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 = 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). 

<image>

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 ≤ 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.

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 DSAWW\underline{D}AW.

In second and third queries you can not decrease the area of Grid(s).
t = int(input())
for c in range(t):
    s = input()
    up_max = down_max = right_max = left_max = 0
    first_up = last_up = first_down = last_down = first_left = last_left = first_right = last_right = 0
    current_x = current_y = 0
    horizontal_count = vertical_count = 0
    for i in range(len(s)):
        if s[i] == 'W':
            current_y += 1
            vertical_count += 1
            if current_y > up_max:
                up_max = current_y
                first_up = last_up = i + 1
            elif current_y == up_max:
                last_up = i + 1
        elif s[i] == 'S':
            current_y -= 1
            vertical_count += 1
            if current_y < down_max:
                down_max = current_y
                first_down = last_down = i + 1
            elif current_y == down_max:
                last_down = i + 1
        elif s[i] == 'D':
            current_x += 1
            horizontal_count += 1
            if current_x > right_max:
                right_max = current_x
                first_right = last_right = i + 1
            elif current_x == right_max:
                last_right = i + 1
        else:
            current_x -= 1
            horizontal_count += 1
            if current_x < left_max:
                left_max = current_x
                first_left = last_left = i + 1
            elif current_x == left_max:
                last_left = i + 1

    h = up_max - down_max + 1
    w = right_max - left_max + 1
    ans = h * w
    if vertical_count > 1 and last_up < first_down:
        ans = min(ans, (h - 1) * w)
    if vertical_count > 1 and last_down < first_up:
        ans = min(ans, (h - 1) * w)
    if horizontal_count > 1 and last_right < first_left:
        ans = min(ans, h * (w - 1))
    if horizontal_count > 1 and last_left < first_right:
        ans = min(ans, h * (w - 1))

    print(ans)