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;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return x * f;
}
const int N = 2e5 + 7;
int T, U, D, L, R;
long long ans;
char s[N];
int main() {
  T = read();
  while (T--) {
    scanf("%s", s);
    int n = strlen(s);
    int x = 0, y = 0;
    U = D = L = R = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] == 'W') y++;
      if (s[i] == 'S') y--;
      if (s[i] == 'A') x--;
      if (s[i] == 'D') x++;
      R = max(R, x);
      L = min(L, x);
      U = max(U, y);
      D = min(D, y);
    }
    ans = 1ll * (R - L + 1) * (U - D + 1);
    x = y = 0;
    bool flag = 0, GG = 0;
    int l = 0, r = 0, u = 0, d = 0;
    for (int i = 0; i < n; i++) {
      if (U - D <= 1 || !D) {
        GG = 1;
        break;
      }
      if (s[i] == 'W') y++;
      if (s[i] == 'S') y--;
      if (s[i] == 'A') x--;
      if (s[i] == 'D') x++;
      if (y == D && !flag) {
        y++;
        flag = 1;
      }
      r = max(r, x);
      l = min(l, x);
      u = max(u, y);
      d = min(d, y);
      if (y <= D || y > U || x < L || x > R) {
        GG = 1;
        break;
      }
    }
    if (!GG) ans = min(ans, 1ll * (r - l + 1) * (u - d + 1));
    x = y = flag = l = r = u = d = GG = 0;
    for (int i = 0; i < n; i++) {
      if (U - D <= 1 || !U) {
        GG = 1;
        break;
      }
      if (s[i] == 'W') y++;
      if (s[i] == 'S') y--;
      if (s[i] == 'A') x--;
      if (s[i] == 'D') x++;
      if (y == U && !flag) {
        y--;
        flag = 1;
      }
      r = max(r, x);
      l = min(l, x);
      u = max(u, y);
      d = min(d, y);
      if (y >= U || y < D || x < L || x > R) {
        GG = 1;
        break;
      }
    }
    if (!GG) ans = min(ans, 1ll * (r - l + 1) * (u - d + 1));
    x = y = flag = l = r = u = d = GG = 0;
    for (int i = 0; i < n; i++) {
      if (R - L <= 1 || !R) {
        GG = 1;
        break;
      }
      if (s[i] == 'W') y++;
      if (s[i] == 'S') y--;
      if (s[i] == 'A') x--;
      if (s[i] == 'D') x++;
      if (x == R && !flag) {
        x--;
        flag = 1;
      }
      r = max(r, x);
      l = min(l, x);
      u = max(u, y);
      d = min(d, y);
      if (y > U || y < D || x < L || x >= R) {
        GG = 1;
        break;
      }
    }
    if (!GG) ans = min(ans, 1ll * (r - l + 1) * (u - d + 1));
    x = y = flag = l = r = u = d = GG = 0;
    for (int i = 0; i < n; i++) {
      if (R - L <= 1 || !L) {
        GG = 1;
        break;
      }
      if (s[i] == 'W') y++;
      if (s[i] == 'S') y--;
      if (s[i] == 'A') x--;
      if (s[i] == 'D') x++;
      if (x == L && !flag) {
        x++;
        flag = 1;
      }
      r = max(r, x);
      l = min(l, x);
      u = max(u, y);
      d = min(d, y);
      if (y > U || y < D || x <= L || x > R) {
        GG = 1;
        break;
      }
    }
    if (!GG) ans = min(ans, 1ll * (r - l + 1) * (u - d + 1));
    printf("%lld\n", ans);
  }
  return 0;
}
