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.*;

public class CP {
    public static void main(String[] args) throws Exception {
        /*new Thread(null, new Runnable() {
            @Override
            public void run() {
                try {
                    new Solver().solve();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }, "Solver", 1l << 30).start();*/

        new Solver().solve();
    }
}

class Solver {
    IO io = new IO(System.in, System.out);

    String S;
    int N;

    void solve() throws Exception {
        int i, j, k;
        for (int tc = io.nextInt(); tc > 0; --tc) {
            ans = Long.MAX_VALUE;

            S = io.next();
            N = S.length();

            int[][] rec = new int[N][];
            int x = 0, y = 0, minX, maxX, minY, maxY;
            minX = maxX = x; minY = maxY = y;

            for (i = N - 1; i >= 0; --i) {
                switch (S.charAt(i)) {
                    case 'W': --y; break;
                    case 'D': --x; break;
                    case 'S': ++y; break;
                    case 'A': ++x; break;
                }
                minX = Math.min(minX, x); maxX = Math.max(maxX, x);
                minY = Math.min(minY, y); maxY = Math.max(maxY, y);

                rec[i] = new int[] {minX - x, maxX - x, minY - y, maxY - y};
            }

            ans = (maxX - minX + 1) * (long) (maxY - minY + 1);

            x = 0; y = 0; minX = maxX = x; minY = maxY = y;
            for (i = 0; i < N - 1; ++i) {
                switch (S.charAt(i)) {
                    case 'W': ++y; break;
                    case 'D': ++x; break;
                    case 'S': --y; break;
                    case 'A': --x; break;
                }
                minX = Math.min(minX, x); maxX = Math.max(maxX, x);
                minY = Math.min(minY, y); maxY = Math.max(maxY, y);

                calc(minX, maxX, minY, maxY, x, y, rec[i + 1]);
                calc(minX, maxX, minY, maxY, x + 1, y, rec[i + 1]);
                calc(minX, maxX, minY, maxY, x - 1, y, rec[i + 1]);
                calc(minX, maxX, minY, maxY, x, y + 1, rec[i + 1]);
                calc(minX, maxX, minY, maxY, x, y - 1, rec[i + 1]);
            }

            io.println(ans);
        }
        io.flush();
    }

    long ans;

    void calc(int minX, int maxX, int minY, int maxY, int x, int y, int[] r) {
        int mnX = r[0] + x, mxX = r[1] + x;
        int mnY = r[2] + y, mxY = r[3] + y;

        int fmnX = Math.min(minX, mnX), fmnY = Math.min(minY, mnY);
        int fmxX = Math.max(maxX, mxX), fmxY = Math.max(maxY, mxY);

        ans = Math.min(ans, (fmxX - fmnX + 1) * (long) (fmxY - fmnY + 1));
    }
}


class IO {
    static byte[] buf = new byte[2048];
    static int index, total;
    static InputStream in;
    static BufferedWriter bw;


    IO(InputStream is, OutputStream os) {
        try {
            in = is;
            bw = new BufferedWriter(new OutputStreamWriter(os));
        } catch (Exception e) {
        }
    }

    IO(String inputFile, String outputFile) {
        try {
            in = new FileInputStream(inputFile);
            bw = new BufferedWriter(new OutputStreamWriter(
                    new FileOutputStream(outputFile)));
        } catch (Exception e) {
        }
    }

    int scan() throws Exception {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
                return -1;
        }
        return buf[index++];
    }

    String next() throws Exception {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan())
            sb.append((char) c);
        return sb.toString();
    }

    int nextInt() throws Exception {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    long nextLong() throws Exception {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    void print(Object a) throws Exception {
        bw.write(a.toString());
    }

    void printsp(Object a) throws Exception {
        print(a);
        bw.write(" ");
    }

    void println() throws Exception {
        bw.write("\n");
    }

    void println(Object a) throws Exception {
        print(a);
        println();
    }

    void flush() throws Exception {
        bw.flush();
        bw.close();
    }
}