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(raw_input())
for _ in range(0,t):
    a= list(raw_input())
    nowx=0
    nowy=0
    maxx=0
    minx=0
    maxy=0
    miny=0
    tmaxx=0
    tminx=0
    tmaxy=0
    tminy=0
    highw=0
    highs=0
    widthd=0
    widtha=0
    for i in range (0,len(a)):
        if a[i] == 'W':
            nowy += 1
            if nowy >= maxy:
                maxy=nowy
                tmaxy=i
        elif a[i] == 'S':
            nowy -= 1
            if nowy <=miny:
                miny=nowy
                tminy=i
        elif a[i] == 'D':
            nowx += 1
            if nowx >= maxx:
                maxx=nowx
                tmaxx=i
        elif a[i] == 'A':
            nowx -= 1
            if nowx <=minx:
                minx=nowx
                tminx=i
        highw= max(highw,nowy-miny)
        highs= max(highs,maxy-nowy)
        widthd=max(widthd,nowx-minx)
        widtha=max(widtha,maxx-nowx)
    y1= max(highw,highs)
    y2= max(highw!=0 or highs!=0, y1- ((highw!=highs)))
    x1= max(widthd,widtha)
    x2= max(widthd!=0 or widtha!=0, x1-((widthd!=widtha)))
    print(min((y1+1)*(x2+1),(1+y2)*(x1+1)))