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;
const int maxn = 40000;
char s[200020];
int main() {
  int t;
  cin >> t;
  while (t--) {
    cin >> s;
    int l = 0, r = 0, lmax = 0, lmin = 0, rmin = 0, rmax = 0, lmaxlen = 0,
        lminlen = 0, rminlen = 0, rmaxlen = 0;
    int n = strlen(s);
    for (int i = 0; i < n; i++) {
      if (s[i] == 'W') {
        l++;
        lmax = max(lmax, l);
      } else if (s[i] == 'S') {
        l--;
        lmin = min(lmin, l);
      } else if (s[i] == 'D') {
        r++;
        rmax = max(rmax, r);
      } else {
        r--;
        rmin = min(rmin, r);
      }
      lmaxlen = max(lmaxlen, lmax - l);
      lminlen = max(lminlen, l - lmin);
      rmaxlen = max(rmaxlen, rmax - r);
      rminlen = max(rminlen, r - rmin);
    }
    long long ans = 1ll * (lmax - lmin + 1) * (rmax - rmin + 1);
    if (lmax - lmin > 1 && lmaxlen != lminlen) {
      ans = min(ans, 1ll * (lmax - lmin) * (rmax - rmin + 1));
    }
    if (rmax - rmin > 1 && rmaxlen != rminlen) {
      ans = min(ans, 1ll * (lmax - lmin + 1) * (rmax - rmin));
    }
    cout << ans << endl;
  }
}
