You Are Given a WASD-string...

你有一个由'W','A','S','D'构成的命令序列，可以控制你的一个玩具机器人在一个方格纸上走来走去，每走一下将会移动一个方格。 在这个命令序列中： - 'W'代表上 - 'A'代表左 - 'S'代表下 - 'D'代表右 你现在还可以给这个序列在任何位置添加上面四种操作中的仅一个操作，使得这个玩具机器人按照你的指令行走后，使得包含你的玩具机器人所经过的所有点的最小矩形的面积最小。(也可以不添加) 这个矩形的面积最小是多少？

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.

3
DSAWWAW
D
WA

8
2
4

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) $ .