CF1202C You Are Given a WASD-string...

You have a string $ s $ — a sequence of commands for your toy robot. The robot is placed in some cell of a rectangular grid. He can perform four commands: - 'W' — move one cell up; - 'S' — move one cell down; - 'A' — move one cell left; - 'D' — move one cell right. Let $ Grid(s) $ be the grid of minimum possible area such that there is a position in the grid where you can place the robot in such a way that it will not fall from the grid while running the sequence of commands $ s $ . For example, if $ s = \text{DSAWWAW} $ then $ Grid(s) $ is the $ 4 \times 3 $ grid: 1. you can place the robot in the cell $ (3, 2) $ ; 2. the robot performs the command 'D' and moves to $ (3, 3) $ ; 3. the robot performs the command 'S' and moves to $ (4, 3) $ ; 4. the robot performs the command 'A' and moves to $ (4, 2) $ ; 5. the robot performs the command 'W' and moves to $ (3, 2) $ ; 6. the robot performs the command 'W' and moves to $ (2, 2) $ ; 7. the robot performs the command 'A' and moves to $ (2, 1) $ ; 8. the robot performs the command 'W' and moves to $ (1, 1) $ . You have $ 4 $ extra letters: one 'W', one 'A', one 'S', one 'D'. You'd like to insert at most one of these letters in any position of sequence $ s $ to minimize the area of $ Grid(s) $ . What is the minimum area of $ Grid(s) $ you can achieve?

The first line contains one integer $ T $ ( $ 1 \le T \le 1000 $ ) — the number of queries. Next $ T $ lines contain queries: one per line. This line contains single string $ s $ ( $ 1 \le |s| \le 2 \cdot 10^5 $ , $ s_i \in \{\text{W}, \text{A}, \text{S}, \text{D}\} $ ) — the sequence of commands. It's guaranteed that the total length of $ s $ over all queries doesn't exceed $ 2 \cdot 10^5 $ .

Print $ T $ integers: one per query. For each query print the minimum area of $ Grid(s) $ you can achieve.

In the first query you have to get string $ \text{DSAWW}\underline{D}\text{AW} $ . In second and third queries you can not decrease the area of $ Grid(s) $ .