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 = "\nfor i in range(int(input())):\n\ts = input()\n\tlm, rm, um, dm = 0, 0, 0, 0\n\txp, yp = 0, 0\n\tfor ch in s:\n\t\tif ch == 'W':\n\t\t\typ += 1\n\t\telif ch == 'A':\n\t\t\txp -= 1\n\t\telif ch == 'S':\n\t\t\typ -= 1\n\t\telse:\n\t\t\txp += 1\n\t\tlm = min(lm, xp)\n\t\trm = max(rm, xp)\n\t\tum = max(um, yp)\n\t\tdm = min(dm, yp)\n\txp, yp = 0, 0\n\tlmfSet, rmfSet, umfSet, dmfSet = 0, 0, 0, 0\n\tif lm == 0:\n\t\tlml = 0\n\t\tlmf = 0\n\t\tlmfSet = 1\n\tif rm == 0:\n\t\trml = 0\n\t\trmf = 0\n\t\trmfSet = 1\n\tif um == 0:\n\t\tuml = 0\n\t\tumf = 0\n\t\tumfSet = 1\n\tif dm == 0:\n\t\tdml = 0\n\t\tdmf = 0\n\t\tdmfSet = 1\n\tfor i, ch in zip(list(range(1, len(s) + 1)), s):\n\t\tif ch == 'W':\n\t\t\typ += 1\n\t\telif ch == 'A':\n\t\t\txp -= 1\n\t\telif ch == 'S':\n\t\t\typ -= 1\n\t\telse:\n\t\t\txp += 1\n\t\tif xp == lm:\n\t\t\tlml = i\n\t\t\tif not lmfSet:\n\t\t\t\tlmf = i\n\t\t\t\tlmfSet = 1\n\t\tif xp == rm:\n\t\t\trml = i\n\t\t\tif not rmfSet:\n\t\t\t\trmf = i\n\t\t\t\trmfSet = 1\n\t\tif yp == um:\n\t\t\tuml = i\n\t\t\tif not umfSet:\n\t\t\t\tumf = i\n\t\t\t\tumfSet = 1\n\t\tif yp == dm:\n\t\t\tdml = i\n\t\t\tif not dmfSet:\n\t\t\t\tdmf = i\n\t\t\t\tdmfSet = 1\n\tcanx, cany = 0, 0\n\tif dml + 1 < umf or uml + 1 < dmf:\n\t\tcany = 1\n\tif lml + 1 < rmf or rml + 1 < lmf:\n\t\tcanx = 1\n\tif canx:\n\t\tif cany:\n\t\t\tprint(min((um - dm) * (rm - lm + 1), (um - dm + 1) * (rm - lm)))\n\t\telse:\n\t\t\tprint((rm - lm) * (um - dm + 1))\n\telse:\n\t\tif cany:\n\t\t\tprint((um - dm) * (rm - lm + 1))\n\t\telse:\n\t\t\tprint((rm - lm + 1) * (um - dm + 1))\n\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13821