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 = DSAWWAW then Grid(s) is the 4 × 3 grid:

  1. you can place the robot in the cell (3, 2); 
  2. the robot performs the command 'D' and moves to (3, 3); 
  3. the robot performs the command 'S' and moves to (4, 3); 
  4. the robot performs the command 'A' and moves to (4, 2); 
  5. the robot performs the command 'W' and moves to (3, 2); 
  6. the robot performs the command 'W' and moves to (2, 2); 
  7. the robot performs the command 'A' and moves to (2, 1); 
  8. 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 ≤ T ≤ 1000) — the number of queries.

Next T lines contain queries: one per line. This line contains single string s (1 ≤ |s| ≤ 2 ⋅ 10^5, s_i ∈ \{W, A, S, D\}) — the sequence of commands.

It's guaranteed that the total length of s over all queries doesn't exceed 2 ⋅ 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 DSAWW\underline{D}AW.

In second and third queries you can not decrease the area of Grid(s).
from __future__ import division, print_function

DEBUG = 0

INF = float('inf')
MOD = 10**9 + 7

import os, sys
from atexit import register
from io import BytesIO
import itertools

if sys.version_info[0] < 3:
    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip

if DEBUG:
    debug_print = print
else:
    sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
    sys.stdout = BytesIO()
    register(lambda: os.write(1, sys.stdout.getvalue()))

    input = lambda: sys.stdin.readline().rstrip('\r\n')
    debug_print = lambda *x, **y: None


def input_as_list():
    return list(map(int, input().split()))

def array_of(f, *dim):
    return [array_of(f, *dim[1:]) for _ in range(dim[0])] if dim else f()

def main():
    q = int(input())

    df = {'W': (0, 1), 'A': (-1, 0), 'S': (0, -1), 'D': (1, 0)}
    rdf = {'W': (0, -1), 'A': (1, 0), 'S': (0, 1), 'D': (-1, 0)}

    for _ in range(q):
        s = input()


        px, py = 0, 0
        minx, miny, maxx, maxy = 0, 0, 0, 0
        sbd = [[minx, miny, maxx, maxy]]

        for c in s:
            d = df[c]

            px += d[0]
            py += d[1]

            minx = min(minx, px)
            miny = min(miny, py)
            maxx = max(maxx, px)
            maxy = max(maxy, py)

            sbd.append([minx, miny, maxx, maxy])


        minx, miny, maxx, maxy = px, py, px, py
        ebd = [[minx, miny, maxx, maxy]]
        for c in reversed(s):
            d = rdf[c]

            px += d[0]
            py += d[1]

            minx = min(minx, px)
            miny = min(miny, py)
            maxx = max(maxx, px)
            maxy = max(maxy, py)

            ebd.append([minx, miny, maxx, maxy])

        g = INF
        for i in range(len(s)):
            ed = ebd[i]
            sd = sbd[len(s)-i]

            for dx, dy in (0, 1), (0, -1), (1, 0), (-1, 0):
                edmod = (ed[0]+dx, ed[1]+dy, ed[2]+dx, ed[3]+dy)
                newbd = (min(edmod[0], sd[0]), min(edmod[1], sd[1]),
                         max(edmod[2], sd[2]), max(edmod[3], sd[3]))

                g = min(g, (newbd[3]-newbd[1]+1) * (newbd[2]-newbd[0]+1))

        print(g)

        debug_print(sbd)
        debug_print(ebd)

main()