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).

for i in range(int(input())):
	s = input()
	lm, rm, um, dm = 0, 0, 0, 0
	xp, yp = 0, 0
	for ch in s:
		if ch == 'W':
			yp += 1
		elif ch == 'A':
			xp -= 1
		elif ch == 'S':
			yp -= 1
		else:
			xp += 1
		lm = min(lm, xp)
		rm = max(rm, xp)
		um = max(um, yp)
		dm = min(dm, yp)
	xp, yp = 0, 0
	lmfSet, rmfSet, umfSet, dmfSet = 0, 0, 0, 0
	if lm == 0:
		lml = 0
		lmf = 0
		lmfSet = 1
	if rm == 0:
		rml = 0
		rmf = 0
		rmfSet = 1
	if um == 0:
		uml = 0
		umf = 0
		umfSet = 1
	if dm == 0:
		dml = 0
		dmf = 0
		dmfSet = 1
	for i, ch in zip(range(1, len(s) + 1), s):
		if ch == 'W':
			yp += 1
		elif ch == 'A':
			xp -= 1
		elif ch == 'S':
			yp -= 1
		else:
			xp += 1
		if xp == lm:
			lml = i
			if not lmfSet:
				lmf = i
				lmfSet = 1
		if xp == rm:
			rml = i
			if not rmfSet:
				rmf = i
				rmfSet = 1
		if yp == um:
			uml = i
			if not umfSet:
				umf = i
				umfSet = 1
		if yp == dm:
			dml = i
			if not dmfSet:
				dmf = i
				dmfSet = 1
	canx, cany = 0, 0
	if dml + 1 < umf or uml + 1 < dmf:
		cany = 1
	if lml + 1 < rmf or rml + 1 < lmf:
		canx = 1
	if canx:
		if cany:
			print(min((um - dm) * (rm - lm + 1), (um - dm + 1) * (rm - lm)))
		else:
			print((rm - lm) * (um - dm + 1))
	else:
		if cany:
			print((um - dm) * (rm - lm + 1))
		else:
			print((rm - lm + 1) * (um - dm + 1))


