Given a pair of binary numbers $$$(a_1, b_1)$$$, both of which have a length of $$$n$$$. For all $$$1 \leq i < n$$$, $$$a_{i + 1}$$$ is derived by changing no more than one $$$0$$$ (if any) in $$$a_i$$$ to $$$1$$$, and $$$b_{i + 1}$$$ is derived by changing no more than one $$$1$$$ (if any) in $$$b_i$$$ to $$$0$$$. Determine whether the bitwise OR of each pair is equal to $$$2^n - 1$$$ (that is, every bit is $$$1$$$).

It is guaranteed that $$$n \leq 3 \times 10^5$$$.