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.util.concurrent.ThreadLocalRandom;
import java.io.*;
import java.math.*;
import java.util.*;
public class A {
	public static void main(String[] args) throws NumberFormatException, IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int tc = sc.nextInt();
        while(tc-- > 0){
            char[] arr = sc.next().toCharArray();
            int[] x = new int[arr.length+1];
            int[] y = new int[arr.length+1];
            int[] maxX = new int[arr.length+1];
            int[] maxY = new int[arr.length+1];
            int[] minX = new int[arr.length+1];
            int[] minY = new int[arr.length+1];
            maxX[0] = x[0]; minX[0] = x[0]; maxY[0] = y[0]; minY[0] = y[0];
            for(int i=1;i<=arr.length;i++){
                x[i] = x[i-1]; y[i] = y[i-1];
                if(arr[i-1] == 'W'){
                    x[i] = x[i-1] + 1;
                }
                if(arr[i-1] == 'S'){
                    x[i] = x[i-1] - 1;
                }
                if(arr[i-1] == 'A'){
                    y[i] = y[i-1] + 1;
                }
                if(arr[i-1] == 'D'){
                    y[i] = y[i-1] - 1;
                }
                maxX[i] = Math.max(maxX[i-1], x[i]);
                maxY[i] = Math.max(maxY[i-1], y[i]);
                minX[i] = Math.min(minX[i-1], x[i]);
                minY[i] = Math.min(minY[i-1], y[i]);
            }
            int maxXSoFar = -1000000;
            int maxYSoFar = -10000000;
            int minXSoFar = 1000000;
            int minYSoFar = 10000000;
            long ans = 1l * (maxX[maxX.length - 1] - minX[minX.length - 1]+1)
                        * (maxY[maxY.length - 1] - minY[minY.length - 1]+1);
            // System.err.println(ans);
            for(int i=x.length-1;i>0;i--){
                maxXSoFar = Math.max(maxXSoFar, x[i]-1);
                maxYSoFar = Math.max(maxYSoFar, y[i]);
                minXSoFar = Math.min(minXSoFar, x[i]-1);
                minYSoFar = Math.min(minYSoFar, y[i]);
                int xnew = x[i-1] - 1;
                int ynew = y[i-1];
                int mxX = Math.max(maxXSoFar, Math.max(xnew, maxX[i-1]));
                int mnX = Math.min(minXSoFar, Math.min(xnew, minX[i-1]));
                int mxY = Math.max(maxYSoFar, Math.max(ynew, maxY[i-1]));
                int mnY = Math.min(minYSoFar, Math.min(ynew, minY[i-1]));
                ans = Math.min(ans, 1l * (mxX - mnX + 1) * (mxY - mnY + 1));
            }
            maxXSoFar = -1000000;
            maxYSoFar = -10000000;
            minXSoFar = 1000000;
            minYSoFar = 10000000;
            for(int i=x.length-1;i>0;i--){
                maxXSoFar = Math.max(maxXSoFar, x[i]+1);
                maxYSoFar = Math.max(maxYSoFar, y[i]);
                minXSoFar = Math.min(minXSoFar, x[i]+1);
                minYSoFar = Math.min(minYSoFar, y[i]);
                int xnew = x[i-1] + 1;
                int ynew = y[i-1];
                int mxX = Math.max(maxXSoFar, Math.max(xnew, maxX[i-1]));
                int mnX = Math.min(minXSoFar, Math.min(xnew, minX[i-1]));
                int mxY = Math.max(maxYSoFar, Math.max(ynew, maxY[i-1]));
                int mnY = Math.min(minYSoFar, Math.min(ynew, minY[i-1]));
                ans = Math.min(ans, 1l * (mxX - mnX + 1) * (mxY - mnY + 1));
            }
            maxXSoFar = -1000000;
            maxYSoFar = -10000000;
            minXSoFar = 1000000;
            minYSoFar = 10000000;
            for(int i=x.length-1;i>0;i--){
                maxXSoFar = Math.max(maxXSoFar, x[i]);
                maxYSoFar = Math.max(maxYSoFar, y[i]-1);
                minXSoFar = Math.min(minXSoFar, x[i]);
                minYSoFar = Math.min(minYSoFar, y[i]-1);
                int xnew = x[i-1];
                int ynew = y[i-1] - 1;
                int mxX = Math.max(maxXSoFar, Math.max(xnew, maxX[i-1]));
                int mnX = Math.min(minXSoFar, Math.min(xnew, minX[i-1]));
                int mxY = Math.max(maxYSoFar, Math.max(ynew, maxY[i-1]));
                int mnY = Math.min(minYSoFar, Math.min(ynew, minY[i-1]));
                // System.err.println("ddd  " + (mxX - mnX + 1) * (mxY - mnY + 1));
                ans = Math.min(ans, 1l *(mxX - mnX + 1) * (mxY - mnY + 1));
            }
            maxXSoFar = -1000000;
            maxYSoFar = -10000000;
            minXSoFar = 1000000;
            minYSoFar = 10000000;
            for(int i=x.length-1;i>0;i--){
                maxXSoFar = Math.max(maxXSoFar, x[i]);
                maxYSoFar = Math.max(maxYSoFar, y[i]+1);
                minXSoFar = Math.min(minXSoFar, x[i]);
                minYSoFar = Math.min(minYSoFar, y[i]+1);
                int xnew = x[i-1];
                int ynew = y[i-1] + 1;
                int mxX = Math.max(maxXSoFar, Math.max(xnew, maxX[i-1]));
                int mnX = Math.min(minXSoFar, Math.min(xnew, minX[i-1]));
                int mxY = Math.max(maxYSoFar, Math.max(ynew, maxY[i-1]));
                int mnY = Math.min(minYSoFar, Math.min(ynew, minY[i-1]));
                ans = Math.min(ans, 1l *(mxX - mnX + 1) * (mxY - mnY + 1));
            }
            pw.println(ans);
            // System.err.println(Arrays.toString(x));
            // System.err.println(Arrays.toString(y));
            // System.err.println(Arrays.toString(maxX));
            // System.err.println(Arrays.toString(maxY));
            // System.err.println(Arrays.toString(minX));
            // System.err.println(Arrays.toString(minY));
            
        }
        pw.flush();
    }
    

	static void shuffle(int[] ar)
	{
	  Random rnd = ThreadLocalRandom.current();
	  for (int i = ar.length - 1; i > 0; i--)
	  {
		int index = rnd.nextInt(i + 1);
		int a = ar[index];
		ar[index] = ar[i];
		ar[i] = a;
	  }
	}


	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}