#P1202C. You Are Given a WASD-string...
You Are Given a WASD-string...
Description
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:
- 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?
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.
Input
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 $2 \cdot 10^5$.
Output
Print $T$ integers: one per query. For each query print the minimum area of $Grid(s)$ you can achieve.
Samples
3
DSAWWAW
D
WA
8
2
4
Note
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 $Grid(s)$.