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).
n = int(input())

def area(width, height) :
    return (width+1) * (height+1)

def calcul(s1, c, s2) :
    maxx, maxy, minx, miny = 0, 0, 0, 0
    x, y = 0, 0
    for k in range(len(s1)) :
        if s1[k] == "W" :
            y += 1
        if s1[k] == "S" :
            y -= 1
        if s1[k] == "A" :
            x -= 1
        if s1[k] == "D" :
            x += 1
        maxx = max(maxx, x)
        minx = min(minx, x)

        maxy = max(maxy, y)
        miny = min(miny, y)




    if c == "W" :
        y += 1
    elif c == "S" :
        y -= 1
    elif c == "A" :
        x -= 1
    elif c == "D" :
        x += 1
    else :
        print(c, "ok")

    maxx = max(maxx, x)
    minx = min(minx, x)

    maxy = max(maxy, y)
    miny = min(miny, y)

    for k in range(len(s2)) :
        if s2[k] == "W" :
            y += 1
        if s2[k] == "S" :
            y -= 1
        if s2[k] == "A" :
            x -= 1
        if s2[k] == "D" :
            x += 1
        maxx = max(maxx, x)
        minx = min(minx, x)

        maxy = max(maxy, y)
        miny = min(miny, y)



    diffx = maxx - minx
    diffy = maxy - miny
    tmp = area(diffx, diffy)


    return tmp

def pre_calcul(s, moment, pre_avant, date_debut) :
    x, y, maxx, minx, maxy, miny = pre_avant
    for k in range(date_debut, moment) :
        if s[k] == "W" :
            y += 1
        if s[k] == "S" :
            y -= 1
        if s[k] == "A" :
            x -= 1
        if s[k] == "D" :
            x += 1
        maxx = max(maxx, x)
        minx = min(minx, x)

        maxy = max(maxy, y)
        miny = min(miny, y)

    return (x, y, maxx, minx, maxy, miny)

def calcul2(s, c, moment, precalcul) :
    x, y, maxx, minx, maxy, miny = precalcul



    if c == "W" :
        y += 1
    elif c == "S" :
        y -= 1
    elif c == "A" :
        x -= 1
    elif c == "D" :
        x += 1
    else :
        print(c, "ok")

    maxx = max(maxx, x)
    minx = min(minx, x)

    maxy = max(maxy, y)
    miny = min(miny, y)

    for k in range(moment, len(s)) :
        if s[k] == "W" :
            y += 1
        if s[k] == "S" :
            y -= 1
        if s[k] == "A" :
            x -= 1
        if s[k] == "D" :
            x += 1
        maxx = max(maxx, x)
        minx = min(minx, x)

        maxy = max(maxy, y)
        miny = min(miny, y)



    diffx = maxx - minx
    diffy = maxy - miny
    tmp = area(diffx, diffy)


    return tmp

for _ in range(n) :
    s = input()
    maxx, maxy, minx, miny = 0, 0, 0, 0
    x, y = 0, 0
    momentminx, momentmaxx, momentminy, momentmaxy = -1, -1, -1, -1
    for k in range(len(s)) :
        if s[k] == "W" :
            y += 1
        if s[k] == "S" :
            y -= 1
        if s[k] == "A" :
            x -= 1
        if s[k] == "D" :
            x += 1

        if x > maxx :
            momentmaxx = k
        if y > maxy :
            momentmaxy = k
        if x < minx :
            momentminx = k
        if y < miny :
            momentminy = k
        maxx = max(maxx, x)
        minx = min(minx, x)

        maxy = max(maxy, y)
        miny = min(miny, y)
    diffx = maxx - minx
    diffy = maxy - miny


    tmp = 999999999999999999999999999999999999
    l = [momentmaxx, momentmaxy, momentminx, momentminy]
    l = list(set(l))
    l = [i for i in l if i != -1]
    l.sort()
    if l != [] :
        precalcul = pre_calcul(s, l[0], (0, 0, 0, 0, 0, 0), 0)
        avant = l[0]
        for moment in l :
            precalcul = pre_calcul(s, moment, precalcul, avant)
            avant = moment
            tmp = min(tmp, calcul2(s, 'W', moment, precalcul))
            tmp = min(tmp, calcul2(s, 'S', moment, precalcul))
            tmp = min(tmp, calcul2(s, 'A', moment, precalcul))
            tmp = min(tmp, calcul2(s, 'D', moment, precalcul))
    print(tmp)
