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 t;
char a[200010];
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%s", a);
    int le = 0, ri = 0, up = 0, dw = 0, len = strlen(a), x = 0, y = 0;
    int fle = 0, fri = 0, fup = 0, fdw = 0;
    for (int i = 0; i < len; i++) {
      if (a[i] == 'W') {
        if (++y > up)
          up = y, fdw = 0, fup = 1;
        else if (y == up)
          fup = 1;
      }
      if (a[i] == 'A') {
        if (--x < le)
          le = x, fri = 0, fle = 1;
        else if (x == le)
          fle = 1;
      }
      if (a[i] == 'S') {
        if (--y < dw)
          dw = y, fup = 0, fdw = 1;
        else if (y == dw)
          fdw = 1;
      }
      if (a[i] == 'D') {
        if (++x > ri)
          ri = x, fle = 0, fri = 1;
        else if (x == ri)
          fri = 1;
      }
    }
    x = ri - le + 1, y = up - dw + 1;
    long long s = 1LL * x * y, k = s;
    if (x > 2 && fle * fri == 0) s = k - y;
    if (y > 2 && fup * fdw == 0 && k - x < s) s = k - x;
    printf("%lld\n", s);
  }
}
