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 java.util.*;
import java.io.*;
import java.math.*;
public class Solution{
    public static int[] tab;
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        int t = Integer.parseInt(st.nextToken());
        for(int z=0;z<t;z++){
            st = new StringTokenizer(br.readLine());
            char[] c = st.nextToken().toCharArray();
            int n = c.length;
            int x=0,y=0;
            int u=0,d=0,l=0,r=0;
            for(int i=0;i<n;i++){
                if(c[i]=='W') y++;
                if(c[i]=='S') y--;
                if(c[i]=='A') x--;
                if(c[i]=='D') x++;
                u = Math.max(y,u);
                d = Math.min(y,d);
                l = Math.min(x,l);
                r = Math.max(x,r);
            }
            long tol = (long)(u-d+1);
            long ard = (long)(r-l+1);
            boolean ok1 = false;
            boolean ok2 = false;
            boolean ok3 = false;
            boolean ok4 = false;
            boolean rok1 = true;
            boolean rok2 = true;
            boolean rok3 = true;
            boolean rok4 = true;
            if(tol<=2){
                rok3 = false;
                rok4 = false;
            }
            if(ard<=2){
                rok1 = false;
                rok2 = false;
            }
            x = 0;
            y = 0;
            //out.println(tol+" "+ard);
            if(l==0) rok1 = false;
            if(r==0) rok2 = false;
            if(d==0) rok3 = false;
            if(u==0) rok4 = false;
            for(int i=0;i<n;i++){
                if(c[i]=='W') y++;
                if(c[i]=='S') y--;
                if(c[i]=='A') x--;
                if(c[i]=='D') x++;
                if(ard>2){
                    if(ok1&&x==r){
                        rok1 = false;
                    }
                    if(ok2&&x==l){
                        rok2 = false;
                    }
                    if(x==l&&ok1==false){
                        ok1 = true;
                    }
                    if(x==r&&ok2==false){
                        ok2 = true;
                    }
                }
                if(tol>2){
                    if(ok3&&y==u){
                        rok3 = false;
                    }
                    if(ok4&&y==d){
                        rok4 = false;
                    }
                    if(y==d&&ok3==false){
                        ok3 = true;
                    }
                    if(y==u&&ok4==false){
                        ok4 = true;
                    }
                }
            }
            boolean o1 = rok1||rok2;
            boolean o2 = rok3||rok4;
            if(o1&&o2){
                if(tol>ard){
                    ard--;
                }else tol--;
            }else if(o1){
                ard--;
            }else if(o2){
                tol--;
            }
            out.println(tol*ard);
        }
        
        out.flush();
    }
}