Doubled Distances

You are given $N$ integers $\{A_1, A_2, \ldots, A_N\}$. Determine whether they can be reordered such that each pair of consecutive differences differ by a factor of $2$. Formally, determine whether there exists a rearrangement of the given integers into an array $[B_1, B_2, \ldots, B_N]$ such that, for each $2 \leq i \leq N-1$, **at least one** of the following two conditions holds: - $B_i - B_{i