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).
import sys

revmap = {'W': 'S', 'A': 'D', 'S': 'W', 'D': 'A'}

def apply(re, c):
    ct, cr, cd, cl = re
    if c == 'W':
        cd += 1
        ct -= 1
    elif c == 'A':
        cr += 1
        cl -= 1
    elif c == 'S':
        ct += 1
        cd -= 1
    elif c == 'D':
        cl += 1
        cr -= 1
    return max(0, ct), max(0, cr), max(0, cd), max(0, cl)

def compute_prefixes(cmds, rev=False):
    re = [(0, 0, 0, 0)]  # top right down left
    for c in cmds:
        if rev:
            c = revmap[c]
        re.append(apply(re[-1], c))
    return re

def solve(C):
    p1 = compute_prefixes(C)
    p2 = compute_prefixes(C[::-1], rev=True)[::-1]
    areas = []
    for j in xrange(len(p1)):
        for p11 in (p1[j], apply(p1[j], 'W'), apply(p1[j], 'A'), apply(p1[j], 'S'), apply(p1[j], 'D')):
            re = (max(p11[0], p2[j][0]), max(p11[1], p2[j][1]), max(p11[2], p2[j][2]), max(p11[3], p2[j][3]))
            areas.append((re[0] + re[2] + 1) * (re[1] + re[3] + 1))
    return min(areas)

T = int(sys.stdin.readline())
for t in xrange(T):
    c = sys.stdin.readline().strip()
    print solve(c)
