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 Main {
    static int inf = (int) (1e9 + 7);

    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        for(int test = sc.nextInt();test > 0;test--) {
            char h[] = sc.next().toCharArray();
            int n = h.length;
            int x[] = new int [n + 1];
            int y[] = new int [n + 1];
            int this_x = 0;
            int this_y = 0;
            int id1_min = 0, id1_max = 0, id2_min = 0, id2_max = 0, id3_min = 0, id3_max = 0, id4_min = 0, id4_max = 0;

            for(int i = 1;i <= n;i++) {
                if (h[i - 1] == 'D') this_x--;
                if (h[i - 1] == 'A') this_x++;
                if (h[i - 1] == 'W') this_y++;
                if (h[i - 1] == 'S') this_y--;
                x[i] = this_x;
                y[i] = this_y;

                if (x[i] <= x[id1_max]) id1_max = i;
                if (x[i] >= x[id2_max]) id2_max = i;
                if (y[i] <= y[id3_max]) id3_max = i;
                if (y[i] >= y[id4_max]) id4_max = i;

                if (x[i] < x[id1_min]) id1_min = i;
                if (x[i] > x[id2_min]) id2_min = i;
                if (y[i] < y[id3_min]) id3_min = i;
                if (y[i] > y[id4_min]) id4_min = i;
            }

            for(int i = id1_max + 1;i <= n;i++) {
                if (h[i - 1] == 'A') {
                    id1_max = i;
                    break;
                }
            }

            for(int i = id2_max + 1;i <= n;i++) {
                if (h[i - 1] == 'D') {
                    id2_max = i;
                    break;
                }
            }

            for(int i = id3_max + 1;i <= n;i++) {
                if (h[i - 1] == 'W') {
                    id3_max = i;
                    break;
                }
            }

            for(int i = id4_max + 1;i <= n;i++) {
                if (h[i - 1] == 'S') {
                    id4_max = i;
                    break;
                }
            }

            long ans1 = x[id2_min] - x[id1_min] + 1;
            long ans2 = y[id4_min] - y[id3_min] + 1;

            boolean one = id1_max < id2_min || id2_max < id1_min;
            boolean two = id3_max < id4_min || id4_max < id3_min;
            if (one && (!two || (ans1 - 1) * ans2 < ans1 * (ans2 - 1))) ans1--;
            else if (two) ans2--;
            pw.println(ans1 * ans2);
        }
        pw.close();
    }

    static Scanner sc;
    static PrintWriter pw;

    static class Scanner {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        Scanner(InputStream in) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(in));
        }

        Scanner(String in) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(in));
        }

        String next() throws IOException {
            while (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

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

}