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;
using ll = long long;
const int INF = 1000000000;
const ll LINF = 1001002003004005006ll;
int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
struct IOSetup {
  IOSetup() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(12);
  }
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++)
    os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
  return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &x : v) is >> x;
  return is;
}
void solve() {
  string s;
  cin >> s;
  ll l = 0, r = 0, u = 0, d = 0;
  ll i = 0, j = 0;
  for (auto &c : s) {
    if (c == 'W') i++;
    if (c == 'S') i--;
    if (c == 'A') j--;
    if (c == 'D') j++;
    chmin(l, j);
    chmax(r, j);
    chmin(d, i);
    chmax(u, i);
  }
  ll res = (r - l + 1) * (u - d + 1);
  if (l < 0) {
    int rem = 1;
    int j = 0;
    bool f = true;
    for (auto &c : s) {
      if (c == 'A') {
        if (j == l + 1) {
          j++;
          if (j > r) f = false;
          rem--;
        }
        j--;
      }
      if (c == 'D') j++;
      if (j > r) f = false;
    }
    if (rem < 0) f = false;
    if (f and rem == 0) chmin(res, (r - l) * (u - d + 1));
  }
  if (r > 0) {
    int rem = 1;
    int j = 0;
    bool f = true;
    for (auto &c : s) {
      if (c == 'A') j--;
      if (c == 'D') {
        if (j == r - 1) {
          j--;
          if (j < l) f = false;
          rem--;
        }
        j++;
      }
      if (j < l) f = false;
    }
    if (rem < 0) f = false;
    if (f and rem == 0) chmin(res, (r - l) * (u - d + 1));
  }
  if (d < 0) {
    int rem = 1;
    int i = 0;
    bool f = true;
    for (auto &c : s) {
      if (c == 'S') {
        if (i == d + 1) {
          i++;
          if (i > u) f = false;
          rem--;
        }
        i--;
      }
      if (c == 'W') i++;
      if (i > u) f = false;
    }
    if (rem < 0) f = false;
    if (f and rem == 0) chmin(res, (r - l + 1) * (u - d));
  }
  if (u > 0) {
    int rem = 1;
    int i = 0;
    bool f = true;
    for (auto &c : s) {
      if (c == 'S') i--;
      if (c == 'W') {
        if (i == u - 1) {
          i--;
          if (i < d) f = false;
          rem--;
        }
        i++;
      }
      if (i < d) f = false;
    }
    if (rem < 0) f = false;
    if (f and rem == 0) chmin(res, (r - l + 1) * (u - d));
  }
  cout << res << endl;
}
signed main() {
  int q;
  cin >> q;
  while (q--) solve();
  return 0;
}
