Button Pressing

You are given $N$ buttons (numbered from $1$ to $N$) and $N$ lamps (numbered from $1$ to $N$). Each lamp can be either on or off. Initially, lamp $i$ is on if $A_i = 1$, and off if $A_i = 0$.

Button $i$ is connected to lamp $i - 1$ (if $i > 1$) and lamp $i + 1$ (if $i < N$). In one move, you can press button $i$ only if lamp $i$ is on. When a button is pressed, the state of the lamps connected to it is toggled: a lamp that was off turns on, and a lamp that was on turns off. Button $i$ is not connected to lamp $i$, so pressing button $i$ does not change the state of lamp $i$.

After zero or more moves, you want lamp $i$ to be on if $B_i = 1$, and off if $B_i = 0$. Determine whether this is possible.

The first line contains an integer $T$ ($1 \le T \le 1000$), the number of test cases. Each test case consists of three lines.

The first line of each test case contains an integer $N$ ($3 \le N \le 200000$). The sum of $N$ over all test cases does not exceed 200000.

The second line contains a string $A$ of length $N$. Each character is 0 or 1. The $i$-th character is the initial state of lamp $i$.

The third line contains a string $B$ of length $N$. Each character is 0 or 1. The $i$-th character is the desired final state of lamp $i$.

For each test case, print YES on a single line if all lamps can be brought to their desired states, or NO otherwise.