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;
pair<int, int> get_length(vector<int> &arr) {
  vector<int> prefix;
  prefix.push_back(0);
  for (int i = 0; i < arr.size(); i++) {
    prefix.push_back(prefix[prefix.size() - 1] + arr[i]);
  }
  int first_min = 0, last_max = 0;
  for (int i = 0; i < prefix.size(); i++) {
    if (prefix[i] < prefix[first_min]) first_min = i;
    if (prefix[i] >= prefix[last_max]) last_max = i;
  }
  int length = prefix[last_max] - prefix[first_min] + 1;
  pair<int, int> p;
  p.first = length;
  if (last_max < first_min && length > 2) {
    length--;
  } else {
    for (int i = 0; i < prefix.size(); i++) prefix[i] = -prefix[i];
    first_min = 0, last_max = 0;
    for (int i = 0; i < prefix.size(); i++) {
      if (prefix[i] < prefix[first_min]) first_min = i;
      if (prefix[i] >= prefix[last_max]) last_max = i;
    }
    if (last_max < first_min && prefix[last_max] - prefix[first_min] + 1 > 2)
      length--;
  }
  p.second = length;
  return p;
}
int main() {
  int test;
  cin >> test;
  for (int t = 1; t <= test; t++) {
    string s;
    cin >> s;
    vector<int> WS;
    vector<int> AD;
    for (int i = 0; i < s.length(); i++) {
      if (s[i] == 'W')
        WS.push_back(1);
      else if (s[i] == 'S')
        WS.push_back(-1);
      else if (s[i] == 'A')
        AD.push_back(1);
      else
        AD.push_back(-1);
    }
    pair<int, int> heights = get_length(WS);
    pair<int, int> widths = get_length(AD);
    cout << min((long long int)heights.first * (long long int)widths.second,
                (long long int)heights.second * (long long int)widths.first)
         << endl;
  }
  return 0;
}
