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;
vector<long long> v[2];
long long get(long long a, long long b) { return (a + b != 0); }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  string s;
  long long ans, x, y, a, b, c, d;
  long long minx, maxx, miny, maxy, maxl, maxr, maxu, maxd;
  while (t--) {
    cin >> s;
    x = 0;
    y = 0;
    minx = 0;
    maxx = 0;
    miny = 0;
    maxy = 0;
    maxl = 0;
    maxr = 0;
    maxu = 0;
    maxd = 0;
    for (auto it : s) {
      if (it == 'W') y++;
      if (it == 'S') y--;
      if (it == 'A') x--;
      if (it == 'D') x++;
      maxx = max(maxx, x);
      minx = min(minx, x);
      maxy = max(maxy, y);
      miny = min(miny, y);
      maxu = max(maxu, y - miny);
      maxd = max(maxd, maxy - y);
      maxr = max(maxr, x - minx);
      maxl = max(maxl, maxx - x);
    }
    a = max(maxl, maxr);
    b = max(get(maxl, maxr), a - (maxl != maxr));
    c = max(maxu, maxd);
    d = max(get(maxu, maxd), c - (maxu != maxd));
    a++;
    b++;
    c++;
    d++;
    ans = min(a * d, b * c);
    cout << ans << "\n";
  }
  return 0;
}
