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<int> max_(2), min_(2);
vector<vector<int>> in_(2);
long long preob(bool st) {
  int x = 1;
  if (st == true) {
    x = 0;
  }
  bool st1 = false, st2 = true;
  auto it = in_[x].begin();
  for (int i = 0; i < in_[x].size(); ++i, it++) {
    if (*it == max_[x]) {
      st1 = true;
      if (i == 0) {
      } else {
        it--;
        if (min_[x] > *it - 1) {
          st2 = false;
        }
        it++;
      }
    }
    if (*it == min_[x] && st1 == true) {
      st2 = false;
    }
  }
  if (st2) {
    return abs(min_[x]) + max_[x];
  }
  st1 = false, st2 = true;
  it = in_[x].begin();
  for (int i = 0; i < in_[x].size(); ++i, it++) {
    if ((*it) == min_[x]) {
      st1 = true;
      if (i == 0) {
      } else {
        it--;
        if (max_[x] < *it + 1) {
          st2 = false;
        }
        it++;
      }
    }
    if ((*it) == max_[x] && st1 == true) {
      st2 = false;
    }
  }
  if (st2) {
    return abs(min_[x]) + max_[x];
  } else {
    return abs(min_[x]) + max_[x] + 1;
  }
}
void solve() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string in_s;
  cin >> in_s;
  int coun_1 = 0, coun_2 = 0;
  max_ = {0, 0};
  min_ = {0, 0};
  in_[0].clear();
  in_[1].clear();
  in_[0].push_back(0);
  in_[1].push_back(0);
  for (int i = 0; i < in_s.size(); ++i) {
    if (in_s[i] == 'W') {
      coun_1++;
      in_[0].push_back(coun_1);
    }
    if (in_s[i] == 'S') {
      coun_1--;
      in_[0].push_back(coun_1);
    }
    if (in_s[i] == 'D') {
      coun_2++;
      in_[1].push_back(coun_2);
    }
    if (in_s[i] == 'A') {
      coun_2--;
      in_[1].push_back(coun_2);
    }
    max_[0] = max(coun_1, max_[0]);
    max_[1] = max(coun_2, max_[1]);
    min_[0] = min(coun_1, min_[0]);
    min_[1] = min(coun_2, min_[1]);
  }
  long long a = max_[0] + abs(min_[0]) + 1;
  long long b = max_[1] + abs(min_[1]) + 1;
  cout << min(a * preob(false), b * preob(true)) << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}
