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).
#include <bits/stdc++.h>
using namespace std;
const int N = 210000;
int row[N];
int col[N];
char str[N];
int main() {
  int T, n;
  scanf("%d", &T);
  for (int t = 1; t <= T; t++) {
    scanf("%s", str + 1);
    int len = strlen(str + 1);
    int row_index = 0, col_index = 0;
    int row_max_left = 0, row_max_right = 0;
    int col_max_left = 0, col_max_right = 0;
    int row_min_left = 0, row_min_right = 0;
    int col_min_left = 0, col_min_right = 0;
    int row_max = 0, row_min = 0;
    int col_max = 0, col_min = 0;
    for (int i = 1; i <= len; i++) {
      if (str[i] == 'W') {
        ++col_index;
        col[col_index] = col[col_index - 1] + 1;
        if (col[col_index] > col_max) {
          col_max_left = col_index;
          col_max = col[col_index];
        }
        if (col[col_index] >= col_max) {
          col_max_right = col_index;
          col_max = col[col_index];
        }
      }
      if (str[i] == 'S') {
        ++col_index;
        col[col_index] = col[col_index - 1] - 1;
        if (col[col_index] < col_min) {
          col_min_left = col_index;
          col_min = col[col_index];
        }
        if (col[col_index] <= col_min) {
          col_min_right = col_index;
          col_min = col[col_index];
        }
      }
      if (str[i] == 'A') {
        ++row_index;
        row[row_index] = row[row_index - 1] - 1;
        if (row[row_index] < row_min) {
          row_min_left = row_index;
          row_min = row[row_index];
        }
        if (row[row_index] <= row_min) {
          row_min_right = row_index;
          row_min = row[row_index];
        }
      }
      if (str[i] == 'D') {
        ++row_index;
        row[row_index] = row[row_index - 1] + 1;
        if (row[row_index] > row_max) {
          row_max_left = row_index;
          row_max = row[row_index];
        }
        if (row[row_index] >= row_max) {
          row_max_right = row_index;
          row_max = row[row_index];
        }
      }
    }
    long long l = row_max - row_min + 1;
    long long w = col_max - col_min + 1;
    long long ans = (long long)l * w;
    long long tmp = (long long)ans;
    if (row_max_right < row_min_left && l > 2 ||
        row_min_right < row_max_left && l > 2)
      tmp = min(tmp, ans - w);
    if (col_max_right < col_min_left && w > 2 ||
        col_min_right < col_max_left && w > 2)
      tmp = min(tmp, ans - l);
    printf("%lld\n", tmp);
  }
  return 0;
}
