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).
// No sorceries shall previal. //
     
import java.util.Scanner; 
import java.io.PrintWriter;
import java.util.*;

public class InVoker {
	
	public static void main(String args[]) {
		
		Scanner inp = new Scanner(System.in);
		PrintWriter out= new PrintWriter(System.out);
		int q=inp.nextInt();
		
		while(q-->0)
		{
		
		String s=inp.next();
		
        long x = 0;
        long y = 0;
        long minX = 0;
        boolean xDown = false;
        long minY = 0;
        boolean yDown = false;
        long maxX = 0;
        boolean xUp = false;
        long maxY = 0;
        boolean yUp = false;
        for (int i = 0; i < s.length(); i++) {
            switch (s.charAt(i)) {
                case 'W': {
                    y++;
                    if (y >= maxY) {
                        yUp = true;
                    }
                    if (y > maxY) {
                        maxY = y;
                        yDown = false;
                    }
                } break;
                case 'A': {
                    x--;
                    if (x <= minX) {
                        xDown = true;
                    }
                    if (x < minX) {
                        minX = x;
                        xUp = false;
                    }
                } break;
                case 'S': {
                    y--;
                    if (y <= minY) {
                        yDown = true;
                    }
                    if (y < minY) {
                        minY = y;
                        yUp = false;
                    }
                } break;
                case 'D': {
                    x++;
                    if (x >= maxX) {
                        xUp = true;
                    }
                    if (x > maxX) {
                        maxX = x;
                        xDown = false;
                    }
                }
            }
        }
        long dx = maxX - minX;
        long dy = maxY - minY;
        boolean canReduceX = dx > 1 && !(xDown && xUp);
        boolean canReduceY = dy > 1 && !(yDown && yUp);
        if (canReduceX && (!canReduceY || dx <= dy)) {
            out.println(dx * (dy + 1));
        } else if (canReduceY) {
            out.println((dx + 1) * dy);
        } else {
            out.println((dx + 1) * (dy + 1));
        }
    
		}
		
		out.close();
		inp.close();
		
		
			
	}
	
}

