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>
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
using namespace std;
const long long __BS = 4096;
static char __bur[__BS + 16], *__er = __bur + __BS, *__ir = __er;
template <class T = long long>
T readInt() {
  auto c = [&]() {
    if (__ir == __er)
      std::fill(__bur, __bur + __BS, 0), cin.read(__bur, __BS), __ir = __bur;
  };
  c();
  while (*__ir && (*__ir < '0' || *__ir > '9') && *__ir != '-') ++__ir;
  c();
  bool m = false;
  if (*__ir == '-') ++__ir, c(), m = true;
  T r = 0;
  while (*__ir >= '0' && *__ir <= '9') r = r * 10 + *__ir - '0', ++__ir, c();
  ++__ir;
  return m ? -r : r;
}
long long t;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> t;
  for (long long _i = 0; _i < t; _i++) {
    string s;
    cin >> s;
    long long mx = 0, _mx = 0, my = 0, _my = 0;
    long long first = 0, second = 0;
    for (long long j = 0; j < s.size(); j++) {
      if (s[j] == 'S') --second;
      if (s[j] == 'W') ++second;
      if (s[j] == 'A') --first;
      if (s[j] == 'D') ++first;
      mx = max(mx, first);
      _mx = min(_mx, first);
      my = max(my, second);
      _my = min(_my, second);
    }
    first = 0;
    second = 0;
    long long ca = (mx - _mx + 1) * (my - _my + 1);
    long long mrx = -1, mry = -1, _mrx = -1, _mry = -1;
    for (long long j = 0; j < s.size(); j++) {
      if (first == mx) mrx = j;
      if (second == my) mry = j;
      if (first == _mx) _mrx = j;
      if (second == _my) _mry = j;
      if (s[j] == 'S') --second;
      if (s[j] == 'W') ++second;
      if (s[j] == 'A') --first;
      if (s[j] == 'D') ++first;
    }
    if (first == mx) mrx = s.size();
    if (second == my) mry = s.size();
    if (first == _mx) _mrx = s.size();
    if (second == _my) _mry = s.size();
    first = 0;
    second = 0;
    bool f1 = 0, f2 = 0, f3 = 0, f4 = 0;
    f1 = (mx == 0);
    f2 = (_mx == 0);
    f3 = (my == 0);
    f4 = (_my == 0);
    for (long long j = 0; j < s.size(); j++) {
      if (s[j] == 'S') --second;
      if (s[j] == 'W') ++second;
      if (s[j] == 'A') --first;
      if (s[j] == 'D') ++first;
      if (first == mx && !f1) {
        f1 = 1;
        if (_mrx <= j - 1) ca = min(ca, (mx - _mx) * (my - _my + 1));
      }
      if (first == _mx && !f2) {
        f2 = 1;
        if (mrx <= j - 1) ca = min(ca, (mx - _mx) * (my - _my + 1));
      }
      if (second == my && !f3) {
        f3 = 1;
        if (_mry <= j - 1) ca = min(ca, (mx - _mx + 1) * (my - _my));
      }
      if (second == _my && !f4) {
        f4 = 1;
        if (mry <= j - 1) ca = min(ca, (mx - _mx + 1) * (my - _my));
      }
    }
    cout << ca << '\n';
  }
  return 0;
}
