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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    string s;
    cin >> s;
    int n = s.size() + 3;
    int sufmnx[n], sufmxx[n], sufmny[n], sufmxy[n], ax[n], ay[n];
    int cntx = 0, cnty = 0;
    ax[0] = ay[0] = sufmnx[0] = sufmxx[0] = sufmny[0] = sufmxy[0] = 0;
    for (int i = 0; i < s.size(); ++i) {
      if (s[i] == 'W')
        --cntx;
      else if (s[i] == 'S')
        ++cntx;
      else if (s[i] == 'D')
        ++cnty;
      else
        --cnty;
      sufmnx[i + 1] = sufmxx[i + 1] = ax[i + 1] = cntx;
      sufmny[i + 1] = sufmxy[i + 1] = ay[i + 1] = cnty;
    }
    for (int i = s.size() - 1; i >= 0; --i) {
      sufmnx[i] = min(sufmnx[i], sufmnx[i + 1]);
      sufmxx[i] = max(sufmxx[i], sufmxx[i + 1]);
      sufmny[i] = min(sufmny[i], sufmny[i + 1]);
      sufmxy[i] = max(sufmxy[i], sufmxy[i + 1]);
    }
    long long ans =
        1LL * (sufmxx[0] - sufmnx[0] + 1) * (sufmxy[0] - sufmny[0] + 1);
    if (sufmxx[0] - sufmnx[0] > 1) {
      for (int i = 1; i <= s.size(); ++i) {
        if (ax[i] == sufmnx[0] && sufmnx[0] != 0) {
          if (sufmxx[i] != sufmxx[0])
            ans = min(ans, 1LL * (sufmxx[0] - sufmnx[0]) *
                               (sufmxy[0] - sufmny[0] + 1));
          break;
        }
      }
      for (int i = 1; i <= s.size(); ++i) {
        if (ax[i] == sufmxx[0] && sufmxx[0] != 0) {
          if (sufmnx[i] != sufmnx[0])
            ans = min(ans, 1LL * (sufmxx[0] - sufmnx[0]) *
                               (sufmxy[0] - sufmny[0] + 1));
          break;
        }
      }
    }
    if (sufmxy[0] - sufmny[0] > 1) {
      for (int i = 1; i <= s.size(); ++i) {
        if (ay[i] == sufmny[0] && sufmny[0] != 0) {
          if (sufmxy[i] != sufmxy[0])
            ans = min(ans, 1LL * (sufmxx[0] - sufmnx[0] + 1) *
                               (sufmxy[0] - sufmny[0]));
          break;
        }
      }
      for (int i = 1; i <= s.size(); ++i) {
        if (ay[i] == sufmxy[0] && sufmxy[0] != 0) {
          if (sufmny[i] != sufmny[0])
            ans = min(ans, 1LL * (sufmxx[0] - sufmnx[0] + 1) *
                               (sufmxy[0] - sufmny[0]));
          break;
        }
      }
    }
    cout << ans << '\n';
  }
}
