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
import math
import bisect
import atexit
import io
import heapq
from collections import defaultdict, Counter
MOD = int(1e9+7)



# n = map(int, raw_input().split())
# input = map(int, raw_input().split())
def main():
    n = map(int, raw_input().split())[0]
    for i in range(n):
        st = raw_input()
        dx, dy = defaultdict(list), defaultdict(list)
        x, y = 0, 0
        mxx, mix, mxy, miy = 0, 0, 0, 0
        dy[0].append(0)
        dx[0].append(0)
        for idx, c in enumerate(st):
            if c=='A':
                y-=1
                dy[y].append(idx)
            if c=='D':
                y+=1
                dy[y].append(idx)
            if c=='W':
                x+=1
                dx[x].append(idx)
            if c=='S':
                x-=1
                dx[x].append(idx)
            mxx = max(x, mxx)
            mix = min(mix, x)
            mxy = max(mxy, y)
            miy = min(miy, y)
        # print mxx,mix,mxy,miy
        xx, yy = 0, 0
        if mxx!=0:
            if mxx - mix >1 and dx[mxx] and dx[mix] and dx[mxx][0] > dx[mix][-1]:
                xx = 1
        if mix!=0:
            if mxx - mix >1 and dx[mxx] and dx[mix] and dx[mix][0] > dx[mxx][-1]:
                xx = 1
        # print dy[mxy],mxy
        if mxy!=0:
            if mxy - miy >1 and dy[mxy] and dy[miy] and dy[mxy][0]>dy[miy][-1]:
                yy = 1
        if miy!=0:
            if mxy - miy >1 and dy[mxy] and dy[miy] and dy[mxy][-1]<dy[miy][0]:
                yy = 1
        print min((mxx-mix+1-xx)*(mxy-miy+1), (mxx-mix+1)*(mxy-miy+1-yy))




main()
