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 = 'T = int(input())\n\nfor _ in range(T):\n\ts = input()\n\n\tcleft=cup=cdown=cright=0\n\tleft=up=down=right=0\n\tfleft=lleft=0\n\tfright=lright=0\n\tfup=lup=0\n\tfdown=ldown=0\n\n\tx=y=0\n\tfor i, c in enumerate(s):\n\t\tif c=="W":\n\t\t\ty -= 1\n\t\t\tcup += 1\n\t\telif c=="S":\n\t\t\ty += 1\n\t\t\tcdown += 1\n\t\telif c=="A":\n\t\t\tx -= 1\n\t\t\tcleft += 1\n\t\telif c=="D":\n\t\t\tx += 1\n\t\t\tcright += 1\n\n\t\tif x == left:\n\t\t\tlleft = i\n\t\tif x == right:\n\t\t\tlright = i\n\t\tif y == down:\n\t\t\tldown = i\n\t\tif y == up:\n\t\t\tlup = i\n\n\t\tif x < left:\n\t\t\tleft = x\n\t\t\tfleft=i\n\t\t\tlleft=i\n\n\t\tif x > right:\n\t\t\tright = x\n\t\t\tfright=i\n\t\t\tlright=i\n\n\n\t\tif y < up:\n\t\t\tup = y\n\t\t\tfup=i\n\t\t\tlup=i\n\n\n\t\tif y > down:\n\t\t\tdown = y\n\t\t\tfdown=i\n\t\t\tldown=i\n\n\twidth = right - left + 1\n\theight = down - up + 1\n\n\tbest = width * height\n\n\tif height > 2:\n\t\tif ldown < fup or lup < fdown:\n\t\t\tbest = min(best, width * (height-1))\n\tif width > 2:\n\t\tif lleft < fright or lright < fleft:\n\t\t\tbest = min(best, (width-1) * height)\n\tprint(best)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13429