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).
from sys import setrecursionlimit as SRL, stdin

SRL(10 ** 7)
rd = stdin.readline
rrd = lambda: map(int, rd().strip().split())

n = int(input())

while n:
    s = map(str,rd().strip())

    l = 0
    pl = 1
    r = 0
    pr = 1
    u = 0
    pu = 1
    b = 0
    pb = 1
    curx = 0
    cury = 0

    for x in s:
        if x == 'S':
            cury -= 1
            if cury < b:
                b = cury
                if u-b > 1:
                    pu = 0
            elif cury == b:
                pb = 1
        elif x == 'W':
            cury += 1
            if cury > u:
                u = cury
                if u - b > 1:
                    pb = 0
            elif cury == u:
                pu = 1
        elif x == 'A':
            curx -= 1
            if curx < l:
                l = curx
                if r - l > 1:
                    pr = 0
            elif curx == l:
                pl = 1
        elif x == 'D':
            curx += 1
            if curx > r:
                r = curx
                if r - l > 1:
                    pl = 0
            elif curx == r:
                pr = 1

    ans = (r-l+1)*(u-b+1)
    if not pl or not pr:
        ans = min(ans,(r-l)*(u-b+1))
    if not pb or not pu:
        ans = min(ans,(r-l+1)*(u-b))
    print(ans)

    n -= 1

