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


Q = int(input())
Query = [list(input().rstrip()) for _ in range(Q)]

for S in Query:
    L = len(S)
    T = [(0, 0)]
    for s in S:
        x, y = T[-1]
        if s == "W":
            T.append((x, y+1))
        elif s == "S":
            T.append((x, y-1))
        elif s == "A":
            T.append((x-1, y))
        else:
            T.append((x+1, y))
    
    # up, down, left, right
    dp1 = [[0, 0, 0, 0] for _ in range(L+1)]
    for i, (x, y) in enumerate(T):
        if i == 0: continue
        dp1[i][0] = max(y, dp1[i-1][0])
        dp1[i][1] = min(y, dp1[i-1][1])
        dp1[i][2] = min(x, dp1[i-1][2])
        dp1[i][3] = max(x, dp1[i-1][3])
    

    lx, ly = T[-1]
    dp2 = [[ly, ly, lx, lx] for _ in range(L+1)]
    for i in reversed(range(L)):
        x, y = T[i]
        dp2[i][0] = max(y, dp2[i+1][0])
        dp2[i][1] = min(y, dp2[i+1][1])
        dp2[i][2] = min(x, dp2[i+1][2])
        dp2[i][3] = max(x, dp2[i+1][3])
    
    Y, X = dp1[L][0]-dp1[L][1]+1, dp1[L][3]-dp1[L][2]+1
    ans = 0
    for i in range(L):
        if dp1[i][0] < dp2[i][0] and dp1[i][1] < dp2[i][1]:
            ans = max(ans, X)
        if dp1[i][0] > dp2[i][0] and dp1[i][1] > dp2[i][1]:
            ans = max(ans, X)
        if dp1[i][2] < dp2[i][2] and dp1[i][3] < dp2[i][3]:
            ans = max(ans, Y)
        if dp1[i][2] > dp2[i][2] and dp1[i][3] > dp2[i][3]:
            ans = max(ans, Y)
    print(X*Y-ans)