You Are Given a WASD-string...

2000ms

262144K

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 $$$(1, 1)$$$.

$\text{[math]}$

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?

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.

Sample Input:

3
DSAWWAW
D
WA

Sample Output:

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 $$$Grid(s)$$$.

Informação

Provedor Codeforces

Código CF1202C