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    cmd = input()\n\n    mostL, mostR, mostB, mostT = 0, 0, 0, 0\n    mostLs, mostRs, mostBs, mostTs = [0],[0],[0],[0]\n    x,y=0,0\n    i = 0\n    for c in cmd:\n        i += 1\n        if c == "W":\n            y += 1\n            if y>mostT:\n                mostT = y\n                mostTs = [i]\n            elif y == mostT:\n                mostTs.append(i)\n        elif c == "S":\n            y -= 1\n            if y<mostB:\n                mostB = y\n                mostBs = [i]\n            elif y == mostB:\n                mostBs.append(i)\n        elif c == "A":\n            x -= 1\n            if x < mostL:\n                mostL = x\n                mostLs = [i]\n            elif x == mostL:\n                mostLs.append(i)\n        elif c == "D":\n            x += 1\n            if x > mostR:\n                mostR = x\n                mostRs = [i]\n            elif x == mostR:\n                mostRs.append(i)\n\n    LR = mostR - mostL + 1\n    if LR >= 3:\n        firstL, lastL = mostLs[0], mostLs[-1]\n        firstR, lastR = mostRs[0], mostRs[-1]\n\n        cross = lastR > firstL and lastL > firstR\n        LR_extra = not cross\n    else:\n        LR_extra = False\n\n    BT = mostT - mostB + 1\n    if BT >= 3:\n        firstB, lastB = mostBs[0], mostBs[-1]\n        firstT, lastT = mostTs[0], mostTs[-1]\n\n        cross = lastB > firstT and lastT > firstB\n        BT_extra = not cross\n    else:\n        BT_extra = False\n\n    if LR_extra and BT_extra:\n        area = min((LR-1)*BT,LR*(BT-1))\n    elif LR_extra:\n        area = (LR-1)*BT\n    elif BT_extra:\n        area = LR*(BT-1)\n    else:\n        area = LR*BT\n    print(area)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13703