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())\nfor _ in range(t):\n\ts = input()\n\tn = len(s)\n\tfa, fd, fs, fw = [0], [0], [0], [0]\n\tba, bd, bs, bw = [0], [0], [0], [0]\n\tcur = [0, 0]\n\tfor i in range(n):\n\t\tif s[i] == "A":\n\t\t\tcur[0] -= 1\n\t\t\t\n\t\telif s[i] == "D":\n\t\t\tcur[0] += 1\n\t\t\t\n\t\telif s[i] == "S":\n\t\t\tcur[1] -= 1\n\t\t\t\n\t\telif s[i] == "W":\n\t\t\tcur[1] += 1\n\t\t\t\n\t\tfa.append(min(fa[-1], cur[0]))\n\t\tfd.append(max(fd[-1], cur[0]))\n\t\tfs.append(min(fs[-1], cur[1]))\n\t\tfw.append(max(fw[-1], cur[1]))\n\n\th = fd[-1]-fa[-1]\n\tv = fw[-1]-fs[-1]\n\tarea = (h+1)*(v+1)\n\n\tcur = [0, 0]\n\tfor i in range(n-1, -1, -1):\n\t\tif s[i] == "D":\n\t\t\tcur[0] -= 1\n\t\telif s[i] == "A":\n\t\t\tcur[0] += 1\n\t\telif s[i] == "W":\n\t\t\tcur[1] -= 1\n\t\telif s[i] == "S":\n\t\t\tcur[1] += 1\n\n\t\tba.append(min(ba[-1], cur[0]))\n\t\tbd.append(max(bd[-1], cur[0]))\n\t\tbs.append(min(bs[-1], cur[1]))\n\t\tbw.append(max(bw[-1], cur[1]))\n\n\tba.reverse()\n\tbd.reverse()\n\tbs.reverse()\n\tbw.reverse()\n\n\t#print(fa, fd, fs, fw)\n\t#print(ba, bd, bs, bw)\n\n\thok, vok = False, False\n\tfor i in range(1, n):\n\t\t#print(n, i)\n\t\tif fd[i]-fa[i] < h and abs(bd[i]-ba[i]) < h:\n\t\t\thok = True\n\t\tif fw[i]-fs[i] < v and abs(bw[i]-bs[i]) < v:\n\t\t\tvok = True\n\n\tif hok:\n\t\tarea = min(area, h*(v+1))\n\tif vok:\n\t\tarea = min(area, v*(h+1))\n\tprint(area)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14761