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 fileinput
def D(a):print(a)
def S(s,I):return int(s.split(" ")[I])
def main():
    z=0
    for l in fileinput.input():
        z+=1
        if(z<2):continue;
        s=l[:-1]
        N=len(s)
        x=[0]*(N+1)
        X=[0]*(N+1)
        y=[0]*(N+1)
        Y=[0]*(N+1)
        o=pow(10,18)
        for i in xrange(N-1,-1,-1):
            X[i]=X[i+1]
            Y[i]=Y[i+1]
            x[i]=x[i+1]
            y[i]=y[i+1]
            if(s[i]=='A'):
                x[i]-=1
                X[i]=max(X[i]-1,0)
            if(s[i]=='D'):
                X[i]+=1
                x[i]=min(x[i]+1,0)
            if(s[i]=='S'):
                y[i]-=1
                Y[i]=max(Y[i]-1,0)
            if(s[i]=='W'):
                Y[i]+=1
                y[i]=min(y[i]+1,0)
        a=0
        b=0
        u=0
        U=0
        v=0
        V=0
        for i in range(N+1):
            #D("["+str(a)+","+str(b)+"]:"+str(u)+"/"+str(U)+".."+str(v)+"/"+str(V)+"|||"+str(x[i])+"/"+str(X[i])+".."+str(y[i])+"/"+str(Y[i]))
            #D((max(a+max(X[i]-1,0),U)-min(a+x[i]-1,u)+1)*(1+max(b+Y[i],V)-min(b+y[i],v)))
            #D((max(a+X[i]+1,U)-min(a+min(x[i]+1,0),u)+1)*(1+max(b+Y[i],V)-min(b+y[i],v)))
            #D((max(a+X[i],U)-min(a+x[i],u)+1)*(1+max(b+max(Y[i]-1,0),V)-min(b+y[i]-1,v)))
            #D((max(a+X[i],U)-min(a+x[i],u)+1)*(1+max(b+Y[i]+1,V)-min(b+min(y[i]+1,0),v)))
            #o=min(o,(max(a+X[i],U)-min(a+x[i],u))*(max(b+Y[i],V)-min(b+y[i],v)))
            o=min(o,(max(a+max(X[i]-1,0),U)-min(a+x[i]-1,u)+1)*(1+max(b+Y[i],V)-min(b+y[i],v)))
            o=min(o,(max(a+X[i]+1,U)-min(a+min(x[i]+1,0),u)+1)*(1+max(b+Y[i],V)-min(b+y[i],v)))
            o=min(o,(max(a+X[i],U)-min(a+x[i],u)+1)*(1+max(b+max(Y[i]-1,0),V)-min(b+y[i]-1,v)))
            o=min(o,(max(a+X[i],U)-min(a+x[i],u)+1)*(1+max(b+Y[i]+1,V)-min(b+min(y[i]+1,0),v)))
            if(i<N):
                if(s[i]=='A'):a-=1;
                if(s[i]=='D'):a+=1;
                if(s[i]=='W'):b+=1;
                if(s[i]=='S'):b-=1;
                u=min(u,a)
                U=max(U,a)
                v=min(v,b)
                V=max(V,b)
        D(o)

main()
