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). 

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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
input = sys.stdin.readline

for _ in range(int(input())):
    s = input()
    l, r, u, d, fl, fr, fu, fd, x, y = [0] * 10
    for i in range(len(s)):
        if s[i] == 'W':
            y += 1
            if y > u:
                u = y
                fd = 0
                fu = 1
            if y == u:
                fu = 1
        elif s[i] == 'A':
            x -= 1
            if x < l:
                l = x
                fl = 1
                fr = 0
            if x == l:
                fl = 1
        elif s[i] == 'S':
            y -= 1
            if y < d:
                d = y
                fd = 1
                fu = 0
            if y == d:
                fd = 1
        elif s[i] == 'D':
            x += 1
            if x > r:
                r = x
                fr = 1
                fl = 0
            if x == r:
                fr = 1
    #bless Ctrl+C Ctrl+V
    x, y = r - l + 1, u - d + 1
    s, k = x * y, x * y
    if x > 2 and not fl * fr:
        s = k - y
    if y > 2 and not fu * fd and k - x < s:
        s = k - x
    print(s)