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.*;

@SuppressWarnings("unused")
public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
		PrintWriter writer = new PrintWriter(System.out);
		int t = Integer.parseInt(tokenizer.nextToken());
		for (int testNumber = 1; testNumber <= t; testNumber++) {
			tokenizer = new StringTokenizer(reader.readLine());
			char[] s = tokenizer.nextToken().toCharArray();
			int n = s.length;
			int[] x = new int[n + 1], y = new int[n + 1];
			x[0] = 0;
			y[0] = 0;
			for (int i = 0; i < n; i++) {
				x[i + 1] = x[i];
				y[i + 1] = y[i];
				if (s[i] == 'W') {
					x[i + 1]--;
				}
				if (s[i] == 'S') {
					x[i + 1]++;
				}
				if (s[i] == 'A') {
					y[i + 1]--;
				}
				if (s[i] == 'D') {
					y[i + 1]++;
				}
			}
			int[] minX = new int[n + 1], maxX = new int[n + 1], minY = new int[n + 1], maxY = new int[n + 1];
			minX[n] = x[n];
			maxX[n] = x[n];
			minY[n] = y[n];
			maxY[n] = y[n];
			for (int i = n - 1; i > -1; i--) {
				minX[i] = Math.min(x[i], minX[i + 1]);
				maxX[i] = Math.max(x[i], maxX[i + 1]);
				minY[i] = Math.min(y[i], minY[i + 1]);
				maxY[i] = Math.max(y[i], maxY[i + 1]);
			}
			long answer = ((long)maxX[0] - minX[0] + 1) * (maxY[0] - minY[0] + 1);
			int curMinX = x[0], curMaxX = x[0], curMinY = y[0], curMaxY = y[0];
			for (int i = 1; i < n + 1; i++) {
				int realMinX = Math.min(Math.min(curMinX, minX[i] + 1), x[i - 1] + 1);
				int realMaxX = Math.max(Math.max(curMaxX, maxX[i] + 1), x[i - 1] + 1);
				int realMinY = Math.min(curMinY, minY[i]);
				int realMaxY = Math.max(curMaxY, maxY[i]);
				answer = Math.min(answer, (long)(realMaxX - realMinX + 1) * (realMaxY - realMinY + 1));
				realMinX = Math.min(Math.min(curMinX, minX[i] - 1), x[i - 1] - 1);
				realMaxX = Math.max(Math.max(curMaxX, maxX[i] - 1), x[i - 1] - 1);
				realMinY = Math.min(curMinY, minY[i]);
				realMaxY = Math.max(curMaxY, maxY[i]);
				answer = Math.min(answer, (long)(realMaxX - realMinX + 1) * (realMaxY - realMinY + 1));
				realMinX = Math.min(curMinX, minX[i]);
				realMaxX = Math.max(curMaxX, maxX[i]);
				realMinY = Math.min(Math.min(curMinY, minY[i] + 1), y[i - 1] + 1);
				realMaxY = Math.max(Math.max(curMaxY, maxY[i] + 1), y[i - 1] + 1);
				answer = Math.min(answer, (long)(realMaxX - realMinX + 1) * (realMaxY - realMinY + 1));
				realMinX = Math.min(curMinX, minX[i]);
				realMaxX = Math.max(curMaxX, maxX[i]);
				realMinY = Math.min(Math.min(curMinY, minY[i] - 1), y[i - 1] - 1);
				realMaxY = Math.max(Math.max(curMaxY, maxY[i] - 1), y[i - 1] - 1);
				answer = Math.min(answer, (long)(realMaxX - realMinX + 1) * (realMaxY - realMinY + 1));
				curMinX = Math.min(curMinX, x[i]);
				curMaxX = Math.max(curMaxX, x[i]);
				curMinY = Math.min(curMinY, y[i]);
				curMaxY = Math.max(curMaxY, y[i]);
			}
			writer.println(answer);
		}
		writer.flush();
		writer.close();
	}
}
