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\ninput = sys.stdin.readline\n\n\nQ = int(input())\nQuery = [list(input().rstrip()) for _ in range(Q)]\n\nfor S in Query:\n    L = len(S)\n    T = [(0, 0)]\n    for s in S:\n        x, y = T[-1]\n        if s == "W":\n            T.append((x, y+1))\n        elif s == "S":\n            T.append((x, y-1))\n        elif s == "A":\n            T.append((x-1, y))\n        else:\n            T.append((x+1, y))\n    \n    # up, down, left, right\n    dp1 = [[0, 0, 0, 0] for _ in range(L+1)]\n    for i, (x, y) in enumerate(T):\n        if i == 0: continue\n        dp1[i][0] = max(y, dp1[i-1][0])\n        dp1[i][1] = min(y, dp1[i-1][1])\n        dp1[i][2] = min(x, dp1[i-1][2])\n        dp1[i][3] = max(x, dp1[i-1][3])\n    \n\n    lx, ly = T[-1]\n    dp2 = [[ly, ly, lx, lx] for _ in range(L+1)]\n    for i in reversed(range(L)):\n        x, y = T[i]\n        dp2[i][0] = max(y, dp2[i+1][0])\n        dp2[i][1] = min(y, dp2[i+1][1])\n        dp2[i][2] = min(x, dp2[i+1][2])\n        dp2[i][3] = max(x, dp2[i+1][3])\n    \n    Y, X = dp1[L][0]-dp1[L][1]+1, dp1[L][3]-dp1[L][2]+1\n    ans = 0\n    for i in range(L):\n        if dp1[i][0] < dp2[i][0] and dp1[i][1] < dp2[i][1]:\n            ans = max(ans, X)\n        if dp1[i][0] > dp2[i][0] and dp1[i][1] > dp2[i][1]:\n            ans = max(ans, X)\n        if dp1[i][2] < dp2[i][2] and dp1[i][3] < dp2[i][3]:\n            ans = max(ans, Y)\n        if dp1[i][2] > dp2[i][2] and dp1[i][3] > dp2[i][3]:\n            ans = max(ans, Y)\n    print(X*Y-ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14839