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 = "import sys\nfrom collections import defaultdict\ninput = sys.stdin.readline\nimport math\n\n\ndef main():\n    t = int(input())\n    for _ in range(t):\n        s = input().rstrip()\n        a1 = []\n        a2 = []\n        ws = {'W': 1, 'S': -1}\n        ad = {'A': 1, 'D': -1}\n        for c in s:\n            if c in ('W', 'S'):\n                a1.append(ws[c])\n            else:\n                a2.append(ad[c])\n        pref_a1 = [0] + a1.copy()\n        pref_a2 = [0] + a2.copy()\n        for i in range(1, len(pref_a1)):\n            pref_a1[i] += pref_a1[i-1]\n        for i in range(1, len(pref_a2)):\n            pref_a2[i] += pref_a2[i-1]\n\n        def canDecrease(a):\n            _min = min(a)\n            _max = max(a)\n\n            # decrease max\n            _min_rindex = a.index(_min)\n            for i in range(_min_rindex, len(a)):\n                if a[i] == _min:\n                    _min_rindex = i\n            _max_index = a.index(_max)\n            if _max_index > _min_rindex:\n                return True\n\n            # increase min\n            _max_rindex = a.index(_max)\n            for i in range(_max_rindex, len(a)):\n                if a[i] == _max:\n                    _max_rindex = i\n            _min_index = a.index(_min)\n            if _max_rindex < _min_index:\n                return True\n\n            return False\n\n        x = max(pref_a1)-min(pref_a1)\n        y = max(pref_a2)-min(pref_a2)\n        res = (x+1) * (y+1)\n        if x > 1 and canDecrease(pref_a1):\n            res = min(res, x * (y+1))\n        if y > 1 and canDecrease(pref_a2):\n            res = min(res, (x+1) * y)\n\n        print(res)\n\n\ndef __starting_point():\n    main()\n\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15173