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).
T = int(input())

for _ in range(T):
	s = input()

	cleft=cup=cdown=cright=0
	left=up=down=right=0
	fleft=lleft=0
	fright=lright=0
	fup=lup=0
	fdown=ldown=0

	x=y=0
	for i, c in enumerate(s):
		if c=="W":
			y -= 1
			cup += 1
		elif c=="S":
			y += 1
			cdown += 1
		elif c=="A":
			x -= 1
			cleft += 1
		elif c=="D":
			x += 1
			cright += 1

		if x == left:
			lleft = i
		if x == right:
			lright = i
		if y == down:
			ldown = i
		if y == up:
			lup = i

		if x < left:
			left = x
			fleft=i
			lleft=i

		if x > right:
			right = x
			fright=i
			lright=i


		if y < up:
			up = y
			fup=i
			lup=i


		if y > down:
			down = y
			fdown=i
			ldown=i

	width = right - left + 1
	height = down - up + 1

	best = width * height

	if height > 2:
		if ldown < fup or lup < fdown:
			best = min(best, width * (height-1))
	if width > 2:
		if lleft < fright or lright < fleft:
			best = min(best, (width-1) * height)
	print(best)