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.io.*;
import java.util.*;
import java.util.stream.*;

import static java.lang.Integer.*;

public class m implements Runnable {
  private static final boolean ONLINE_JUDGE = true; //System.getProperty("ONLINE_JUDGE") != null;

  public static void main(String[] args) {
    new Thread(new m()).run();
  }

  @Override
  public void run() {
    try (BufferedReader reader = ONLINE_JUDGE ? new BufferedReader(new InputStreamReader(System.in))
                                              : new BufferedReader(new FileReader("input"));
         Writer writer = ONLINE_JUDGE ? new OutputStreamWriter(System.out) : new FileWriter("output");
         PrintWriter printWriter = new PrintWriter(writer);) {
      Solver solver = new Solver(reader, printWriter);
      while (solver.solve());
    } catch (IOException e) {
      e.printStackTrace(System.err);
    }
  }

  static final class Solver {
    final BufferedReader in;
    final PrintWriter out;

    public Solver(BufferedReader reader, PrintWriter writer) {
      in = reader;
      out = writer;
    }

    boolean solve() throws IOException {
      String line = in.readLine();
      if (line == null) {
        return false;
      }
      if (line.isEmpty()) {
        return true;
      }
      StringTokenizer tok = new StringTokenizer(line);
      int q = parseInt(tok.nextToken());
MAIN: for (int qq = 0; qq < q ; ++qq) {
        char[] s = in.readLine().toCharArray();
        int n = s.length;
        List[] horver = new List[2];
        horver[0] = new ArrayList<Integer>();
        horver[1] = new ArrayList<Integer>();
        for (int i = 0; i < n; ++i) {
          if (s[i] == 'W') {
            horver[1].add(1);
          } else if (s[i] == 'A') {
            horver[0].add(-1);
          } else if (s[i] == 'S') {
            horver[1].add(-1);
          } else if (s[i] == 'D') {
            horver[0].add(1);
          }
        }
        boolean can[] = new boolean[2];
        int[] maxxx = new int[2];
        int[] minnn = new int[2];
        for (int hh = 0 ; hh < 2; ++hh) {
          List<Integer> coms = (List<Integer>) horver[hh];
          int cord = 0;
          int max = 0;
          int min = 0;
          int time = 0;
          int firstTimeMax = 0;
          int firstTimeMin = 0;
          int lastTimeMin = 0;
          int lastTimeMax = 0;
          for (Integer com : coms) {
            cord += com;
            if (max < cord) {
              max = cord;
              firstTimeMax = time;
            } else if (max == cord) {
              lastTimeMax = time;
            }
            if (min > cord) {
              min = cord;
              firstTimeMin = time;
            } else if (min == cord) {
              lastTimeMin = time;
            }
            ++time;
          }
          maxxx[hh] = max;
          minnn[hh] = min;
          if (max - min <= 1) {
            can[hh] = false;
          } else {
            if (firstTimeMin > lastTimeMax || firstTimeMax > lastTimeMin) {
              can[hh] = true;
            } else {
              can[hh] = false;
            }
          }
        }
        int h = maxxx[0] - minnn[0] + 1;
        int w = maxxx[1] - minnn[1] + 1;
        if (can[0] && can[1]) {
          out.println((Math.min(w, h) - 1) * 1L * Math.max(w, h));
        } else if (can[0]) {
          out.println((h - 1) * 1L * w);
        } else if (can[1]) {
          out.println((h) * 1L * (w - 1));
        } else {
          out.println((h) * 1L * (w));
        }
}

return true;
    }
  }

  static void debug(String s) {
    System.out.println(s);
  }
}
