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). 

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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 _ in range(t):
    ss = input()
    minx=0
    fminxpos = -1
    lminxpos = -1
    maxx=0
    fmaxxpos = -1
    lmaxxpos = -1
    miny=0
    fminypos = -1
    lminypos = -1
    maxy=0
    fmaxypos = -1
    lmaxypos = -1
    x = 0
    y = 0
    for i,s in enumerate(ss):
        if s == 'W':
            y +=1
            if y > maxy:
                maxy=y
                fmaxypos=i
            if y == maxy:
                lmaxypos=i
        elif s == 'S':
            y -= 1
            if y < miny:
                miny = y
                fminypos = i
            if y == miny:
                lminypos = i
        elif s == 'D':
            lastd = i
            x += 1
            if x > maxx:
                maxx = x
                fmaxxpos = i
            if x == maxx:
                lmaxxpos = i
        elif s == 'A':
            lasta = i
            x -= 1
            if x < minx:
                minx = x
                fminxpos = i
            if x == minx:
                lminxpos = i
    xsize = maxx - minx + 1
    ysize = maxy - miny + 1
    if xsize > 2 and (fmaxxpos > lminxpos or fminxpos > lmaxxpos):
        xmin = xsize - 1
    else:
        xmin = xsize
    if ysize > 2 and (fmaxypos > lminypos or fminypos > lmaxypos):
        ymin = ysize - 1
    else:
        ymin = ysize
    print(min(xmin*ysize, xsize*ymin))