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.Scanner;

public class Main {

    static class Result {
        int iW, iA, iS, iD;
        long area;

        public Result(int iW, int iA, int iS, int iD, long area) {
            this.iW = iW;
            this.iA = iA;
            this.iS = iS;
            this.iD = iD;
            this.area = area;
        }
    }

    static Result process(String s) {
        int iW = -1;
        int iA = -1;
        int iS = -1;
        int iD = -1;
        int xMax = 0;
        int xMin = 0;
        int yMax = 0;
        int yMin = 0;
        int x = 0;
        int y = 0;

        for (int i = 0; i < s.length(); i++) {
            switch (s.charAt(i)) {
                case 'W':
                    y++;
                    if (y > yMax) {
                        iS = i;
                        yMax = y;
                    }
                    break;
                case 'A':
                    x--;
                    if (x < xMin) {
                        iD = i;
                        xMin = x;
                    }
                    break;
                case 'S':
                    y--;
                    if (y < yMin) {
                        iW = i;
                        yMin = y;
                    }
                    break;
                case 'D':
                    x++;
                    if (x > xMax) {
                        iA = i;
                        xMax = x;
                    }
                    break;
            }
        }

        long area = ((long) (xMax - xMin + 1)) * (yMax - yMin + 1);
        return new Result(iW, iA, iS, iD, area);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int T = sc.nextInt();

        for (int query = 0; query < T; query++) {
            String s = sc.next();
            Result result = process(s);
            long sol = result.area;
            if (result.iW != -1) sol = Math.min(sol, process(s.substring(0, result.iW) + "W" + s.substring(result.iW)).area);
            if (result.iA != -1) sol = Math.min(sol, process(s.substring(0, result.iA) + "A" + s.substring(result.iA)).area);
            if (result.iS != -1) sol = Math.min(sol, process(s.substring(0, result.iS) + "S" + s.substring(result.iS)).area);
            if (result.iD != -1) sol = Math.min(sol, process(s.substring(0, result.iD) + "D" + s.substring(result.iD)).area);
            System.out.println(sol);
        }
    }
}
