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
from collections import defaultdict
input = sys.stdin.readline
import math


def main():
    t = int(input())
    for _ in range(t):
        s = input().rstrip()
        a1 = []
        a2 = []
        ws = {'W': 1, 'S': -1}
        ad = {'A': 1, 'D': -1}
        for c in s:
            if c in ('W', 'S'):
                a1.append(ws[c])
            else:
                a2.append(ad[c])
        pref_a1 = [0] + a1.copy()
        pref_a2 = [0] + a2.copy()
        for i in range(1, len(pref_a1)):
            pref_a1[i] += pref_a1[i-1]
        for i in range(1, len(pref_a2)):
            pref_a2[i] += pref_a2[i-1]

        def canDecrease(a):
            _min = min(a)
            _max = max(a)

            # decrease max
            _min_rindex = a.index(_min)
            for i in range(_min_rindex, len(a)):
                if a[i] == _min:
                    _min_rindex = i
            _max_index = a.index(_max)
            if _max_index > _min_rindex:
                return True

            # increase min
            _max_rindex = a.index(_max)
            for i in range(_max_rindex, len(a)):
                if a[i] == _max:
                    _max_rindex = i
            _min_index = a.index(_min)
            if _max_rindex < _min_index:
                return True

            return False

        x = max(pref_a1)-min(pref_a1)
        y = max(pref_a2)-min(pref_a2)
        res = (x+1) * (y+1)
        if x > 1 and canDecrease(pref_a1):
            res = min(res, x * (y+1))
        if y > 1 and canDecrease(pref_a2):
            res = min(res, (x+1) * y)

        print(res)


if __name__ == '__main__':
    main()

