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).
def solve(pos):
    firstHighestIndex = 0
    firstLowestIndex = 0

    lastLowestIndex = 0
    lastHightestIndex = 0

    firstMostLeftIndex = 0
    lastMostLeftIndex = 0
    firstMostRightIndex = 0
    lasetMostRightIndex = 0
    for i in xrange(1, len(pos)):
        x, y = pos[i]
        if y > pos[firstHighestIndex][1]:
            firstHighestIndex = i
        if y >= pos[lastHightestIndex][1]:
            lastHightestIndex = i
        if y < pos[firstLowestIndex][1]:
            firstLowestIndex = i
        if y <= pos[lastLowestIndex][1]:
            lastLowestIndex = i

        if x > pos[firstMostRightIndex][0]:
            firstMostRightIndex = i
        if x >= pos[lasetMostRightIndex][0]:
            lasetMostRightIndex = i
        if x < pos[firstMostLeftIndex][0]:
            firstMostLeftIndex = i
        if x <= pos[lastMostLeftIndex][0]:
            lastMostLeftIndex = i
    w = pos[lasetMostRightIndex][0] - pos[firstMostLeftIndex][0] + 1
    h = pos[firstHighestIndex][1] - pos[firstLowestIndex][1] + 1
    haha = w * h
    if lastLowestIndex < firstHighestIndex and pos[firstHighestIndex][1] - 1 > pos[lastLowestIndex][1]:
        haha = min(haha, w * (h - 1))
    if lastHightestIndex < firstLowestIndex and pos[firstLowestIndex][1] + 1 < pos[lastHightestIndex][1]:
        haha = min(haha, w * (h - 1))
    if lastMostLeftIndex < firstMostRightIndex and pos[firstMostRightIndex][0] - 1 > pos[lastMostLeftIndex][0]:
        haha = min(haha, (w - 1) * h)
    if lasetMostRightIndex < firstMostLeftIndex and pos[firstMostLeftIndex][0] + 1 < pos[lasetMostRightIndex][0]:
        haha = min(haha, (w - 1) * h)

    return haha


import sys

t = input()

for tt in xrange(t):
    x, y = 0, 0
    arr = [(x, y)]
    ss = sys.stdin.readline()
    for i in xrange(len(ss) - 1):
        c = ss[i]
        if c == "W":
            y += 1
        elif c == "A":
            x -= 1
        elif c == "D":
            x += 1
        elif c == "S":
            y -= 1

        arr.append((x, y))
    print solve(arr)
