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;
template <typename T>
void no(T s) {
  cout << s;
  exit(0);
}
void no() {
  cout << "NO";
  exit(0);
}
const int maxn = 240000;
char s[maxn];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cout << fixed << setprecision(20);
  int T;
  for (cin >> T; T; T -= 1) {
    cin >> s;
    int cw = 0, cd = 0;
    int ma = 0, md = 0, mw = 0, ms = 0;
    int sa = 0, sd = 0, sw = 0, ss = 0;
    for (int i = 0; s[i]; i += 1) {
      if (s[i] == 'W') cw += 1;
      if (s[i] == 'S') cw -= 1;
      if (s[i] == 'D') cd += 1;
      if (s[i] == 'A') cd -= 1;
      mw = max(mw, cw);
      ms = min(ms, cw);
      md = max(md, cd);
      ma = min(ma, cd);
      sw = max(sw, cw - ms);
      ss = max(ss, mw - cw);
      sd = max(sd, cd - ma);
      sa = max(sa, md - cd);
    }
    LL x[2], y[2];
    x[0] = max(sw, ss);
    x[1] = max(LL(sw or ss), x[0] - !(sw == ss));
    y[0] = max(sd, sa);
    y[1] = max(LL(sd or sa), y[0] - !(sd == sa));
    LL ans = min((x[0] + 1) * (y[1] + 1), (x[1] + 1) * (y[0] + 1));
    cout << ans << "\n";
  }
  return 0;
}
