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).
def read_int():
    return int(input())


def read_ints():
    return map(int, input().split(' '))


t = read_int()
INF = int(1e7)
for case_num in range(t):
    s = input()
    x = 0
    y = 0
    xlist = [0]
    ylist = [0]
    for c in s:
        if c == 'W':
            y += 1
        elif c == 'S':
            y -= 1
        elif c == 'A':
            x -= 1
        else:
            x += 1
        xlist.append(x)
        ylist.append(y)
    n = len(s)
    l = [0]
    r = [0]
    u = [0]
    d = [0]
    for i in range(1, n + 1):
        l.append(min(l[-1], xlist[i]))
        r.append(max(r[-1], xlist[i]))
        u.append(max(u[-1], ylist[i]))
        d.append(min(d[-1], ylist[i]))
    lr = [xlist[n]]
    rr = [xlist[n]]
    ur = [ylist[n]]
    dr = [ylist[n]]
    for i in range(1, n + 1):
        lr.append(min(lr[-1], xlist[n - i]))
        rr.append(max(rr[-1], xlist[n - i]))
        ur.append(max(ur[-1], ylist[n - i]))
        dr.append(min(dr[-1], ylist[n - i]))
    ans = INF * INF
    coeff = [[-1, 0], [1, 0], [0, -1], [0, 1]]
    for k in range(4):
        for i in range(n):
            nl = min(l[i], lr[n - i] + coeff[k][0])
            nr = max(r[i], rr[n - i] + coeff[k][0])
            nu = max(u[i], ur[n - i] + coeff[k][1])
            nd = min(d[i], dr[n - i] + coeff[k][1])
            area = (nr - nl + 1) * (nu - nd + 1)
            ans = min(ans, area)
    print(ans)
