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;
void calc(vector<int> &a, vector<int> &b, string &second, bool flip) {
  int curad = 0, curws = 0;
  a.push_back(curad), b.push_back(curws);
  for (int i = 0; i < second.length(); i++) {
    if (!flip) {
      if (second[i] == 'A') curad--;
      if (second[i] == 'D') curad++;
      if (second[i] == 'W') curws--;
      if (second[i] == 'S') curws++;
    } else {
      if (second[i] == 'A') curad++;
      if (second[i] == 'D') curad--;
      if (second[i] == 'W') curws++;
      if (second[i] == 'S') curws--;
    }
    a.push_back(curad), b.push_back(curws);
  }
}
void test_case() {
  string second;
  cin >> second;
  bool adchange = 0, wschange = 0;
  long long adwidth = -1, wswidth = -1;
  for (int ok = 0; ok <= 1; ok++) {
    vector<int> ad, ws;
    calc(ad, ws, second, ok);
    int admin = *min_element(ad.begin(), ad.end()),
        admax = *max_element(ad.begin(), ad.end());
    int wsmin = *min_element(ws.begin(), ws.end()),
        wsmax = *max_element(ws.begin(), ws.end());
    if (adwidth == -1) adwidth = admax - admin + 1;
    if (wswidth == -1) wswidth = wsmax - wsmin + 1;
    int adminfirst = -1, admaxlast, wsminfirst = -1, wsmaxlast;
    for (int i = 0; i < ad.size(); i++) {
      if (ad[i] == admin && adminfirst == -1) adminfirst = i;
      if (ad[i] == admax) admaxlast = i;
    }
    for (int i = 0; i < ws.size(); i++) {
      if (ws[i] == wsmin && wsminfirst == -1) wsminfirst = i;
      if (ws[i] == wsmax) wsmaxlast = i;
    }
    adchange |= admaxlast < adminfirst;
    wschange |= wsmaxlast < wsminfirst;
  }
  if (adchange && wschange) {
    if (adwidth > wswidth) swap(adwidth, wswidth);
    cout << (adwidth - 1 >= 2     ? (adwidth - 1) * wswidth
             : (wswidth - 1 >= 2) ? (wswidth - 1) * adwidth
                                  : adwidth * wswidth)
         << '\n';
  } else if (adchange && !wschange) {
    cout << (adwidth - 1 >= 2 ? (adwidth - 1) * wswidth : adwidth * wswidth)
         << '\n';
  } else if (!adchange && wschange) {
    cout << (wswidth - 1 >= 2 ? adwidth * (wswidth - 1) : adwidth * wswidth)
         << '\n';
  } else {
    cout << adwidth * wswidth << '\n';
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int iteration = 1;
  cin >> iteration;
  while (iteration--) {
    test_case();
  }
}
