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):
    cmd = input()

    mostL, mostR, mostB, mostT = 0, 0, 0, 0
    mostLs, mostRs, mostBs, mostTs = [0],[0],[0],[0]
    x,y=0,0
    i = 0
    for c in cmd:
        i += 1
        if c == "W":
            y += 1
            if y>mostT:
                mostT = y
                mostTs = [i]
            elif y == mostT:
                mostTs.append(i)
        elif c == "S":
            y -= 1
            if y<mostB:
                mostB = y
                mostBs = [i]
            elif y == mostB:
                mostBs.append(i)
        elif c == "A":
            x -= 1
            if x < mostL:
                mostL = x
                mostLs = [i]
            elif x == mostL:
                mostLs.append(i)
        elif c == "D":
            x += 1
            if x > mostR:
                mostR = x
                mostRs = [i]
            elif x == mostR:
                mostRs.append(i)

    LR = mostR - mostL + 1
    if LR >= 3:
        firstL, lastL = mostLs[0], mostLs[-1]
        firstR, lastR = mostRs[0], mostRs[-1]

        cross = lastR > firstL and lastL > firstR
        LR_extra = not cross
    else:
        LR_extra = False

    BT = mostT - mostB + 1
    if BT >= 3:
        firstB, lastB = mostBs[0], mostBs[-1]
        firstT, lastT = mostTs[0], mostTs[-1]

        cross = lastB > firstT and lastT > firstB
        BT_extra = not cross
    else:
        BT_extra = False

    if LR_extra and BT_extra:
        area = min((LR-1)*BT,LR*(BT-1))
    elif LR_extra:
        area = (LR-1)*BT
    elif BT_extra:
        area = LR*(BT-1)
    else:
        area = LR*BT
    print(area)