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 = 'n = int(input())\n\ndef area(width, height) :\n    return (width+1) * (height+1)\n\ndef calcul(s1, c, s2) :\n    maxx, maxy, minx, miny = 0, 0, 0, 0\n    x, y = 0, 0\n    for k in range(len(s1)) :\n        if s1[k] == "W" :\n            y += 1\n        if s1[k] == "S" :\n            y -= 1\n        if s1[k] == "A" :\n            x -= 1\n        if s1[k] == "D" :\n            x += 1\n        maxx = max(maxx, x)\n        minx = min(minx, x)\n\n        maxy = max(maxy, y)\n        miny = min(miny, y)\n\n\n\n\n    if c == "W" :\n        y += 1\n    elif c == "S" :\n        y -= 1\n    elif c == "A" :\n        x -= 1\n    elif c == "D" :\n        x += 1\n    else :\n        print(c, "ok")\n\n    maxx = max(maxx, x)\n    minx = min(minx, x)\n\n    maxy = max(maxy, y)\n    miny = min(miny, y)\n\n    for k in range(len(s2)) :\n        if s2[k] == "W" :\n            y += 1\n        if s2[k] == "S" :\n            y -= 1\n        if s2[k] == "A" :\n            x -= 1\n        if s2[k] == "D" :\n            x += 1\n        maxx = max(maxx, x)\n        minx = min(minx, x)\n\n        maxy = max(maxy, y)\n        miny = min(miny, y)\n\n\n\n    diffx = maxx - minx\n    diffy = maxy - miny\n    tmp = area(diffx, diffy)\n\n\n    return tmp\n\ndef pre_calcul(s, moment, pre_avant, date_debut) :\n    x, y, maxx, minx, maxy, miny = pre_avant\n    for k in range(date_debut, moment) :\n        if s[k] == "W" :\n            y += 1\n        if s[k] == "S" :\n            y -= 1\n        if s[k] == "A" :\n            x -= 1\n        if s[k] == "D" :\n            x += 1\n        maxx = max(maxx, x)\n        minx = min(minx, x)\n\n        maxy = max(maxy, y)\n        miny = min(miny, y)\n\n    return (x, y, maxx, minx, maxy, miny)\n\ndef calcul2(s, c, moment, precalcul) :\n    x, y, maxx, minx, maxy, miny = precalcul\n\n\n\n    if c == "W" :\n        y += 1\n    elif c == "S" :\n        y -= 1\n    elif c == "A" :\n        x -= 1\n    elif c == "D" :\n        x += 1\n    else :\n        print(c, "ok")\n\n    maxx = max(maxx, x)\n    minx = min(minx, x)\n\n    maxy = max(maxy, y)\n    miny = min(miny, y)\n\n    for k in range(moment, len(s)) :\n        if s[k] == "W" :\n            y += 1\n        if s[k] == "S" :\n            y -= 1\n        if s[k] == "A" :\n            x -= 1\n        if s[k] == "D" :\n            x += 1\n        maxx = max(maxx, x)\n        minx = min(minx, x)\n\n        maxy = max(maxy, y)\n        miny = min(miny, y)\n\n\n\n    diffx = maxx - minx\n    diffy = maxy - miny\n    tmp = area(diffx, diffy)\n\n\n    return tmp\n\nfor _ in range(n) :\n    s = input()\n    maxx, maxy, minx, miny = 0, 0, 0, 0\n    x, y = 0, 0\n    momentminx, momentmaxx, momentminy, momentmaxy = -1, -1, -1, -1\n    for k in range(len(s)) :\n        if s[k] == "W" :\n            y += 1\n        if s[k] == "S" :\n            y -= 1\n        if s[k] == "A" :\n            x -= 1\n        if s[k] == "D" :\n            x += 1\n\n        if x > maxx :\n            momentmaxx = k\n        if y > maxy :\n            momentmaxy = k\n        if x < minx :\n            momentminx = k\n        if y < miny :\n            momentminy = k\n        maxx = max(maxx, x)\n        minx = min(minx, x)\n\n        maxy = max(maxy, y)\n        miny = min(miny, y)\n    diffx = maxx - minx\n    diffy = maxy - miny\n\n\n    tmp = 999999999999999999999999999999999999\n    l = [momentmaxx, momentmaxy, momentminx, momentminy]\n    l = list(set(l))\n    l = [i for i in l if i != -1]\n    l.sort()\n    if l != [] :\n        precalcul = pre_calcul(s, l[0], (0, 0, 0, 0, 0, 0), 0)\n        avant = l[0]\n        for moment in l :\n            precalcul = pre_calcul(s, moment, precalcul, avant)\n            avant = moment\n            tmp = min(tmp, calcul2(s, \'W\', moment, precalcul))\n            tmp = min(tmp, calcul2(s, \'S\', moment, precalcul))\n            tmp = min(tmp, calcul2(s, \'A\', moment, precalcul))\n            tmp = min(tmp, calcul2(s, \'D\', moment, precalcul))\n    print(tmp)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13721