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 F {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        int T = Integer.parseInt(reader.readLine());
        while(T > 0){
            --T;
            char[] b = reader.readLine().toCharArray();
            int x = 0;
            int y = 0;
            long min_x = 0;
            int count1 = 0;
            int count2 = 0;
            int count3 = 0;
            int count4 = 0;
            int last1 = 0;
            int last2 = 0;
            int last3 = 0;
            int last4 = 0;
            long max_x = 0;
            long min_y = 0;
            long max_y = 0;
            for(int i = 1; i <= b.length; ++i){
                if(b[i - 1] == 'W'){
                    ++x;
                    if(x > max_x){
                        max_x = x;
                        count1 = i;
                        last1 = i;
                    }
                    else if(x == max_x){
                        last1 = i;
                    }
                }
                else if(b[i - 1] == 'S'){
                    --x;
                    if(x < min_x){
                        min_x = x;
                        count2 = i;
                        last2 = i;
                    }
                    else if(x == min_x){
                        last2 = i;
                    }
                }
                else if(b[i - 1] == 'D'){
                    ++y;
                    if(y > max_y){
                        max_y = y;
                        count3 = i;
                        last3 = i;
                    }
                    else if(y == max_y){
                        last3 = i;
                    }
                }
                else{
                    --y;
                    if(y < min_y){
                        min_y = y;
                        last4 = i;
                        count4 = i;
                    }
                    else if(y == min_y){
                        last4 = i;
                    }
                }
            }
            long ans = (max_x - min_x + 1) * (max_y - min_y + 1);
            if(max_x > 0 && (min_x < 0 || max_x > 1) && count1 > last2 || min_x < 0 && (max_x > 0 || min_x < -1) && count2 > last1){
                ans = Math.min(ans, (max_x - min_x) * (max_y - min_y + 1));
            }
            if(max_y > 0 && (min_y < 0 || max_y > 1) && count3 > last4 || min_y < 0 && (max_y > 0 || min_y < -1) && count4 > last3){
                ans = Math.min(ans,(max_x - min_x + 1) * (max_y - min_y));
            }
            writer.println(ans);
        }
        writer.close();
    }
}