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;
using ld = long double;
constexpr ll inf = 0x3FFFFFFFF;
struct res {
  ll l = 0;
  ll r = 0;
  ll d = 0;
  ll u = 0;
  ll lastl = 0;
  ll lastr = 0;
  ll lastd = 0;
  ll lastu = 0;
  ll get() { return (r + 1 - l) * (u + 1 - d); }
};
res calc(const string& s) {
  ll x = 0;
  ll y = 0;
  res r;
  for (ll i = 0; i < (int)(s).size(); i++) {
    char c = s[i];
    if (c == 'W') y++;
    if (c == 'S') y--;
    if (c == 'A') x--;
    if (c == 'D') x++;
    if (x > r.r) {
      r.r = x;
      r.lastr = i;
    }
    if (x < r.l) {
      r.l = x;
      r.lastl = i;
    }
    if (y > r.u) {
      r.u = y;
      r.lastu = i;
    }
    if (y < r.d) {
      r.d = y;
      r.lastd = i;
    }
  }
  return r;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ll n;
  cin >> n;
  for (ll i = 0; i < n; i++) {
    string s;
    cin >> s;
    res r = calc(s);
    ll out = r.get();
    string a, b, c, d;
    for (ll i = 0; i < (int)(s).size(); i++) {
      if (i == r.lastl) a += 'D';
      if (i == r.lastr) b += 'A';
      if (i == r.lastu) c += 'S';
      if (i == r.lastd) d += 'W';
      a += s[i];
      b += s[i];
      c += s[i];
      d += s[i];
    }
    for (const string& x : {a, b, c, d}) {
      res c = calc(x);
      out = min(out, c.get());
    }
    cout << out << endl;
  }
}
