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.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class C {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int T = Integer.parseInt(bf.readLine());
        for(int t=0; t<T; t++) {
          boolean decreaseUD = false;
          boolean decreaseLR = false;
          int UDlen = 1;
          int LRlen = 1;

          String s = bf.readLine();
          int min = 0;
          int max = 0;
          int cur = 0;
          for(int i=0; i<s.length(); i++) {
            if(s.charAt(i) == 'W') {
              cur++;
              if(cur > max)
                max = cur;
            }
            if(s.charAt(i) == 'S') {
              cur--;
              if(cur < min)
                min = cur;

            }
          }
          int curLen = max-min+1;
          UDlen = curLen;
          if(curLen >= 3) {
            int firstMax = -1;
            int lastMax = -1;
            int firstMin = -1;
            int lastMin = -1;
            if(max==0) {
              firstMax = -2;
              lastMax = -2;
            }
            else if(min ==0) {
              firstMin = -2;
              lastMin = -2;
            }
            cur = 0;
            for(int i=0; i<s.length(); i++) {
              if(s.charAt(i) == 'W') {
                cur++;
                if(cur == max) {
                  if(firstMax == -1) firstMax = i;
                  lastMax = i;
                }
              }
              else if(s.charAt(i) == 'S') {
                cur--;
                if(cur == min) {
                  if(firstMin == -1) firstMin = i;
                  lastMin = i;
                }
              }
            }
            cur = 0;
            boolean minBetween = false;
            boolean maxBetween = false;
            for(int i=0; i<s.length(); i++) {
              if(s.charAt(i) == 'W') {
                cur++;
                if(cur == max) {
                  if((firstMin <= i) && (i <= lastMin)) maxBetween = true;
                }
              }
              else if(s.charAt(i) == 'S') {
                cur--;
                if(cur == min) {
                  if((firstMax <= i) && (i <= lastMax)) minBetween = true;
                }
              }
            }
            if(!minBetween && !maxBetween) decreaseUD = true;
          }




          min = 0;
          max = 0;
          cur = 0;
          for(int i=0; i<s.length(); i++) {
            if(s.charAt(i) == 'A') {
              cur++;
              if(cur > max)
                max = cur;
            }
            if(s.charAt(i) == 'D') {
              cur--;
              if(cur < min)
                min = cur;

            }
          }
          curLen = max-min+1;
          LRlen = curLen;
          if(curLen >= 3) {
            int firstMax = -1;
            int lastMax = -1;
            int firstMin = -1;
            int lastMin = -1;
            cur = 0;
            if(max==0) {
              firstMax = -2;
              lastMax = -2;
            }
            else if(min ==0) {
              firstMin = -2;
              lastMin = -2;
            }
            for(int i=0; i<s.length(); i++) {
              if(s.charAt(i) == 'A') {
                cur++;
                if(cur == max) {
                  if(firstMax == -1) firstMax = i;
                  lastMax = i;
                }
              }
              else if(s.charAt(i) == 'D') {
                cur--;
                if(cur == min) {
                  if(firstMin == -1) firstMin = i;
                  lastMin = i;
                }
              }
            }
            cur = 0;
            boolean minBetween = false;
            boolean maxBetween = false;
            for(int i=0; i<s.length(); i++) {
              if(s.charAt(i) == 'A') {
                cur++;
                if(cur == max) {
                  if((firstMin <= i) && (i <= lastMin)) maxBetween = true;
                }
              }
              else if(s.charAt(i) == 'D') {
                cur--;
                if(cur == min) {
                  if((firstMax <= i) && (i <= lastMax)) minBetween = true;
                }
              }
            }
            if(!minBetween && !maxBetween) decreaseLR = true;
          }

          long ans1 = 1L * LRlen * UDlen;
          long ans2 = ans1;
          long ans3 = ans1;
          if(decreaseUD) ans2 = 1L * LRlen * (UDlen - 1);
          if(decreaseLR) ans3 = 1L * (LRlen - 1) * UDlen;
          out.println(Math.min(Math.min(ans1, ans2), ans3));
        }
        // StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        // int n = Integer.parseInt(st.nextToken());

        out.close(); System.exit(0);
    }
}
