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).
t=int(input())
def possible(presum):
    l=len(presum)
    lastmax=-1
    firstmin=l
    mx=max(presum)
    mn=min(presum)
    for i in range(l):
        if(mx==presum[i]):
            lastmax=max(lastmax,i)
        if(mn==presum[i]):
            firstmin=min(i,firstmin)
    if lastmax<firstmin:
        return True
    return False
for i in range(t):
    s=input()
    l1=[0]
    l2=[0]
    for i in s:
        if i=='S':
            l1.append(l1[-1]-1)
        elif i=='W':
            l1.append(l1[-1]+1)
        elif i=="D":
            l2.append(l2[-1]+1)
        else:
            l2.append(l2[-1]-1)
    length=max(l1)-min(l1)+1
    breadth=max(l2)-min(l2)+1
    ans=length*breadth
    if length>2 and possible(l1):
        ans=min(ans,(length-1)*breadth)
    for i in range(len(l1)):
        l1[i]*=-1
    if length>2 and possible(l1):
        ans=min(ans,(length-1)*breadth)
    if breadth>2 and possible(l2):
        ans=min(ans,(length)*(breadth-1))
    for i in range(len(l2)):
        l2[i]*=-1
    if breadth>2 and possible(l2):
        ans=min(ans,(length)*(breadth-1))
    print(ans)