Rating changes for the last round are temporarily rolled back. They will be returned soon. ×

C. You Are Given a WASD-string...
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

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.

Example
Input
3
DSAWWAW
D
WA
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 $$$Grid(s)$$$.