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 $s = \text{DSAWWAW}$ then $Grid(s)$ is the $4 \times 3$ grid:  you can place the robot in the cell $(3, 2)$;  the robot performs the command 'D' and moves to $(3, 3)$;  the robot performs the command 'S' and moves to $(4, 3)$;  the robot performs the command 'A' and moves to $(4, 2)$;  the robot performs the command 'W' and moves to $(3, 2)$;  the robot performs the command 'W' and moves to $(2, 2)$;  the robot performs the command 'A' and moves to $(2, 1)$;  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 $T$ ($1 \le T \le 1000$) — the number of queries.

Next $T$ lines contain queries: one per line. This line contains single string $s$ ($1 \le |s| \le 2 \cdot 10^5$, $s_i \in \{\text{W}, \text{A}, \text{S}, \text{D}\}$) — the sequence of commands.

It's guaranteed that the total length of $s$ over all queries doesn't exceed $2 \cdot 10^5$.


-----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 $\text{DSAWW}\underline{D}\text{AW}$.

In second and third queries you can not decrease the area of $Grid(s)$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "def read_int():\n    return int(input())\n\n\ndef read_ints():\n    return list(map(int, input().split(' ')))\n\n\nt = read_int()\nINF = int(1e7)\nfor case_num in range(t):\n    s = input()\n    x = 0\n    y = 0\n    xlist = [0]\n    ylist = [0]\n    for c in s:\n        if c == 'W':\n            y += 1\n        elif c == 'S':\n            y -= 1\n        elif c == 'A':\n            x -= 1\n        else:\n            x += 1\n        xlist.append(x)\n        ylist.append(y)\n    n = len(s)\n    l = [0]\n    r = [0]\n    u = [0]\n    d = [0]\n    for i in range(1, n + 1):\n        l.append(min(l[-1], xlist[i]))\n        r.append(max(r[-1], xlist[i]))\n        u.append(max(u[-1], ylist[i]))\n        d.append(min(d[-1], ylist[i]))\n    lr = [xlist[n]]\n    rr = [xlist[n]]\n    ur = [ylist[n]]\n    dr = [ylist[n]]\n    for i in range(1, n + 1):\n        lr.append(min(lr[-1], xlist[n - i]))\n        rr.append(max(rr[-1], xlist[n - i]))\n        ur.append(max(ur[-1], ylist[n - i]))\n        dr.append(min(dr[-1], ylist[n - i]))\n    ans = INF * INF\n    coeff = [[-1, 0], [1, 0], [0, -1], [0, 1]]\n    for k in range(4):\n        for i in range(n):\n            nl = min(l[i], lr[n - i] + coeff[k][0])\n            nr = max(r[i], rr[n - i] + coeff[k][0])\n            nu = max(u[i], ur[n - i] + coeff[k][1])\n            nd = min(d[i], dr[n - i] + coeff[k][1])\n            area = (nr - nl + 1) * (nu - nd + 1)\n            ans = min(ans, area)\n    print(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14997