CF1766C.Hamiltonian Wall

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".

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.