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).
import sys
def work(c,c1, s):
    maxlast, maxfirst,minlast,minfirst = 0,0,0,0
    max = 0
    min = 0
    y = 0
    for i in range(len(s)):
        if s[i] == c:
            y += 1
        elif s[i] == c1:
            y -=1

        if max < y:
            maxfirst,maxlast = i,i
            max = y
        elif max ==y :
            maxlast = i

        if y < min:
            minlast,minfirst =i,i
            min = y
        elif min == y:
            minlast = i
    flag = 0
    if (maxlast<minfirst or maxfirst>minlast) and max-min > 1:
        flag = 1
    return  max-min+1,flag

count = 0
for line in sys.stdin:
    if count == 0:
        n = int(line.strip().split(' ')[0])
        #k = int(line.strip().split(' ')[1])
        #m = int(line.strip().split(' ')[2])
        count += 1
        continue
    s = line.strip()
    flag,flag1 =0,0
    n,flag = work('W','S', s)
    m,flag1 = work('A', 'D', s)

    res = n * m
    if flag1 and flag:
        res = min(n*(m-1),m*(n-1))
    elif flag:
        res = m*(n-1)
    elif flag1:
        res = (m-1)*n
    print(res)