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).
for q in range(int(input())):

    data = input()
    # if data in ["WW", "AA", "SS", "DD"]:
    #     print(2)
    #     continue
    mx = [0,0,0,0]
    x = 0
    y = 0
    pos = [[-1],[-1],[-1],[-1]]
    for i in range(len(data)):
        # print(x,y)
        d = data[i]
        if d == "W":
            y += 1
            if y > mx[0]:
                
                mx[0] = y
                pos[0] = []
        elif d == "S":
            y -= 1
            if y < mx[2]:
                
                mx[2] = y
                pos[2] = []
        elif d == "A":
            x -= 1
            if x < mx[1]:
                
                mx[1] = x
                pos[1] = []
        else:
            x += 1
            if x > mx[3]:
                
                mx[3] = x
                pos[3] = []
        if x == mx[3]:
            pos[3].append(i)
        if x == mx[1]:
            pos[1].append(i)
        if y == mx[0]:
            pos[0].append(i)
        if y == mx[2]:
            pos[2].append(i)

    # print(mx)
    # print(pos)
    wid = mx[3] - mx[1] + 1
    hei = mx[0] - mx[2] + 1
    ans = wid * hei

    
    
    if pos[3][0] > pos[1][-1] + 1 or pos[1][0] > pos[3][-1] + 1:
        ans -= hei
    if pos[0][0] > pos[2][-1] + 1 or pos[2][0] > pos[0][-1] + 1:
        ans = min((hei-1)*(wid), ans)
    print(ans)