C. You Are Given a WASD-string...time limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:  you can place the robot in the cell (3, 2);  the robot performs the command 'D' and moves to (3, 3);  the robot performs the command 'S' and moves to (4, 3);  the robot performs the command 'A' and moves to (4, 2);  the robot performs the command 'W' and moves to (3, 2);  the robot performs the command 'W' and moves to (2, 2);  the robot performs the command 'A' and moves to (2, 1);  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?InputThe 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.OutputPrint T integers: one per query. For each query print the minimum area of Grid(s) you can achieve.ExampleInput
3
DSAWWAW
D
WA
Output
8
2
4
NoteIn 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).
3
DSAWWAW
D
WA

8 2 4 
['brute force', 'data structures', 'dp', 'greedy', 'implementation', 'math', 'strings', '*2100']