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 * 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?

The first line contains one integer T (1 ≤ T ≤ 1000) — the number of queries.

Next T lines contain queries: one per line. This line contains single string s (1 ≤ |s| ≤ 2*10^5, s_i ∈ {W, A, S, D}) — the sequence of commands.

It's guaranteed that the total length of s over all queries doesn't exceed 2*10^5.

Print T integers: one per query. For each query print the minimum area of Grid(s) you can achieve.

3
DSAWWAW
D
WA

8
2
4

 Note

In the first query you have to get string {DSAWW\underline{D}AW}.
In second and third queries you can not decrease the area of Grid(s).