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).
import sys
n =sys.stdin.readline().strip()
n =int(n)
for T in range(n):

	h=[0]
	w=[0]
	height=0
	widh=0
	hmax=0
	hmin=0
	wmax=0
	wmin=0
	strr= sys.stdin.readline().strip()
	for one in strr:
		if one=="W":
			height+=1;
			h.append(height)
			hmax=hmax if hmax > height else height
		if one =="S":
			height-=1;
			h.append(height)
			hmin = hmin if hmin<height else height
		if one =="D":
			widh+=1
			w.append(widh)
			wmax=wmax if wmax > widh else widh
		if one=="A":
			widh-=1
			w.append(widh)
			wmin=wmin if wmin <widh else widh
	al=[]
	flag=0
	lflag=True
	rflag=True
	for i in range(len(h)) :
		if hmin==h[i]:
			if len(al)==0:
				al.append(1)
			else:
				if al[-1]==0:
					if flag!=0:
						lflag=False
						break
					flag=1
					al.append(1)
		if hmax==h[i]:
			if len(al)==0:
				al.append(0)
			else:
				if al[-1]==1:
					if flag!=0:
						lflag=False
						break
					flag=1
					al.append(0)
	flag=0
	al=[]
	for i in range(len(w)):
		if wmin==w[i]:
			if len(al)==0:
				al.append(1)
			else:
				if(al[-1]==0):
					if flag!=0:
						rflag=False
						break
					flag=1
					al.append(1)
		if wmax==w[i]:
			if len(al)==0:
				al.append(0)
			else:
				if al[-1]==1:
					if flag!=0:
						rflag=False
						break
					flag=1
					al.append(0)
	l=hmax-hmin+1
	r=wmax-wmin+1
	ll=[l]
	rl=[r]
	if (l>2) and lflag:
		ll.append(l-1)
	if (r>2) and rflag:
		rl.append(r-1)
	res=ll[0]*rl[-1]
	res=res if (ll[-1]*rl[0]) > res else (ll[-1]*rl[0])
	print res
	  		  	  	  	  				  			 			 	