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()
	n = len(s)
	fa, fd, fs, fw = [0], [0], [0], [0]
	ba, bd, bs, bw = [0], [0], [0], [0]
	cur = [0, 0]
	for i in range(n):
		if s[i] == "A":
			cur[0] -= 1
			
		elif s[i] == "D":
			cur[0] += 1
			
		elif s[i] == "S":
			cur[1] -= 1
			
		elif s[i] == "W":
			cur[1] += 1
			
		fa.append(min(fa[-1], cur[0]))
		fd.append(max(fd[-1], cur[0]))
		fs.append(min(fs[-1], cur[1]))
		fw.append(max(fw[-1], cur[1]))

	h = fd[-1]-fa[-1]
	v = fw[-1]-fs[-1]
	area = (h+1)*(v+1)

	cur = [0, 0]
	for i in range(n-1, -1, -1):
		if s[i] == "D":
			cur[0] -= 1
		elif s[i] == "A":
			cur[0] += 1
		elif s[i] == "W":
			cur[1] -= 1
		elif s[i] == "S":
			cur[1] += 1

		ba.append(min(ba[-1], cur[0]))
		bd.append(max(bd[-1], cur[0]))
		bs.append(min(bs[-1], cur[1]))
		bw.append(max(bw[-1], cur[1]))

	ba.reverse()
	bd.reverse()
	bs.reverse()
	bw.reverse()

	#print(fa, fd, fs, fw)
	#print(ba, bd, bs, bw)

	hok, vok = False, False
	for i in range(1, n):
		#print(n, i)
		if fd[i]-fa[i] < h and abs(bd[i]-ba[i]) < h:
			hok = True
		if fw[i]-fs[i] < v and abs(bw[i]-bs[i]) < v:
			vok = True

	if hok:
		area = min(area, h*(v+1))
	if vok:
		area = min(area, v*(h+1))
	print(area)
