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).
def solve():
    i = 0
    j = 0
    imax = imin = 0
    jmax = jmin = 0
    fjmin = ljmin = fjmax = ljmax = fimax = limax = fimin = limin = -1
    for ind, e in enumerate(input()):
        if e == 'W':
            i += 1
            if i > imax:
                imax = i
                fimax = ind
                limax = ind
        elif e == 'S':
            i -= 1
            if i < imin:
                imin = i
                fimin = ind
                limin = ind
        elif e == "A":
            j -= 1
            if j < jmin:
                jmin = j
                fjmin = ind
                ljmin = ind
        elif e == 'D':
            j += 1
            if j > jmax:
                jmax = j
                fjmax = ind
                ljmax = ind
        if j == jmin:
            ljmin = ind
        if j == jmax:
            ljmax = ind
        if i == imin:
            limin = ind
        if i == imax:
            limax = ind
    ans = 0
    if fjmax > ljmin + 1 or fjmin > ljmax + 1:
        ans = imax - imin + 1
    if fimax > limin + 1 or fimin > limax + 1:
        ans = max(ans, jmax - jmin + 1)
    print((imax - imin + 1) * (jmax - jmin + 1) - ans)


for _ in range(int(input())):
    solve()
