B'Turtle Alice is currently designing a fortune cookie box, and she would like to incorporate the theory of LuoShu into it. The box can be seen as an n x m grid ( n, m ge 5 ), where the rows are numbered 1, 2, ... , n and columns are numbered 1, 2, ... , m . Each cell can either be empty or have a single fortune cookie of one of the following shapes: circle or square. The cell at the intersection of the a -th row and the b -th column is denoted as (a, b) . Initially, the entire grid is empty. Then, Alice performs q operations on the fortune cookie box. The i -th operation ( 1 <= i <= q ) is as follows: specify a currently empty cell (r_i,c_i) and a shape (circle or square), then put a fortune cookie of the specified shape on cell (r_i,c_i) . Note that after the i -th operation, the cell (r_i,c_i) is no longer empty. Before all operations and after each of the q operations, Alice wonders what the number of ways to place fortune cookies in all remaining empty cells is, such that the following condition is satisfied: No three consecutive cells (in horizontal, vertical, and both diagonal directions) contain cookies of the same shape. Formally: You should output all answers modulo 998 ,244 ,353 . Also note that it is possible that after some operations, the condition is already not satisfied with the already placed candies, in this case you should output 0 . The first line of the input contains a single integer t ( 1 <= t <= 10^3 ) -- the number of test cases. The first line of each test case contains three integers n , m , q ( 5 <= n, m <= 10^9, 0 <= q <= min(n x m, 10^5) ). The i -th of the next q lines contains two integers r_i , c_i and a single string text{shape}_i ( 1 <= r_i <= n, 1 <= c_i <= m , text{shape}_i= "circle" or "square"), representing the operations. It is guara'...