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;
string s;
long long int t, qwertyuiop[200005], ad[200005], wslmin, wsrmin, wslmax, wsrmax,
    adlmin, adlmax, adrmin, adrmax, ans;
int main() {
  cin >> t;
  while (t--) {
    cin >> s;
    wslmin = wsrmin = adlmin = adrmin = 0;
    wslmax = wsrmax = adlmax = adrmax = 0;
    for (int i = 1; i <= s.size(); i++) {
      if (s[i - 1] == 'W') {
        qwertyuiop[i] = qwertyuiop[i - 1] + 1;
        ad[i] = ad[i - 1];
        if (qwertyuiop[wslmin] > qwertyuiop[i]) wslmin = i;
        if (qwertyuiop[wslmax] < qwertyuiop[i]) wslmax = i;
        if (qwertyuiop[wsrmin] >= qwertyuiop[i]) wsrmin = i;
        if (qwertyuiop[wsrmax] <= qwertyuiop[i]) wsrmax = i;
      }
      if (s[i - 1] == 'A') {
        ad[i] = ad[i - 1] - 1;
        qwertyuiop[i] = qwertyuiop[i - 1];
        if (ad[adlmin] > ad[i]) adlmin = i;
        if (ad[adlmax] < ad[i]) adlmax = i;
        if (ad[adrmin] >= ad[i]) adrmin = i;
        if (ad[adrmax] <= ad[i]) adrmax = i;
      }
      if (s[i - 1] == 'S') {
        qwertyuiop[i] = qwertyuiop[i - 1] - 1;
        ad[i] = ad[i - 1];
        if (qwertyuiop[wslmin] > qwertyuiop[i]) wslmin = i;
        if (qwertyuiop[wslmax] < qwertyuiop[i]) wslmax = i;
        if (qwertyuiop[wsrmin] >= qwertyuiop[i]) wsrmin = i;
        if (qwertyuiop[wsrmax] <= qwertyuiop[i]) wsrmax = i;
      }
      if (s[i - 1] == 'D') {
        ad[i] = ad[i - 1] + 1;
        qwertyuiop[i] = qwertyuiop[i - 1];
        if (ad[adlmin] > ad[i]) adlmin = i;
        if (ad[adlmax] < ad[i]) adlmax = i;
        if (ad[adrmin] >= ad[i]) adrmin = i;
        if (ad[adrmax] <= ad[i]) adrmax = i;
      }
    }
    ans = (qwertyuiop[wsrmax] - qwertyuiop[wslmin] + 1) *
          (ad[adrmax] - ad[adlmin] + 1);
    if ((wslmax > wsrmin or wslmin > wsrmax) and
        qwertyuiop[wsrmax] - qwertyuiop[wslmin] > 1) {
      ans = min(ans, (qwertyuiop[wsrmax] - qwertyuiop[wslmin]) *
                         (ad[adrmax] - ad[adlmin] + 1));
    }
    if ((adlmax > adrmin or adlmin > adrmax) and ad[adrmax] - ad[adlmin] > 1) {
      ans = min(ans, (qwertyuiop[wsrmax] - qwertyuiop[wslmin] + 1) *
                         (ad[adrmax] - ad[adlmin]));
    }
    cout << ans << endl;
  }
}
