Hamiltonian Wall
Description
Sir Monocarp Hamilton is planning to paint his wall. The wall can be represented as a grid, consisting of $2$ rows and $m$ columns. Initially, the wall is completely white.
Monocarp wants to paint a black picture on the wall. In particular, he wants cell $(i, j)$ (the $j$-th cell in the $i$-th row) to be colored black, if $c_{i, j} =$ 'B', and to be left white, if $c_{i, j} =$ 'W'. Additionally, he wants each column to have at least one black cell, so, for each $j$, the following constraint is satisfied: $c_{1, j}$, $c_{2, j}$ or both of them will be equal to 'B'.
In order for the picture to turn out smooth, Monocarp wants to place down a paint brush in some cell $(x_1, y_1)$ and move it along the path $(x_1, y_1), (x_2, y_2), \dots, (x_k, y_k)$ so that:
- for each $i$, $(x_i, y_i)$ and $(x_{i+1}, y_{i+1})$ share a common side;
- all black cells appear in the path exactly once;
- white cells don't appear in the path.
Determine if Monocarp can paint the wall.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains a single integer $m$ ($1 \le m \le 2 \cdot 10^5$) — the number of columns in the wall.
The $i$-th of the next two lines contains a string $c_i$, consisting of $m$ characters, where each character is either 'B' or 'W'. $c_{i, j}$ is 'B', if the cell $(i, j)$ should be colored black, and 'W', if the cell $(i, j)$ should be left white.
Additionally, for each $j$, the following constraint is satisfied: $c_{1, j}$, $c_{2, j}$ or both of them are equal to 'B'.
The sum of $m$ over all testcases doesn't exceed $2 \cdot 10^5$.
For each testcase, print "YES" if Monocarp can paint a wall. Otherwise, print "NO".
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.
The first line of each testcase contains a single integer $m$ ($1 \le m \le 2 \cdot 10^5$) — the number of columns in the wall.
The $i$-th of the next two lines contains a string $c_i$, consisting of $m$ characters, where each character is either 'B' or 'W'. $c_{i, j}$ is 'B', if the cell $(i, j)$ should be colored black, and 'W', if the cell $(i, j)$ should be left white.
Additionally, for each $j$, the following constraint is satisfied: $c_{1, j}$, $c_{2, j}$ or both of them are equal to 'B'.
The sum of $m$ over all testcases doesn't exceed $2 \cdot 10^5$.
Output
For each testcase, print "YES" if Monocarp can paint a wall. Otherwise, print "NO".
6
3
WBB
BBW
1
B
B
5
BWBWB
BBBBB
2
BW
WB
5
BBBBW
BWBBB
6
BWBBWB
BBBBBB
YES
YES
NO
NO
NO
YES
Note
In the first testcase, Monocarp can follow a path $(2, 1)$, $(2, 2)$, $(1, 2)$, $(1, 3)$ with his brush. All black cells appear in the path exactly once, no white cells appear in the path.
In the second testcase, Monocarp can follow a path $(1, 1)$, $(2, 1)$.
In the third testcase:
- the path $(1, 1)$, $(2, 1)$, $(2, 2)$, $(2, 3)$, $(1, 3)$, $(2, 4)$, $(2, 5)$, $(1, 5)$ doesn't suffice because a pair of cells $(1, 3)$ and $(2, 4)$ doesn't share a common side;
- the path $(1, 1)$, $(2, 1)$, $(2, 2)$, $(2, 3)$, $(1, 3)$, $(2, 3)$, $(2, 4)$, $(2, 5)$, $(1, 5)$ doesn't suffice because cell $(2, 3)$ is visited twice;
- the path $(1, 1)$, $(2, 1)$, $(2, 2)$, $(2, 3)$, $(2, 4)$, $(2, 5)$, $(1, 5)$ doesn't suffice because a black cell $(1, 3)$ doesn't appear in the path;
- the path $(1, 1)$, $(2, 1)$, $(2, 2)$, $(2, 3)$, $(2, 4)$, $(2, 5)$, $(1, 5)$, $(1, 4)$, $(1, 3)$ doesn't suffice because a white cell $(1, 4)$ appears in the path.