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 = '# coding=utf-8\nINF = 1e11\n\n# move = {\'W\': (0, 0), \'A\': (0, 0), \'S\': (0, 0), \'D\': (0, 0)}\nmove = {\'W\': (0, 1), \'A\': (-1, 0), \'S\': (0, -1), \'D\': (1, 0)}\n\n\ndef getExtremes(positions):\n    minX, minY, maxX, maxY = [positions[0][0]], [positions[0][1]], [positions[0][0]], [positions[0][1]]\n    for p in positions[1:]:\n        minX.append(min(minX[-1], p[0]))\n        minY.append(min(minY[-1], p[1]))\n        maxX.append(max(maxX[-1], p[0]))\n        maxY.append(max(maxY[-1], p[1]))\n    return minX, minY, maxX, maxY\n\n\nt = int(input())\n\nwhile t > 0:\n    t -= 1\n    s = input()\n    x, y = 0, 0\n    positions = [(0, 0)]\n    for c in s:\n        x, y = x + move[c][0], y + move[c][1]\n        positions.append((x, y))\n    # print(positions)\n    # print()\n    minXBeg, minYBeg, maxXBeg, maxYBeg = getExtremes(positions)\n    # print(minXBeg, minYBeg, maxXBeg, maxYBeg, sep="\\n")\n    # print()\n    positions.reverse()\n    minXEnd, minYEnd, maxXEnd, maxYEnd = getExtremes(positions)\n    minXEnd.reverse()\n    minYEnd.reverse()\n    maxXEnd.reverse()\n    maxYEnd.reverse()\n    # print(minXEnd, minYEnd, maxXEnd, maxYEnd, sep="\\n")\n    # print()\n    positions.reverse()\n    ans = INF\n    for i in range(len(s)):\n        for c in move:\n            minX = min(minXBeg[i], positions[i][0] + move[c][0], minXEnd[i + 1] + move[c][0])\n            maxX = max(maxXBeg[i], positions[i][0] + move[c][0], maxXEnd[i + 1] + move[c][0])\n            minY = min(minYBeg[i], positions[i][1] + move[c][1], minYEnd[i + 1] + move[c][1])\n            maxY = max(maxYBeg[i], positions[i][1] + move[c][1], maxYEnd[i + 1] + move[c][1])\n            area = (maxX - minX + 1) * (maxY - minY + 1)\n            # print(i, c, minX, maxX, minY, maxY, area)\n            ans = min(ans, area)\n    print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14361