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
input = sys.stdin.readline

for _ in range(int(input())):
    s = input().strip()

    ans = 10**15

    suffix_change = [0]*len(s)
    mx_x = mn_x = mx_y = mn_y = 0
    curr_x = curr_y = 0

    for j in range(len(s)-1,-1,-1):
        i = s[j]
        if i == 'W':
            curr_y -= 1
        elif i == 'A':
            curr_x += 1
        elif i == 'S':
            curr_y += 1
        elif i == 'D':
            curr_x -= 1

        mx_x = max(mx_x, curr_x)
        mn_x = min(mn_x, curr_x)
        mx_y = max(mx_y, curr_y)
        mn_y = min(mn_y, curr_y)

        suffix_change[j] = [mx_x,mn_x,mx_y,mn_y]

    final_x = -curr_x
    final_y = -curr_y

    ans = (mx_x-mn_x+1)*(mx_y-mn_y+1)

    mx_x = mn_x = mx_y = mn_y = 0
    curr_x = curr_y = 0

    changes = [[0,1],[0,-1],[1,0],[-1,0]]

    for j in range(len(s)):
        i = s[j]
        if i == 'W':
            curr_y += 1
        elif i == 'A':
            curr_x -= 1
        elif i == 'S':
            curr_y -= 1
        elif i == 'D':
            curr_x += 1

        mx_x = max(mx_x, curr_x)
        mn_x = min(mn_x, curr_x)
        mx_y = max(mx_y, curr_y)
        mn_y = min(mn_y, curr_y)

        if j < len(s) - 1:
            mx_x2, mn_x2, mx_y2, mn_y2 = suffix_change[j+1]
            mx_x2 += final_x
            mn_x2 += final_x
            mx_y2 += final_y
            mn_y2 += final_y

            for change in changes:
                ans = min(ans, (max(mx_x,mx_x2 + change[0]) - min(mn_x,mn_x2 + change[0]) + 1) * \
                          (max(mx_y, mx_y2 + change[1]) - min(mn_y, mn_y2 + change[1]) + 1))


    print(ans)