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).
# coding=utf-8
INF = 1e11

# move = {'W': (0, 0), 'A': (0, 0), 'S': (0, 0), 'D': (0, 0)}
move = {'W': (0, 1), 'A': (-1, 0), 'S': (0, -1), 'D': (1, 0)}


def getExtremes(positions):
    minX, minY, maxX, maxY = [positions[0][0]], [positions[0][1]], [positions[0][0]], [positions[0][1]]
    for p in positions[1:]:
        minX.append(min(minX[-1], p[0]))
        minY.append(min(minY[-1], p[1]))
        maxX.append(max(maxX[-1], p[0]))
        maxY.append(max(maxY[-1], p[1]))
    return minX, minY, maxX, maxY


t = int(input())

while t > 0:
    t -= 1
    s = input()
    x, y = 0, 0
    positions = [(0, 0)]
    for c in s:
        x, y = x + move[c][0], y + move[c][1]
        positions.append((x, y))
    # print(positions)
    # print()
    minXBeg, minYBeg, maxXBeg, maxYBeg = getExtremes(positions)
    # print(minXBeg, minYBeg, maxXBeg, maxYBeg, sep="\n")
    # print()
    positions.reverse()
    minXEnd, minYEnd, maxXEnd, maxYEnd = getExtremes(positions)
    minXEnd.reverse()
    minYEnd.reverse()
    maxXEnd.reverse()
    maxYEnd.reverse()
    # print(minXEnd, minYEnd, maxXEnd, maxYEnd, sep="\n")
    # print()
    positions.reverse()
    ans = INF
    for i in range(len(s)):
        for c in move:
            minX = min(minXBeg[i], positions[i][0] + move[c][0], minXEnd[i + 1] + move[c][0])
            maxX = max(maxXBeg[i], positions[i][0] + move[c][0], maxXEnd[i + 1] + move[c][0])
            minY = min(minYBeg[i], positions[i][1] + move[c][1], minYEnd[i + 1] + move[c][1])
            maxY = max(maxYBeg[i], positions[i][1] + move[c][1], maxYEnd[i + 1] + move[c][1])
            area = (maxX - minX + 1) * (maxY - minY + 1)
            # print(i, c, minX, maxX, minY, maxY, area)
            ans = min(ans, area)
    print(ans)
