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\nw = [[-1, 0], [1, 0], [0, 1], [0, -1]]\nmp = {'A':0, 'D':1, 'W':2, 'S':3}\nwhile T > 0:\n\tT-=1\n\ts = input()\n\tl = [0]; r = [0];\n\tu = [0]; d = [0];\n\n\tfor dir in s[::-1]:\n\t\tl.append(l[-1])\n\t\tr.append(r[-1])\n\t\tu.append(u[-1])\n\t\td.append(d[-1])\n\t\tif dir == 'A':\n\t\t\tl[-1]+=1\n\t\t\tif r[-1] > 0: r[-1]-=1\n\t\telif dir == 'D':\n\t\t\tr[-1]+=1\n\t\t\tif l[-1] > 0: l[-1]-=1\n\t\telif dir == 'S':\n\t\t\td[-1]+=1\n\t\t\tif u[-1] > 0: u[-1]-=1\n\t\telse:\n\t\t\tu[-1]+=1\n\t\t\tif d[-1] > 0: d[-1]-=1\n\n\tl = l[::-1]; r = r[::-1]; u = u[::-1]; d = d[::-1];\n\n\tx = 0; y = 0\n\tml = 0; mr = 0; mu = 0; md = 0;\n\n\tans = (l[0] + r[0] + 1) * (u[0] + d[0] + 1)\n\tfor i in range(len(s)+1):\n\t\tmml=ml;mmr=mr;mmu=mu;mmd=md;\n\t\tfor j in range(4):\n\t\t\txx=x+w[j][0]\n\t\t\tyy=y+w[j][1]\n\n\t\t\tif xx<0: ml=max(ml,-xx)\n\t\t\tif xx>0: mr=max(mr,xx)\n\t\t\tif yy>0: mu=max(mu,yy)\n\t\t\tif yy<0: md=max(md,-yy)\n\n\t\t\txx-=l[i]\n\t\t\tif xx<0: ml=max(ml,-xx)\n\t\t\txx+=r[i]+l[i];\n\t\t\tif xx>0: mr=max(mr,xx)\n\t\t\tyy-=d[i]\n\t\t\tif yy<0: md=max(md,-yy)\n\t\t\tyy+=u[i]+d[i]\n\t\t\tif yy>0: mu=max(mu,yy)\n\n\t\t\tans = min(ans, (ml+mr+1)*(mu+md+1))\n\t\t\tml=mml;mr=mmr;mu=mmu;md=mmd;\n\n\t\tif i < len(s):\n\t\t\tx+=w[mp[s[i]]][0]\n\t\t\ty+=w[mp[s[i]]][1]\n\t\t\tif x<0: ml=max(ml,-x)\n\t\t\tif x>0: mr=max(mr,x)\n\t\t\tif y>0: mu=max(mu,y)\n\t\t\tif y<0: md=max(md,-y)\n\n\tprint(ans)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14721