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;
long long solve(string t, long long k) {
  long long x = 0, y = 0;
  long long w = 0, a = 0, s = 0, d = 0;
  long long cw = -1, ca = -1, cs = -1, cd = -1, cnt = -1;
  for (auto& i : t) {
    ++cnt;
    if (i == 'W') {
      --x;
    }
    if (i == 'S') {
      ++x;
    }
    if (i == 'A') {
      --y;
    }
    if (i == 'D') {
      ++y;
    }
    if (w > x) {
      w = x;
      cw = cnt;
    }
    if (s < x) {
      s = x;
      cs = cnt;
    }
    if (a > y) {
      a = y;
      ca = cnt;
    }
    if (d < y) {
      d = y;
      cd = cnt;
    }
  }
  if (!k) return ((s - w + 1) * (d - a + 1));
  string s1 = "", s2 = "", s3 = "", s4 = "";
  for (long long i = 0; i < t.length(); ++i) {
    if (i == cw) {
      s1 += "S";
    }
    if (i == ca) {
      s2 += "D";
    }
    if (i == cd) {
      s3 += "A";
    }
    if (i == cs) {
      s4 += "W";
    }
    s1 += t[i];
    s2 += t[i];
    s3 += t[i];
    s4 += t[i];
  }
  long long sol = solve(t, 0);
  sol = min(sol, solve(s1, 0));
  sol = min(sol, solve(s2, 0));
  sol = min(sol, solve(s3, 0));
  sol = min(sol, solve(s4, 0));
  return sol;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cerr.tie(nullptr);
  long long m;
  cin >> m;
  for (long long e = 0; e < m; ++e) {
    string t;
    cin >> t;
    long long sol = solve(t, 1);
    cout << sol << '\n';
  }
}
