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;
string s1, s2, s3, s4, s;
long long n, i, q, MAXX, MINX, MAXY, MINY, j, x, y, RES, l, xa, xb, ya, yb;
int main() {
  cin >> n;
  for (q = 1; q <= n; q++) {
    MAXX = 0;
    MINX = 0;
    MAXY = 0;
    MINY = 0;
    x = 0;
    y = 0;
    xa = xb = ya = yb = 0;
    RES = INT_MAX;
    cin >> s;
    s1 = s2 = s3 = s4 = s;
    l = 0;
    for (i = 0; i <= s.length() - 1; i++) {
      if (s[i] == 'A') x -= 1;
      if (MINX > x) {
        MINX = x;
        xa = i;
      }
      if (s[i] == 'D') x += 1;
      if (MAXX < x) {
        MAXX = x;
        xb = i;
      }
      if (s[i] == 'W') y += 1;
      if (MAXY < y) {
        MAXY = y;
        yb = i;
      }
      if (s[i] == 'S') y -= 1;
      if (MINY > y) {
        MINY = y;
        ya = i;
      }
    }
    RES = (MAXX - MINX + 1) * (MAXY - MINY + 1);
    s1.insert(s1.begin() + xa, 'D');
    s2.insert(s2.begin() + xb, 'A');
    s3.insert(s3.begin() + ya, 'W');
    s4.insert(s4.begin() + yb, 'S');
    x = 0;
    y = 0;
    MAXX = -0;
    MINX = 0;
    MAXY = -0;
    MINY = 0;
    for (i = 0; i <= s1.length() - 1; i++) {
      if (s1[i] == 'A') x -= 1;
      if (MINX > x) MINX = x;
      if (s1[i] == 'D') x += 1;
      if (MAXX < x) MAXX = x;
      if (s1[i] == 'W') y += 1;
      if (MAXY < y) MAXY = y;
      if (s1[i] == 'S') y -= 1;
      if (MINY > y) MINY = y;
    }
    if (((MAXX - MINX + 1) * (MAXY - MINY + 1)) < RES)
      RES = (MAXX - MINX + 1) * (MAXY - MINY + 1);
    x = 0;
    y = 0;
    MAXX = -0;
    MINX = 0;
    MAXY = -0;
    MINY = 0;
    for (i = 0; i <= s2.length() - 1; i++) {
      if (s2[i] == 'A') x -= 1;
      if (MINX > x) MINX = x;
      if (s2[i] == 'D') x += 1;
      if (MAXX < x) MAXX = x;
      if (s2[i] == 'W') y += 1;
      if (MAXY < y) MAXY = y;
      if (s2[i] == 'S') y -= 1;
      if (MINY > y) MINY = y;
    }
    if (((MAXX - MINX + 1) * (MAXY - MINY + 1)) < RES)
      RES = (MAXX - MINX + 1) * (MAXY - MINY + 1);
    x = 0;
    y = 0;
    MAXX = -0;
    MINX = 0;
    MAXY = -0;
    MINY = 0;
    for (i = 0; i <= s3.length() - 1; i++) {
      if (s3[i] == 'A') x -= 1;
      if (MINX > x) MINX = x;
      if (s3[i] == 'D') x += 1;
      if (MAXX < x) MAXX = x;
      if (s3[i] == 'W') y += 1;
      if (MAXY < y) MAXY = y;
      if (s3[i] == 'S') y -= 1;
      if (MINY > y) MINY = y;
    }
    if (((MAXX - MINX + 1) * (MAXY - MINY + 1)) < RES)
      RES = (MAXX - MINX + 1) * (MAXY - MINY + 1);
    x = 0;
    y = 0;
    MAXX = -0;
    MINX = 0;
    MAXY = -0;
    MINY = 0;
    for (i = 0; i <= s4.length() - 1; i++) {
      if (s4[i] == 'A') x -= 1;
      if (MINX > x) MINX = x;
      if (s4[i] == 'D') x += 1;
      if (MAXX < x) MAXX = x;
      if (s4[i] == 'W') y += 1;
      if (MAXY < y) MAXY = y;
      if (s4[i] == 'S') y -= 1;
      if (MINY > y) MINY = y;
    }
    if (((MAXX - MINX + 1) * (MAXY - MINY + 1)) < RES)
      RES = (MAXX - MINX + 1) * (MAXY - MINY + 1);
    cout << RES << endl;
  }
  return 0;
}
