XOR Game

Alice and Bob are playing a game that involves an array $A$ of length $N$ containing non-negative integers. The following sequence of events occurs **exactly once**: - Alice chooses two (not necessarily distinct) indices $i$ and $j$. Then, Alice sets $A_i := A_i \oplus A_j$ where $\oplus$ denotes the bitwise XOR operation. - Then, Bob chooses two (not necessarily distinct) indices $i$ and $j$ an