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
input = sys.stdin.readline
    
Q=int(input())

for testcases in range(Q):
    S=input().strip()

    X=Y=0
    MAXX=MINX=MAXY=MINY=0

    for s in S:
        if s=="D":
            X+=1
            MAXX=max(MAXX,X)

        elif s=="A":
            X-=1
            MINX=min(MINX,X)

        elif s=="W":
            Y+=1
            MAXY=max(MAXY,Y)

        else:
            Y-=1
            MINY=min(MINY,Y)

    #print(MAXX,MINX,MAXY,MINY)

    MAXXLIST=[]
    MINXLIST=[]
    MAXYLIST=[]
    MINYLIST=[]

    if MAXX==0:
        MAXXLIST.append(0)

    if MAXY==0:
        MAXYLIST.append(0)

    if MINX==0:
        MINXLIST.append(0)

    if MINY==0:
        MINYLIST.append(0)

    X=Y=0
        

    for i in range(len(S)):
        s=S[i]
        if s=="D":
            X+=1
            if X==MAXX:
                MAXXLIST.append(i+1)
                
        elif s=="A":
            X-=1
            if X==MINX:
                MINXLIST.append(i+1)

        elif s=="W":
            Y+=1
            if Y==MAXY:
                MAXYLIST.append(i+1)

        else:
            Y-=1
            if Y==MINY:
                MINYLIST.append(i+1)

    #print(MAXXLIST)
    #print(MAXYLIST)
    #print(MINXLIST)
    #print(MINYLIST)

    ANS=(MAXX-MINX+1)*(MAXY-MINY+1)

    #print(ANS)


    if MAXX-MINX>1:
        if MAXXLIST[0]>MINXLIST[-1] or MINXLIST[0]>MAXXLIST[-1]:
            ANS=min(ANS,(MAXX-MINX)*(MAXY-MINY+1))

    if MAXY-MINY>1:
        if MAXYLIST[0]>MINYLIST[-1] or MINYLIST[0]>MAXYLIST[-1]:
            ANS=min(ANS,(MAXX-MINX+1)*(MAXY-MINY))

    print(ANS)
        
