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?

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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) $ .