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.