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.nio.CharBuffer;
import java.util.NoSuchElementException;

public class P1202C {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int caseNum = scanner.nextInt();
        while (caseNum-- > 0) {
            char[] s = scanner.next().toCharArray();
            int n = s.length;
            int[][] minR = new int[2][n + 1];
            int[][] maxR = new int[2][n + 1];
            int[][] minC = new int[2][n + 1];
            int[][] maxC = new int[2][n + 1];
            int[] r = new int[n + 1];
            int[] c = new int[n + 1];
            for (int i = 1; i <= n; ++i) {
                r[i] = r[i - 1];
                c[i] = c[i - 1];
                if (s[i - 1] == 'W')
                    --r[i];
                else if (s[i - 1] == 'S')
                    ++r[i];
                else if (s[i - 1] == 'A')
                    --c[i];
                else //s[i - 1] == 'D'
                    ++c[i];
                minR[0][i] = Math.min(minR[0][i - 1], r[i]);
                maxR[0][i] = Math.max(maxR[0][i - 1], r[i]);
                minC[0][i] = Math.min(minC[0][i - 1], c[i]);
                maxC[0][i] = Math.max(maxC[0][i - 1], c[i]);
            }
            minR[1][n] = r[n];
            maxR[1][n] = r[n];
            minC[1][n] = c[n];
            maxC[1][n] = c[n];
            for (int i = n - 1; i >= 0; --i) {
                minR[1][i] = Math.min(minR[1][i + 1], r[i]);
                maxR[1][i] = Math.max(maxR[1][i + 1], r[i]);
                minC[1][i] = Math.min(minC[1][i + 1], c[i]);
                maxC[1][i] = Math.max(maxC[1][i + 1], c[i]);
            }
            long height = maxR[0][n] - minR[0][n] + 1;
            long width = maxC[0][n] - minC[0][n] + 1;
            long ans = height * width;
            for (int i = 0; i < n; ++i) {
                ans = Math.min(ans, (Math.max(maxR[0][i], maxR[1][i] - 1) - Math.min(minR[0][i], minR[1][i] - 1) + 1) * width);
                ans = Math.min(ans, (Math.max(maxR[0][i], maxR[1][i] + 1) - Math.min(minR[0][i], minR[1][i] + 1) + 1) * width);
                ans = Math.min(ans, (Math.max(maxC[0][i], maxC[1][i] - 1) - Math.min(minC[0][i], minC[1][i] - 1) + 1) * height);
                ans = Math.min(ans, (Math.max(maxC[0][i], maxC[1][i] + 1) - Math.min(minC[0][i], minC[1][i] + 1) + 1) * height);
            }
            writer.println(ans);
        }

        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        int nextInt() {
            return Integer.valueOf(next());
        }

        long nextLong() {
            return Long.valueOf(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
