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 long long INF = 1e18;
int main() {
  int q;
  cin >> q;
  while (q--) {
    string in;
    cin >> in;
    long long x = 0, y = 0;
    long long lmax_y = 0, lmax_x = 0, fmin_x = 0, fmin_y = 0;
    long long fmax_y = 0, fmax_x = 0, lmin_x = 0, lmin_y = 0;
    long long max_y = 0, max_x = 0, min_x = 0, min_y = 0;
    for (int i = 0; i < in.length(); ++i) {
      if (in[i] == 'W') {
        ++y;
        if (max_y < y) {
          fmax_y = i;
          max_y = y;
        } else if (max_y == y)
          lmax_y = i;
      }
      if (in[i] == 'A') {
        --x;
        if (min_x > x) {
          fmin_x = i;
          min_x = x;
        } else if (min_x == x)
          lmin_x = i;
      }
      if (in[i] == 'S') {
        --y;
        if (min_y > y) {
          fmin_y = i;
          min_y = y;
        } else if (min_y == y)
          lmin_y = i;
        ;
      }
      if (in[i] == 'D') {
        ++x;
        if (max_x < x) {
          fmax_x = i;
          max_x = x;
        } else if (max_x == x)
          lmax_x = i;
      }
    }
    long long tmp_min = (max_x - min_x + 1) * (max_y - min_y + 1);
    if (max_x - min_x + 1 > 2 && (lmax_x < fmin_x || lmin_x < fmax_x) &&
        tmp_min > (max_x - min_x) * (max_y - min_y + 1))
      tmp_min = (max_x - min_x) * (max_y - min_y + 1);
    if (max_y - min_y + 1 > 2 && (lmax_y < fmin_y || lmin_y < fmax_y) &&
        tmp_min > (max_x - min_x + 1) * (max_y - min_y))
      tmp_min = (max_x - min_x + 1) * (max_y - min_y);
    cout << tmp_min << "\n";
  }
}
