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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class C {

    private static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    private static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
    private static StringTokenizer st;

    public static void main(String[] args) throws Exception {
        st = new StringTokenizer(reader.readLine());
        int T = Integer.parseInt(st.nextToken());
        Random rnd = new Random();
        while (T-- != 0) {
            st = new StringTokenizer(reader.readLine());
            String s = st.nextToken();
            Long correctedArea = correctedArea(s);
            /*StringBuilder sb0 = new StringBuilder();
            for (int i = 0; i < 10; i++) {
                int n = rnd.nextInt(4);
                switch (n) {
                    case 0: sb0.append('W'); break;
                    case 1: sb0.append('A'); break;
                    case 2: sb0.append('S'); break;
                    case 3: sb0.append('D'); break;
                }
            }
            String s = sb0.toString();
            Long correctedArea = correctedArea(s);

            long minArea = Long.MAX_VALUE;
            for (int i = 0; i <= s.length(); i++) {
                StringBuilder sb = new StringBuilder(s);
                sb.insert(i, 'W');
                long area = area(sb.toString());
                if (area < minArea) {
                    minArea = area;
                }

                sb = new StringBuilder(s);
                sb.insert(i, 'A');
                area = area(sb.toString());
                if (area < minArea) {
                    minArea = area;
                }

                sb = new StringBuilder(s);
                sb.insert(i, 'S');
                area = area(sb.toString());
                if (area < minArea) {
                    minArea = area;
                }

                sb = new StringBuilder(s);
                sb.insert(i, 'D');
                area = area(sb.toString());
                if (area < minArea) {
                    minArea = area;
                }
            }
            if (correctedArea != minArea) {
                writer.write(Long.toString(correctedArea));
                writer.newLine();
                writer.write(Long.toString(minArea));
                writer.newLine();
                writer.write(s);
                writer.newLine();
            }*/
            writer.write(Long.toString(correctedArea));
            writer.newLine();
        }
        writer.flush();
    }

    private static long area(String s) {
        int x = 0;
        int y = 0;
        int left = 0;
        int right = 0;
        int up = 0;
        int down = 0;
        for (int i = 0; i < s.length(); i++) {
            switch (s.charAt(i)) {
                case 'W':
                    y++;
                    break;
                case 'A':
                    x--;
                    break;
                case 'S':
                    y--;
                    break;
                case 'D':
                    x++;
                    break;
            }
            if (y > up) {
                up = y;
            }
            if (y < down) {
                down = y;
            }
            if (x > right) {
                right = x;
            }
            if (x < left) {
                left = x;
            }
        }
        return (long)(up - down + 1) * (right - left + 1);
    }

    private static long correctedArea(String s) {
        int x = 0;
        int y = 0;
        int left = 0;
        int right = 0;
        int up = 0;
        int down = 0;
        List<Integer> lefts = new ArrayList<>();
        lefts.add(-1);
        List<Integer> rights = new ArrayList<>();
        rights.add(-1);
        List<Integer> ups = new ArrayList<>();
        ups.add(-1);
        List<Integer> downs = new ArrayList<>();
        downs.add(-1);
        for (int i = 0; i < s.length(); i++) {
            switch (s.charAt(i)) {
                case 'W':
                    y++;
                    break;
                case 'A':
                    x--;
                    break;
                case 'S':
                    y--;
                    break;
                case 'D':
                    x++;
                    break;
            }
            if (y > up) {
                up = y;
                ups.clear();
                ups.add(i);
            } else if (y == up) {
                ups.add(i);
            }
            if (y < down) {
                down = y;
                downs.clear();
                downs.add(i);
            } else if (y == down) {
                downs.add(i);
            }
            if (x > right) {
                right = x;
                rights.clear();
                rights.add(i);
            } else if (x == right) {
                rights.add(i);
            }
            if (x < left) {
                left = x;
                lefts.clear();
                lefts.add(i);
            } else if (x == left) {
                lefts.add(i);
            }
        }
        boolean xDecreasable = false;
        boolean yDecreasable = false;
        int width = right - left + 1;
        if ((right - left > 1) && (lefts.get(0) > rights.get(rights.size() - 1) || rights.get(0) > lefts.get(lefts.size() - 1))) {
            xDecreasable = true;
        }
        int height = up - down + 1;
        if ((up - down > 1) && (ups.get(0) > downs.get(downs.size() - 1) || downs.get(0) > ups.get(ups.size() - 1))) {
            yDecreasable = true;
        }
        if (xDecreasable && yDecreasable) {
            return Math.min((long)(width - 1) * height, (long)width * (height - 1));
        } else if (xDecreasable) {
            return (long)(width - 1) * height;
        } else if (yDecreasable) {
            return (long)width * (height - 1);
        } else {
            return (long)width * height;
        }
    }

}
