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;
int main(void) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    string inp;
    cin >> inp;
    long long n = inp.size();
    long long prex[n + 1], prey[n + 1];
    long long prexmn[n + 1], prexmx[n + 1], preymn[n + 1], preymx[n + 1];
    prex[0] = 0;
    prey[0] = 0;
    prexmn[0] = 0;
    prexmx[0] = 0;
    preymn[0] = 0;
    preymx[0] = 0;
    long long sufx[n + 1], sufy[n + 1];
    long long sufxmn[n + 1], sufxmx[n + 1], sufymn[n + 1], sufymx[n + 1];
    sufx[n] = 0;
    sufy[n] = 0;
    sufxmn[n] = 0;
    sufxmx[n] = 0;
    sufymn[n] = 0;
    sufymx[n] = 0;
    for (long long int i = 0; i < n; i++) {
      if (inp[i] == 'W') {
        prex[i + 1] = prex[i];
        prey[i + 1] = prey[i] + 1;
      }
      if (inp[i] == 'S') {
        prex[i + 1] = prex[i];
        prey[i + 1] = prey[i] - 1;
      }
      if (inp[i] == 'A') {
        prex[i + 1] = prex[i] - 1;
        prey[i + 1] = prey[i];
      }
      if (inp[i] == 'D') {
        prex[i + 1] = prex[i] + 1;
        prey[i + 1] = prey[i];
      }
      prexmn[i + 1] = min(prexmn[i], prex[i + 1]);
      prexmx[i + 1] = max(prexmx[i], prex[i + 1]);
      preymn[i + 1] = min(preymn[i], prey[i + 1]);
      preymx[i + 1] = max(preymx[i], prey[i + 1]);
    }
    for (long long i = n - 1; i >= 0; i--) {
      if (inp[i] == 'W') {
        sufx[i] = sufx[i + 1];
        sufy[i] = sufy[i + 1] - 1;
      }
      if (inp[i] == 'S') {
        sufx[i] = sufx[i + 1];
        sufy[i] = sufy[i + 1] + 1;
      }
      if (inp[i] == 'A') {
        sufx[i] = sufx[i + 1] + 1;
        sufy[i] = sufy[i + 1];
      }
      if (inp[i] == 'D') {
        sufx[i] = sufx[i + 1] - 1;
        sufy[i] = sufy[i + 1];
      }
      sufxmn[i] = min(sufxmn[i + 1], sufx[i]);
      sufxmx[i] = max(sufxmx[i + 1], sufx[i]);
      sufymn[i] = min(sufymn[i + 1], sufy[i]);
      sufymx[i] = max(sufymx[i + 1], sufy[i]);
    }
    long long ans = (prexmx[n] - prexmn[n] + 1) * (preymx[n] - preymn[n] + 1);
    for (long long int i = 0; i < n + 1; i++) {
      long long currx = prex[i];
      long long curry = prey[i];
      long long tmpx = currx + 1, tmpy = curry, mnx = min(prexmn[i], tmpx),
                mxx = max(prexmx[i], tmpx), mny = min(preymn[i], tmpy),
                mxy = max(preymx[i], tmpy);
      long long tmp2x = tmpx - sufx[i];
      long long tmp2y = tmpy - sufy[i];
      long long xmn = min(mnx, tmp2x + sufxmn[i]);
      long long xmx = max(mxx, tmp2x + sufxmx[i]);
      long long ymn = min(mny, tmp2y + sufymn[i]);
      long long ymx = max(mxy, tmp2y + sufymx[i]);
      ans = min(ans, (xmx - xmn + 1) * (ymx - ymn + 1));
      tmpx = currx - 1, tmpy = curry, mnx = min(prexmn[i], tmpx),
      mxx = max(prexmx[i], tmpx), mny = min(preymn[i], tmpy),
      mxy = max(preymx[i], tmpy);
      tmp2x = tmpx - sufx[i];
      tmp2y = tmpy - sufy[i];
      xmn = min(mnx, tmp2x + sufxmn[i]);
      xmx = max(mxx, tmp2x + sufxmx[i]);
      ymn = min(mny, tmp2y + sufymn[i]);
      ymx = max(mxy, tmp2y + sufymx[i]);
      ans = min(ans, (xmx - xmn + 1) * (ymx - ymn + 1));
      tmpx = currx, tmpy = curry + 1, mnx = min(prexmn[i], tmpx),
      mxx = max(prexmx[i], tmpx), mny = min(preymn[i], tmpy),
      mxy = max(preymx[i], tmpy);
      tmp2x = tmpx - sufx[i];
      tmp2y = tmpy - sufy[i];
      xmn = min(mnx, tmp2x + sufxmn[i]);
      xmx = max(mxx, tmp2x + sufxmx[i]);
      ymn = min(mny, tmp2y + sufymn[i]);
      ymx = max(mxy, tmp2y + sufymx[i]);
      ans = min(ans, (xmx - xmn + 1) * (ymx - ymn + 1));
      tmpx = currx, tmpy = curry - 1, mnx = min(prexmn[i], tmpx),
      mxx = max(prexmx[i], tmpx), mny = min(preymn[i], tmpy),
      mxy = max(preymx[i], tmpy);
      tmp2x = tmpx - sufx[i];
      tmp2y = tmpy - sufy[i];
      xmn = min(mnx, tmp2x + sufxmn[i]);
      xmx = max(mxx, tmp2x + sufxmx[i]);
      ymn = min(mny, tmp2y + sufymn[i]);
      ymx = max(mxy, tmp2y + sufymx[i]);
      ans = min(ans, (xmx - xmn + 1) * (ymx - ymn + 1));
    }
    cout << ans << '\n';
  }
  return 0;
}
