikipedia.org/wiki/Bitwise_operation#OR) of a non-empty subset $S$ of $A$. Find the maximum possible value of $f(S_1) \oplus f(S_2)$ across all ways to **partition** the elements of $A$ into two non-empty subsets $S_1$ and $S_2$. Here, $\oplus$ denotes the [bitwise XOR](https://en