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;
template <typename F, typename S>
ostream &operator<<(ostream &os, const pair<F, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  typename vector<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "}";
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &v) {
  os << "[";
  typename set<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "]";
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &v) {
  os << "[";
  typename unordered_set<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "]";
}
template <typename F, typename S>
ostream &operator<<(ostream &os, const map<F, S> &v) {
  os << "[";
  typename map<F, S>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  return os << "]";
}
template <typename F, typename S>
ostream &operator<<(ostream &os, const unordered_map<F, S> &v) {
  os << "[";
  typename unordered_map<F, S>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  return os << "]";
}
int T;
string s;
void solve_q();
void read_input() {
  cin >> T;
  for (int i = 0; i < T; i++) solve_q();
}
pair<int, bool> process_string(char plus, char minus) {
  int maxi = 0, mini = 0, cnt = 0, first_max = 0, last_max = 0, first_min = 0,
      last_min = 0;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == plus)
      cnt++;
    else if (s[i] == minus)
      cnt--;
    if (cnt > maxi) {
      maxi = cnt;
      first_max = i;
      last_max = i;
    } else if (cnt == maxi) {
      last_max = i;
    }
    if (cnt < mini) {
      mini = cnt;
      first_min = i;
      last_min = i;
    } else if (cnt == mini) {
      last_min = i;
    }
  }
  int l = maxi - mini + 1;
  bool can_decrease = false;
  if (l > 2 && (last_max < first_min || last_min < first_max))
    can_decrease = true;
  return {l, can_decrease};
}
void solve_q() {
  cin >> s;
  int height, width;
  bool can_decrease_height, can_decrease_width;
  tie(height, can_decrease_height) = process_string('W', 'S');
  tie(width, can_decrease_width) = process_string('D', 'A');
  long long sol = (long long)height * (long long)width;
  if (can_decrease_height)
    sol = min(sol, (long long)(height - 1) * (long long)width);
  if (can_decrease_width)
    sol = min(sol, (long long)height * (long long)(width - 1));
  cout << sol << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  read_input();
  return 0;
}
